ANNE~NASTASI Professor of Psychology, Fordham Universiry
Psyclwlvgical Testing
MACMILLAN
PUBLISHING
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Librarlj of Congress Cataloging in Publication Data Anastasi, Anne, (date) Psychological testing. Bibliography: p. Includes indexes. 1. Mental tests. 2. Personality tests. I. Title. [DNLM: 1. Psychological tests. WM145 A534P] BF431.A573 1976 153·9 75-2206 ISBN O-<>2-30298
I N A revised edition, one expects both similarities and differences. This edition shares with the earlier versions the objectives and basic approach of the book. The primary goal of this text is still to contribute toward the proper evaluation of psychological tests and the correct interpretation and use of test results. This goal calls for several kinds of information: ( 1) an understanding of the major principles of test construction, (2) psychological knowledge about the behavior being assessed, (3) sensitivity to the social and ethical implications of test use, and (4) broad familiarity with the types of available instruments and the sources of information about tests. A minor innovation in the fourth edition is the addition of a suggested outline for test evaluation (Appendix C). In successive editions, it has been necessary to exercise more and more restraint to keep the number of specific tests discussed in the book from growing with the field-it has never been my intention to provide a miniature Mental Measurements Yearbook! l:\evertheless, I am aware that principles of test co~struction and interpretation can be better understood when applied to~particular tests. Moreover, acquaintance with the major types of available tests, together with an understanding of their special contributions and limitations, is an es!>entialcomponent of knowledge about contemporary testing. For these reasons, specific tests are again examined and evaluated in Parts 3, 4, and 5. These tests have been chosen either because they are outstanding examples with which the student of testing should be familiar or because they illustrate some special point of test construction or interpretation. In the text itself, the principal focus is on types of tests rather than on specific instruments. At the same time, Appendix E contains a classified list of over 250 tests, including not only those cited in the text but also others added to provide a more representative sample. As for the differences-they loomed especially large during the preparation of this edition. Much that has happened in human society since the mid-1960's has had an impact on psychological testing. Some of these developments were briefly described in the last two chapters of the third edition. Today they have become part of the mairn;tream.;()fpsychological' testing and have been accordingly incorpo~i-ted in the apprqpqate sections throughout the book. Recent changes in psychological Jesting that are reflected in the present edition can be delpribed on three levels: (1) general orientation toward testing, (2) Stlbm,IJ,tiveand inethod()l~ical developments, and (3) "ordinary progress" w1)Q as the publiciitibn of new tests and revision of earlier tests.
Preface
Preface
; An example of changes on the first level is the increasing awareness of ~e ethical, social, and legal implications of t~sting. In the present edilon, this topic has been expanded and treated 111a separate chapter early b the book (Ch. 3) and in Appendixes A and B. A cluster of related evelopments represe~ts a bro~dening of.test u~es..Beside~ the tradi~ion~l 'pplications of tests 111 selectwn and diagnosIs, 111creasmg attention IS eing given to administering tests for self-kuowledge and self-develop~entl and to training individuals in the use of their own test res?lts. in ,lJecisionmaking (Chs. 3 and 4). In the same category are the contmumg ~eplacementof global scores with multitrait profiles and the application bf classificationstrategies, whereby "everyone can be above average" in bne or more socially valued "ariables (Ch. 7). From another angle, rffortsare being made to modify traditional interpretations of test scores, ~n bothcognitive and noncognitive areas, in the light of accumulating psychological knowledge. In this edition, Chapter 12 brings together 'psychologicalissues in the interpretation of intelligence test scores, :touchingon such problems as stability and change in intellectual level .overtime; the nature of intelligence; and the testing of intelligence in :earlychildhood, in old age, and in different cultures. Another example is provided by the increasing emphasis on situational specificity and person-by-situationinteractions in personality testing, stimulated in large partbythe social-learning theorists (Ch. 17). T~e second level, -covering substantive and methodological changes, is illustratedby the impact of computers on the development, administra"tioll,scoring, and interpretation of tests (see especially Chs. 4, 11, 13, 17, 18, W). The use of computers in administering or managing instructional pro/ramshas also stimulated the development of criterion-referenced t~~~ although other conditions have contributed to the upsurge of 'i!restin such tests in education. Criterion-referenced tests are discussed '1 ,. 'pally in Chapters 4,5, and 14. Other types of lllstruments that have to prominence and have received fuller treatment in the present n include: tests for identifying specific learning disabilities (Ch. inventories and other devices for use in behavior modification pro-' (Ch. 20), instruments for assessing early ch~ldhOod education 14), Piagetian "ordinal" scales (Chs. 10 and 14), basic education literacy tests for adults (Cbs. 13 and 14), and techniques for the ment of environments (Ch. 20). Problems to be considered in the , ment of minority groups, including the question of test bias, are ined from different angles in Chapters 3, 7, 8, and 12. the third level, it may be noted that over 100 of the tests listed in edition have been either initially pUblished or revised since the ication of the preceding edition (1968). Major examples include the arthy Scales of Children's Abilities, the WISC-R, the 1972 Stanfordnorms (with all the resulting readjustments in interpretations),
l..
I
c
•
vii
Forms Sand T of the DAT (including a computerized Career Planning Program), the Strong-Campbell Interest Inventory (merged form of the SVIB), and the latest revisions of the Stanford Achievement Test and the Metropolitan Readiness Tests. It is a pleasure to acknowledge the assis~nce received from many sources in the preparation of this edition. The completion of the project was facilitated by a one-semester Faculty Fellowship awarded by Fordham University and by a grant from the Fordham University Research Council covering principally the services of a research assistant. These services were performed by Stanley Friedland with an unusual combination of expertise, responSibility, and graciousness. I am indebted to the many authors and test publishers who provided reprints, unpublished manuscripts, specimen sets of tests, and answers to my innumerable inquiries by mail and telephone. For assistance extending far beyond the interests and responsibilities of any single publisher, I am especially grateful to Anna Dragositz of Educational Testing Service and Blythe Mitchell of Harcourt Brace Jovanovich, Ioc. I want to acknowledge the Significant contribution of John T. Cowles of the University of Pittsburgh, who assumed complete responSibility for the preparation of the Instructor's Manual to accompany this text. For informative discussions and critical comments on particular topics, I want to convey my sincere thanks to Willianl H. Angoff of Educational Testing Service and to several members of the Fordham University Psychology Department, including David R. Chabot, Marvin Reznikoff, Reube~ M. Schonebaum, and 'Warren, W. Tryon. Grateful acknowledgment IS also made of the thoughtful recommendations submitted by course instructors in response to the questionnaire distributed to current users of the third edition. Special thanks in this connection am due to Mary Carol Cahill for her extensive, constructive, and Wide-ranging suggestions. I wish to express my appreciation to Victoria Overton of the Fordham University library staff for her efficient and courteous assistance in bibliographic matters. Finany, I am happy to record the contributions of my husband, John Porter Foley, Jr., who again participated in the solution of countless problems at all stages in the preparation of the book. A.A.
CONTENTS
PART 1 CONTEXT
OF PSYCHOLOGICAL
TESTING
1. FUNCTIONS AND ORIGINS OF PSYCHOLOGICAL TESTING
Q
Current uses of psychological tests Early interest in classification and
training
retarded 5 The first experimental psychologists 7 Contributions of Francis Galton 8 Cattell and the early "mental tests" 9 Binet and the nse of intelligence tests
3 of
the
mentally
10
Group testing 12 Aptitude testing 13 ~ Standardized achievement tests 16 Measurement of personality 18 Sources of information about tests 20
2. NATURE AND USE OF PSYCHOLOGICAL TESTS What is a psychological test? 23 Reasons for controlling the use of psychological tests Test administration 32 Rapport 34 Test anxiet\' 37 Examiner ~nd situational variables 39 Coaching, practice, and test sophistication
3. SOCIAL AND ETHICAL OF TESTING
41
IMPLICATIONS "
User qualifications 45 Testing instruments and procedures 47 . 49 Protection of privacy Confidentiality 52 Communicating test results 56 Testing and the civil rights of minorities ix
57
PART 3 TESTS OF GENERAL
INTELLECTUAL
LEVEL 9. INDIVIDUAL 4. NORMS AND THE INTERPRETATION TEST
OF
Stanford-Binet Intelligence Scale 230 Wechsler Adult Intelligence Scale 245 Wechsler Intelligence Scale for Children 2.'55 Wechsler Preschool and Primary Scale of Intelligence
SCORES
Statistical concepts 68 Developmental norms 73 Within-group norms 77 Relativity of norms 88 Computer utilization in tile interpretation Criterion-referenced
testing
10. TESTS of test scores
TESTS
94
FOR SPECIAL
POPULATIONS
Infant and preschool testing 266 Testing the physically handicapped Cross-cultural testing 287
96
281
5, RELIAB ILITY The correlation coefficient 104 Types of reliability 110 Reliability of speeded tests 122 Dependence of reliability coefficients on the sample tested Standard error of measurement 127 Reliability of criterion-referenced tests 131
Content validity 134 Criterion-related validity Construct validity 151 Overview 158
140
AND
Validity coefficient and error of estimate 163 Test validity and decision theory 167 Moderator variabll;;s 177 Combining information from different tests 180 Use of tests for cl.assification decisions 186 Statistical analyses of test bias 191
ANALYSl-S
Item difficulty 199 Item validity 206 Internal consistency 215 Item analysis of speeded tests Cross validation 219 Item-group interaction 222
12. PSYCHOLOGICAL INTELLIGENCE
ISSUES IN TESTING
Longitudinal studies of intelligence 327. Intelligence in early childhood 332 Problems in the testing of adult intelligence Problems in cross-cultural testing 343 Nature of intelligence 349
7. VALIDITY: MEASUREMENT INTERPRET ATION
8. ITEM
125
Croup tests versus individual tests 299 Multilevel batteries 305 Tests for the college level and beyond 318
PART 4 TESTS OF SEPARATE 13. MEASURING
14. EDUCATIONAL
217
AInLJTIES
MULTIPLE
Factor analysis 362 Theories of trait organization MUltiple aptitude batteries Measurement of creativity
337
APTITUDES 369
378
388
TESTING
Achievement tests: their nature and uses General achievement batteries 403 Standardized tests in separate subjects Teacher-made classroom tests 412
398 410
260
20. OTHER Diagnostic and criterion-rdt:renced tests Specialized prognostic tests 423 Assessment in early childhood education
417 425
~ OCCUPATIONAL TESTING \V Validation of industrial tests 435 Short screening tests .for industrial personnel Special aptitude tests 442 Testing in the profeSSions 458
ASSESSMENT
439
Diagnostic use of intelligence tests 465 Special tests for detecting cognitive dysfunction Identifying specific learning disabilities 478 Clinical judgment 482 Report writing 487
B. Guidelines on Employee Selection Procedures (EEOC) Guidelines for Reporting Criterion-Related and Content Validity (OFCC)
PART 5 PERSON ALITY 17. SELF-REPORT
TESTS
INVENTORIES
Content validation 494 Empirical criterion keying - 496 506 Factor analysis in test development 510 Personality theory in test development 515 Test-taking attitudes and response sets Situational specificity 521 Evaluation of personality inventories
18. MEASURES OF INTERESTS, AND VALUES
ATTITUDES, ;527
Interest inventories 528 Opinion and attitude measurement 543 Attitude scales 546 Assessment of values and related variables
19. PROJECTIVE
552
TECHNIQUES
Nature of projective techniques 558 Inkblot techniques 559 Thematic Apperception Test and related instruments Other projective techniques 569 Evaluation of projective techniques
576
TECHNIQUES
"Objective" performance tests 588 Situational tests 593 SeH-concepts and personal constructs 598 Assessment techniques in behavior modification programs Observer reports 606 Biographical inventories 614 The assessment of environments 616
PART
C01ltext of . Psychological Testing
1
CHAPTER
1
Functions and 01~igiTlS of Psycllological TeStiTlg
' A
NYONE reading this book today could undoubtedly illush'ate what . is meant by a psychological test, It would be easy enough to recall . a test the reader himself has taken in school, in college, in the armed services, in the counseling center, or in the personnel office. Or perhaps the reader has served as a subject in an experiment in which standardized tests were employed. This would certainly not have been the case fifty years ago. Psychological testing is a relatively young branch of one of the youngest of the sciences.
Basically, the function of psychological tests is to measure ,9.:iffe~~~.n~L_ 1Jetween individuals or between the reactions of the same individual on different occasions. One of the first problems that stimulated the development of psychological tests was the identification of the mentally retarded. To this day, the detection of int~i1ectual deficiencies remains an Important application of certain types of psychological tests. Related clinical uses of tests include the examination of the emotionally disturbed, the delinquent, and other types of behavioral deviartts. A strong impetus to the early development of tests was likewise provided by problems arising in education, At present, schools are among the largest test users. The classifica.tiOIlOfchildren with reference to their ability to profit from different types of school instruction, the identi£ication of the intellectually retarded on the one hand and the gifted on the other, the diagnosis of academic failures, the educational and vocational counseling of high school and college students, and the s~~ction of applicants for professional and other special schools are among the many educational ~uses of tests. The selection and classification of industrial personnel represent another major application of psychological testing. From the assembly-line
4
COllfcl't
of Psychological Testing
operator or filing clerk to top management, there is scarcely a type of job for which some kind of psychological test has not proved helpful in such matters as hiring, job assignment, transfer, promotion, or termination. To be sure, the effective employment of tests in many of these situations, es eciiill-"Tri('Onnection with high-level jobs, usuall • re uires that the t!.:ts he used as an adjunct to s -i u interviewing, so that test scores ht of other back ound' rmatiQn may be properly int~rpreteaTnt1leli evertheless, testing constitutes an important part a out the m IVI un. ~ total personnel program. A closely related application of psychological testing is to be found in the selection and classification of military personnel. From simple beginnings in "Vorld 'War I, the scope and variety of psychological tests employed in military sihlations underwent a phenomenal increase during World War II. Subsequently, research on test development has been continuing on a large scale in all branches of the armed services, The use of tests in counseling has gradually broadened from a narrowly defined guidance regarding educational and vocational plans to an involvement with all aspects of the person's life. Emotional wellbeing and effective interpersonal relations have become increasingly prominent objectives of counseling. There is growing emphasis, too, on the use of tests to enhance self-understanding and personal development. Within this framework, test scores are part of the information given to the individual as aids to his own decision-making processes. It is clearly evident that psychological tests are currently being employed in the solution of a wide range of practical problems. One should not, however, lose sight of the fact that such tests are als? serving important functions in basic research Nearly all problems in differential psychology, for example, require testing procedures as a means of gathering data. As illustrations, reference may be made to studies on the nature and extent of individual differences, the identification of psychological traits, the measurement of group:' differences, ~nd the investigationfijo]ogical and cUltural factors associated WIth 6ehavioral differences. For all such areas of research-and for many others-the precise mt>.asurement of individual differences made possible by well-constructed tests is an essential prerequisite. Similarly, psycholOgical tests provide standardized tools for investigating such varied problems as life-span developmental changes within the individual, the relative effectiveness of different educational procedures, the outcomes of psychotherapy, the impact of community programs, and the influence of noise on performance. From the many different uses of psychological tests, it follows that some knowledge of such tests is needed for an adequate understanding of most fields of contemporary psychology. It is primarily with this end in view that the present book has been prepared. The book is not designed to
make the individual either n skilled examiner and test administrator or an"experf on test construction. It is directed, not to the test specialist, but to the general student of psychology. Some acquaintance with the lead·' ing current tests is necessary in order to understand references to the use of such tests in the psychological literature. And a proper evaluation and interpretation of test results must ultimately rest on a knowledge of how the tests were constructe
EARLY INTEREST IN CLASSIFICATION AND TRAINING OF THE MENTALLY RETARDED The nineteenth century witnessed a strong awakening of interest in the humane treatment of the mentally retarded and the insane. Prior to that time, neglect, ridicule, and even torture had been the common lot of these unfortunates. With the growing concern for the proper care of mental I A more detlliled account of the early origins of psycllOlogical tests can be found in Goodenough (1949) and J. Pefers~n (1926~. See also Boring (1950) and Murphy and Kovach (1972) for more general backgrq~md, DuBois (1970) for a brief but comprehensive history of psychologi~l tClsting, and ,Anastasi (1965) for historical antecedents of the study of individual differences.
6
Context of Psychological
Testing
deviates came a realization that some uniform criteria for identifying and classifying these cases were required. The establishment of many special institutions for the care of the mentally retarded in both Europe and America made the need for setting up admission standards and an objective system of classification especially urgent. First it was necessary to differentiate between the insane and the mentallv retarded. The former manifested emotional disorders that might or might not be accompanied by intellectual deteriomtion from an initially normal level; the latter were characterized essentially by i~tellectual defect that had been present from birth or early infancy. What is probably the first explicit statement of this distinction is to be found in a two-volume work published in 1838 by the French physician Esquirol (1838), in which over one hundred pages are de\'oted to mental retardation. Esquirol also pointed out that there an! many degrees of mental retardation, varying along a continuum from normality to low-grade idiOCy. In the effort to develop some system for claSSifying the different degrees and varieties of retardation"Esguiroi tried several procedures but concluded that the individual's use of language provides the m05t de endable criterion of his intellectual level. It is meres mg to note t at current criteria 0 menta retardation are also largely lingUistic ant! that present-day intelligence tests are heavily loaded ~vith Yerbal content. The important part verbal ability plays in our concept of intelligence will be repeatedly demonstrated in subsequent chapters. Of special significance are the contributions of another French physician, S,egll~. who pioneered in the training of the mentally retarded. Having rejected the prevalent notion of the ineurability of mental retardation , SeO'uin (1866) eXIJerimented for many~ "vears with what he v termed the physiological method of training; and in 1837 he,:es,tal:6hed the nrst school devoted to the education of mentally reta .." ~hildren. In 1848 he emigrated to America, where his ideas gaine _ ide recognition. Man~- of the sense-training and muscle-trainirJg techniques currently in use in institutions for the mentally retarded \vere originated by Seguin. By these methods, severely retarded children are given intensive exercise in sensory discrimination and in the development of motor control. Some of the procedures developed by Seguin for this purpose were 'eventually incorporated into performance or nonverbal tests of intelligence. An example is the Seguin Form Board, in which the individual is required to insert variously shaped blocks into the corresponding recesses as quickly as possible. More than half a century after the work of Esquirol and Seguin, the French psychologist Alfred Binet urged that children who failed to respond to normal schooling be examined before dismissal and, if considered educable, be assigned to special classes (T. H. Wolf, 1973). With
Functions and Origins of Psychological
Testing
7
his fellow members of the Society for the Psychological Study of the Child, Binet stimulated the Ministry of Public Instruction to take steps to improve the condition of retarded children. A specific outcome was the <'stablishment of a ministerial commission for the study of retarded children, to which Binet was appointed. This appointment was a momentous event in the history of psychological testing, of which more will be said Jal'er.
The ~arly experimental psycholOgists of the nineteenth century were not, in general, concerned \vith the measurement of individual'differences. The principal aim of psychologists of that period was the fommlation of generalized descriptions of human behavior. It was the uniformities rather than the differences in behavior that were the focus of attention. Individual differences were either ignored or were accepted as a necessary evil that limited the applicability of the generalizations. Thus, the fact that one individual reacted diHerently from another when observed under identical co~ditions was regarded' as a form of -etror. The presence of such error, or individual variability, rendered the generalizations approximate rather than exact. This was the attitude toward individual differences that prevailed in such laborotodes as that founded by '''undt at Leipzig in 1879, where many of the early experimental psychologists received their training. In their choice of topics, as in many other phases of their work, the founoers of experimental psychology reBected the influence of their backgrounds in physiology and physics. The problems studied in their laboraauditory, and~ tories were concerned largely with sensitivit~ to ~al, other sensory stimuli and \vith simple reaction time. This emphasis on sen~ory phenome~a was in tU!'l1reflected in the nature of the £rst psychologICal tests, as will be apparent in subsequent sections. . St:ilI another way in which nineteenth-century experimental psychology Influenced the course of the testing movement may be noted. ,The earlv ps~'chological experiments brought out the need for rigorous control of the conditions under which observations were made. For example, the \\'?rding of directions given to the subject in a reaction-time experiment mIght appreci~bly incre.ase or decrease the speeg 'i\t the subject's response. Or agam, the bnghtness or color oEthe sUtr~,,~:ding field could of mar~edly alter the appearance of a visu~J s~mulU~:".1\h~portance makmg observations on all subjects un4i~.,s~ndardiz~& conditions was ...!fu1svividly demonstrated: Such standardization of proce,dure eventually became one of the special earmarks of psychological tests.
Functions
It "'as the English biologist Sir Francis Galton who ,,:as. primarily r~sponsible for launching the testing movem~l~t: A umfY~lg. factor ~n Calton's numerous and vaI'ied research activities was hiS }nterest llL 'humaJ;rheredit ". In the course of his imestigations on heredity, Calton t~a 'ize t e need for measuring the characteristics of related and unrelated persons. Only in this way could he discover, for example, the exact degree of resemblance bet:w'een p~ren~s and offspring, 1;'rothers and . sisters; cousins, or twins. With this end 11l View, Calton was mstrument~l ' in inducing a number of educational institutions to keep systematic anthropometric recOl:ds on their students. ~e al<;oset up an anthropo~ctric laboratory at the International EXposI~on of ,18~4wh~re, by .pa) mg threepence, visitors could be measured 111 ce~yslcal traIts and could take tests of keenness of vision and hearing, muscular strength, reaction time, and other simple sensorimotor functions. Whe~l the exposition closed, the laboratory was transferred to South Kensmgton Museum, London, where it operated for six years. By such methods, the nrst large, systematic body of data on individual differences in simple psychological processes was gradually aceu~ulated. . . . Galton himself devised most of the sun pIe tests admIDlstered at hIS anthropometric laboratory, many of which are still familiar either in ~heir original or in modified forms. Examples include the Cal~o~ bar for ,,:mual ,discrimination of len h, the Galton whistle for determmlllg the hlghest au i e pitch, and graduated series of weights for measurin? k~ne.sth~tic discrimimltion. It was Calton's belief that tests of sensory discrlrmnatlOn could serve as a means of gauging a person's intellect. In this respec,~' he was partly influenced hy the theories of L?cke. Thus Galton wrote: .The only information that reaches us concernmg outward events appeals to pass through the avenue of our senses; and the n~ore per~ptive the sen~es are of difference, the larger is the field upon which our Judgment and 10telligence can act" (Calton, 1883, ~'. 27). C~lt~n !lad.:~lso noted that idiots tend to be defective in the ability to discrlmmaJe·:heat, cold, and pain-an observation that furtller strengthene5iYnis ~nviction that sens~ry discriminative capacity "would on the whole' be highest among the mtellectualh- ablest" (Galton, 1883, p. 29). . Galton also pioneered in the application of rating-sca~c ~nd ques~lOnnaire methods as well as in the use of the free associatIon techmque subsequently ~mployed for a wide ~arietyof purposes. A .fu.rther contribution of Galton is to be found in hiS development of statistical methods for the analysis of data on individual differences. Galton selected and adapted a n~mber of techniques previously derived ~y m~thematicians. These techniques he put in such form as to permit theIr use by the
and Ol'igills of Psychological Testing
9
mathematically untrained investigator who might wish to treat test results quantitatively. He thereby extended enormously the application of statistical procedures to the analysis of test data. This phase of Galton's work has been carried forward by many of his students, the most eminent of whom was Karl Pearson.
An especially prominent position in the development of psychological testing is occupied by the American psychologist James McKeen Cattell. The newly established science of experimental psychology and the still newer testing movement merged in Cattelfs work. For his doctorate at Leipzig, he completed a dissertation on individual differences in reaction !ime, despite Wundt's resistance to this t'ype of investigation. While lectming at Cambridge in 1888, Cattell's own interest in the measurement of individual differences was reinforced bv contact with Calton. On his return to America, Cattell was active both 'in the- establishment of laboratories for experimental psychology and in the spread of the testing movement. l -;;\';e~ U-U..~ In an article written by Cattell in ,,890, the term "mental test'. was . _ used for the £rst time in the psychological literature. This article described a series of tests that were beinO' o administered anlluallv. to college students in the effort to determine their irteilectuall~yel. The tests, which had to be administered individually, included measures of muscular strength, speed of movement, sensiti~ty to pain, keenness of vision and of hearing, weight discrimination, reaction time, memory, and the like. I In his choice of tests, Cattell shared Galton's view that Jl measure of/M-.,';';;.(,V1.""V'.-(~ i,ntellectual functions could he Qbt<}ined through tests of sensorv cis,- f<.U4-~e.I..t., ;~~ c~pination and reaction time. Cattell's pI'eference for such tests was also ~tl<-.~ bolst.e~ed by the fact that simple functions could be measured with .p!i
!1~
Catten's tests were typical of those to be found in a number of test series developed during the Jast decade of the nineteenth century. Such test series were administered to schoolchilqren, college students', and misccllaneous adults. At the Columbian Exposition Jield in Chicago in 189~, Jastraw set up an exhibit at which visitors wete"'iIllitted to take tests of sensory, motor, and simple perceptual processes and: to compare tlieir skill with the norms (J. Peterson, 1926; Philippe, 1894·~.A few attempts to evaluate such early tests yielded very discOuraging results: The individual's Rerform~Dce showed little correspondence from one test to another (Sharp, 1~1899; Wissler, 1901), and it exhibited little or no
10
Context of PSlJc11010gical Testing
relation to independent estimates of intellectual levC:'1based on teachers' ratings (Bolton, 1891-1892; J. A. Gilbert, 1894) or academic grades (Wissler, 1901). A number of test series assembled by European psychologists of the period tended to cover somewhat more complex functions. Kraepelin (1895), who was interested primarily in the clinical examination of psychiatric patients, prepared a long series of tests to measure what he regarded as basic factors in the characterization of an individual. The tests, employing chiefly simple arithmetic operations, were designed to measure practice effects, memory, and susceptibility to fatigue and to distraction. A few years earlier, Oehrn (1889), a pupil of Kraepelin, had emploY€idtests of perception, memory, association, and motor functions in an investigation on the interrelations of psychological functions. Another German psychologist, Ebbinghaus (1897), administered tests of arithmetic computation, memory span, and sentence completion to schoolchildren. The most complex of the three tests, sentence completion, was the only one that showed a clear correspondence with the children's scholastic achievement. Like Kraepelin, the Italian psychologist Ferrari and his students were interested primarily in the use of tests with pathological cases (Guicciardi & Ferrari, 1896). The test series they devised ranged from physiological measures and motor tests to apprehension span and the interpretation of pictures. In an article published in France in 1895, Binet and Henri criticized most of the available test series as being too largely sensory and as concentrating unduly on simple, specialized abilities. They argued further that, in the measurement of the more complex functions, great precision is not necessary, since individual differences are larger in these functions. An extensive and varied list of tests was proposed, covering such functions as memory, imagination, attention, comprehension, suggestibility, aesthetic appreciation, and many others. In these tests we can recognize the trends that were eventually to lead to the development of the famous Binet intelligence scales.
Binet and his co-workers devoted many years to active and ingenious research on ways of measuring intelligence. Many approaches were tried, including even the measurement of cranial, facial, and hand form, and the analysis of handwriting. The results, however, led to a growing conviction that the direct, even though crude, measurement of com lex 1 fence a unc ons 0 ere t e greatest promise. T en a specific situation arose that brought Binet's efforts to imme(]iate practical fruition. In 1904, the Minister of Public Instruction appointed ~inet to the previ-
Functions and Origi;ls of Psychological
Testing
11
ously cited commission to study procedures for the education of retarded children. It was in connection 'with the objectives of this commission that Binet, in collaboration with Simon, prepared the first Binet-Simon Scale (Binet & Simon, 1905). This scale, known as the 1905 seale, consisted of 30 problems or tests arranged in ascending order of difficulty. The difficulty level was determined empirically by administering the tests to 50 normal children aged 3 to 11 years, and to some mentally retarded children and adults. The tests were designed to cover a wide variety of functions, with speCial emphasis onJ.udgmt;nt, comprehension, and reasoning. Which Binet regarded as essential components of intelligence. Although sensory and perceptual tests were included, a much greater proportion of verbal content was found in this scale than in most test series of the time. The 1905 scale was presented as a preliminary and tentative instrument, and no precise objective method for arriving at a total score was formulated. In the second, or 1908, scale, the number of tests was increased, some unsatisfactory tests from the earlier scale were eliminated, and all tests were grouped into age levels on the basis of the performance of about 300 normal children between.. the ages of 3 and 13 Years. Thus, in the 3-year level were placed all tests passed by 80 to 00 percent of normal 3-year-olds; in the 4-year-Ievel, all tests similarly passed by normal 4-yearolds; and so on to age 13. The child's score on the entire test could then be expressed as a mental level corresponding to the age of normal children whose performance he equaled. In the various translations and adaptations of the Binet scales, the term "mental age" was commonly substituted for "mentalleveI." Since mental age is such a simple concept to~rasE> the introduction of this term undoubtedly did much to popularize intelligence testing.> Binet himself, however, avoided the term "mental age" because of its unverified developmental implications and preferred the more neutral term "mental level" (T. H. \\Tolf, 1973). A third revision of the Binet-Simon Scale appeared in 1911, the year of Binet's untimely death. In this scale, no fundamental changes were introduced. Minor revisions and relocations of specific tests were instituted. More tests were added at several year levels, and the scale was extended to the adult level Even prior to the 1908 revision, the Binet-Simon tests attracted wide > Goodenough (1949, pp. 50-51) notes that in 1881, 2l y~aTs befor~ the appearance of the 1908 Binet-Simon Scale, S. E. Chaille publi!iheq in the New Orleans Medical a~d Surgical Journal a series of tests for infan~ 11l7anged according to the a!1:eat whIch the tests are commonly passed. Partly because' of the limited circulation of the journal 'nd partly, perhaps, because the scientific ~Om!J1l1nity was not ready for it, the significance of this age-scale concept passed unnoticed at the time. Binet's own scale was in~ed by the work oE some oE ~is contemporaries, notably Blin and Damaye, who prepared a set of oral questions from which they derived a single . global score Eor eaclrdiild (T. H. Wolf, 1973).
12
Context
Functions and Origins of Psyc1101ugical Testing
of Psyc11010gical Testing
attention among psychologists throughout the world. Translation~ and adaptations appeared in many lang;uages. In Americ;l, a number of diHerent revisions were prepa.red, the most famous of which is the one developed under the direction of L. ~t Terman a.t Stanford University, and known as the Stanfmd-Binet (Terman, 1916). It was in this test that the intelligence quotient (IQ), or mtio between mental age and chronological age, was first used. The latest revision of this test is widely employed today and will be more full\' considered in Chapter 9. Of special interest, too. is the first Kuhlmann-Binet revision, which extended the scale downward to the age level of 3 months (Kuhlmann, 1912). This scale represents one of the earliest efforts to develop preschool and infant tests of intelligence.
The Binet tests, as well as all their revisions, are indil;iclual scales in the sense that the\" can be administered to onlY one person at a time. Man\' of the tests in these scales require .oral re~ponses from the subject or n~cessitate the manipulation of materials. Some call for individual timing of responses. For these and other reasons, such tests are not adapted to group administration. Another characteristic of the Binet type of test is that" it requires a highly trained examiner. Such tests are essentiallv clinical instruments, suited to the intensive study of individual J
.'
•
cases. Group testing, like the first Binet scale, was developed to meet a pressing practical need. When the United States entered l)!orld 'Var I in 1917, a committee was appointed by the American Psychological Association to consider ways in which psychology might assist in the conduct of 1. Yerkes, recogthe war. This committee, under the direction of !lobert 1.•. nized the need for the rapid classification of the million and a ha1f recruits with respect to general intellectual level. Such informati~.~~~va:s relevant to many admmistrative decisions, including rejection or discharge from military service, assignment to different types of sel'vicei, or admission to officer-training camps. It was in this setting that the first group intelligence test was developed. In this task, the Ar-m~' psychologists drew on all available test materials, and especially on an unpublished group intelligence test prepared by ~rthur S. Otis, which hc turned over to the Army. A major contribution of Otis's test, which he designed while a student in one of Terman's graduate courses, was the introduction of multiple-choice and other "objective" item types. The tests finally developed by the Army psychologists came to be known as the ~rm""yAlpha and the Army Beta The former was designed
13
fo~ g~n~ral routine te~ting; t~e latter was a nonlanguage scale employed WIth Illiterates and wIth foreign-born recruits who were unable to take a tcst in English. Both test~ w~re suitable for administratio~ to large groups. Shortly af~e~ the temunatlOn of "Vorld War I, the Army tests were released for cmhan use. Not only did the Army Alpha and Army Beta themselves pass through many revisions, the latest of which are even now in use, b.ut they also sVVed as ~dels for most group intelligence tests. The te~ting .movement underwent a tremendous spurt of growth. Soon group mtelhgence tests were being devised for all ages and types of ~ersons, from preschool children to graduate students. Large-sc~le test109 progra~ns: previously impossible, were now being launched with ~est~ul optimIsm. Because group. tests were designed as mass testing lUsh uments, they not only permItted the simultaneous examination of large groups but also simplified the instructions and adminish'ation procedu~es so as to demand a minimum of training on the part of the exammer. Schoolteachers began to give intelligence tests to thcir classes. Coll~ge studen~s were routinely examined prio~ to admission. Extensive studies of specIal adult groups, such as prisoners, were undertaken. And soon the general public became IQ-conscious. "--T~e application of such group intelligence tests far outran their technical Improvement. That the tests were still crude instruments was often f?rgotten in the rush of gathering scores and drawing practical conduslO~Sfrom the ~esults. 'Vhen. ~he tests failed to meet unwarranted expectations" skepticism and hostiht)' toward all testing often resulted. JJ1US. the testi boom of the twenties, based on the indiscriminate use of tests i? ma~ have ~one as much to retai' as to ad\'ance the progress of psvcho- --logical test mg. ~
IS
~lthough intelligence tests were originally designed to sample a wide vanety of ~unctions in order to estimate the individual's general intelIectua~ level, It soon became apparent that such tests were quite limited in theIr .cove~age. Not all important functions were represented. IJ:!. fact, most mtelhgence tests were primarily measures of verbal ability and. to a lesser extent, of the ability to handle numerical and other abstract and symb~~ic re~ations. Gr~dually psychologists eame to recogni~e that the ~erm . Il1telhgence test was a misnomer, since only certain aspects of mtelligence were measured by such tests. To be sure, th~ tests cov~red abilities ,t~t are ot p.rime importance in our culture. B~ It was. realized that more'precise designations, in terms of the type of mformation these tests are able to yield, w<;lUlq be prefer-
14
Context of Psyclwlo{!.ical Testing
able, For example, a number of tests that would probably have been caned intelligence tests during the twenties later came to be known as scholastic aptitude tests. This shift ill terminology was made in l'ec:ognition of the fact that mallY so-called intelligence tests measure that combination of abilities demanded by academic work. E\'l'n prior to Vvorld War I, ps\'ch~logists had begun to recognize the need for tests of spE'cial aptitudes to suppkment the global intelligence tests. These s ecial a till/de tests ' , , _ ' vocationa counseling and in the selection and classification of industrial and military ersonn~1. Among the most widely used are tests of.!!lechaniea , c erica, musical, and artistic aptitlldes. -TI~ca~lation of intelligence tests that follm,'ed their widesl>\'eadand indiscriminate use durinlJ0 the twenties also revealed another , lIote"iOlthy fact: an individual's erformance on ' test often -showed mar -c variation. This ,yas especially apparent on gl'OUptests, 111whlch the items ar~mmonly segregated into subtests of relath'e1\- homogeneous content. For example, a person might score relatively high on a verbal subtest and low on a numerical subtest, or vice versa, To some extent, such internal variability is also discernible on a test like the Stanford-Binet, in which, for example, all items involving words might prove difficult for a particular individual, whereas itcms employing pictures or geometric diagrams may place him at an advantage, Test users. and especially clinicians, frequently utilized such interc~l11parisons in order to obtain 1110reinsight into the individual's psychological make-up. Thus, not only tllC'IQ or other global score but also scores on subtests wonld lJt' examined in the e\'aluation of the indhidual case, Such a practice is not to be general1~' recommended, ho,~,('ver. ~)eeaus~ inaphtude tellig('J]ce tests were not designed for the purpose of ,dIHerel,~h,~11 anal;'sis. Often the subtests heing compared contain t0o,14C\\' items to yield a stable or reliable estimate of a specific ability:;jis'a result, the obtained diffl:'rence betwcen subtest scores might be reversed if the individual were retestE'd on a different day or with another foml of the same test. If such intraindividual comparisons are to be made, tests are needed that are specially designed to reveal differences in performance in various functions. While the practical apl)lication of tests demonstrated the l1~.ed for differential aptitude tests, a parallel development in the stu,d)' of trait organization was gradually providing the means for constructing SUC? tests. Statistical studi('s on the nature of intelligence had been explonng the iflterrelatiol1s among scores obtained by many persons on a ,,,ide variety of different tests, Such investigations were begun by the English ,psychologist Charles Spearman (1904, 1927) during the £lrst decade of the
Functions and OrigillS of PSljchological Testing
15
present century. Subsequent methodological developments, based on the work of such American psychologists as T. L. ReIley (1928) and L. L. !hurs~one (1935, 194i), as well as on that of other American and English ll1veshgators, have come to be known as "factor analvsis." The contributions that the methods of factor ana'lysis have made to test c'Onstruction will be more fully examined and ill~strated in Chapter 1:3. For the present, it will suffice to note that the data gathered by such procedures have indicated the presence of a Dumber of rebtiyely ;ndeJ)endent factors. or traits. Some of these traits were represen'ted, in vary~ng proportions, in the traditional intelligence tests. Verbal comprehenSIOn and numerical reasoning are examples of this tvpe of trait. Others, such as spatial, perceptual, and mechanical aptitude~, were found more often in special aptitude tests than in intelligence tests. One of the chief practical outcomes of factor analysis was the development of multiple aptitude batteries. These batteri('s arc desiuned to provide a measure of the individual's standing in each of a number of traits. In place of a total score or IQ, a separate score is obtained for such traits as "erhal comprehension, numerical aptitude, spatial visualization, arithm~tic re~soning, and perce~tual speed, Such batteries thus provide a SUItable mstrument for makin<1 the kind of intraindividual anaJ\'Sis I' 1 e~'e ~nOSls, t at c inicians a een tr\'ing for matiy years to .obtam, wlth crude and often errODl:'OUSresults from intelligence tests. These batteries also incorporate into a comprehensivl:' and svstl:'matic testing program much of the inform,ation formerly obtained fro~l special aptihlde tl:'sts, since the multiple aptitude batteries cover some of the traits not ordinarily me u e JlI IJ1e 1 ence tests. , u tip e ap u e atteries represent a relatively late development in the testing field. Nearl~' all have appeared since 1945. In this connection, the work of thc military psychologists during World War II s.J~d also be noted. ~fuch of the test research conducted in the armed services was based on factor analysis and was directed toward the construction of mu.ltiple aptitude batteries. In the Air Force, for example, special battent's were constructed for pilots, bombardiers, radio operators, range finders, and scores of other military specialists. A report of the batterics prepared in the Air Force alone occupies at least nine of the nineteen volumes devoted to the aviation psychology program during 'Vorld War II (Anny Air Forces, 1947-1948). Research along these line~ is still in progress under the sponsorship of various branches of the armed services. A.~~mber of multiple aptitude batteries !rl,\yelikewise ~en 4,eveloped for clVllian. use and are being widely appliel:l\,n educati0l1~l and vocational counselmg and in personnel' selectioll and' cJassincadqIl. Examples of ,"-' " such butteries will be discussed in Chapter 13, To avoid confusion, a point of terminology shoul\!l be clarified. The
16
COIl!ex! of
Psyclwlogict,{
Tcsrillg
term "aptitude test" has been tracHtiollalJ" cmployed to refer to tests measuring relativel\" homo ('ncous and dparlv defined sc rn1C'nts of • I I \., t le term "intelliO'ence test" customarih' . refers to more hderogence-. ~ests yielding a single global score sm:h as an IQ. S~)ecial aptitu~c tests typically measure a single aptitude. ~lultiple al~tltl1de battenes measure a number of aptitudes but pro\"ide a profile of scores, one for eaeh aptitude. Co)
While psychologists were busy developing intelligence and aptitude tests, traditional school examinations were undergoing a number of technical improvements (Caldwell & Courtis, 192:3; Ebel & Damrin, 1960 ~. An important step in this direction was taken by the Boston pubhc schools in 1845, when written examinations wefe substituted for the oral interroO'ation of students by visiting examiners. Commenting on this innDvati~l, Horacc ~fann cit~d arguments remarkably similar to those used much later to justify the replacement of essay questions hy objective multiple-choice items. The written examiuations, \lann noted, put all students in a uniform situation, permitted a wider cO\'erage of content, reduced the chance element in question choice, and eliminated tIll' possibilitv of h\'oritism on the examiner's part. Aft~r the turn of the centurv, the first stand-ardized tests for measuring the outeomes of school instnl~tion began to appear. Spearheaded h~' the work of E. L. Thorndike. these tests utilized measurement principks developed in the psychological laboratory. Examples include scales for rating the quality of handwriting and written compos.itiol1s, as. well ~s tests in spelling, arithmetic computation, and arithmetic reasol1lng. Stl11 later came the achie\"ement batteries, initiated by the publication of the first edition of the Stanford Achievement Test in 192:3. Its authors were three earl" It'aders in test development: Truman L. Kelley, GHes ~f. Ruch, ami Lewis M. Terman. Foreshadowing many characteri·stic'S of modern t'fsting, this battery provided com~arable measu~'es of perfo~ance in different school subjects, evaluated 111 terms of a smgle norma live group. At the same time, evidence was accumulating regarding the lack of agreement among teachers in grading essay tests. By .1930 it was.widely recognized that essay tests were not only more hme-cOnsumll1g for examiners and examinees, but also yielded less reliable results than the "new type" of objective items. As the latter came into increasing use in standardized achievement tests, there was a growing emphaSiS on the design of items to test the understanding and application of knowledge
FI/I1C!iol1.\' mltl Origi/l.~ of Psyc1IO/
17
and other hroad educational objectives. The deeade of the 19:305 also witnessed the introduction of test-seoring maehines, for which the new ohjec:tive tests could be readily adapted. The establishment of statewide, regional. and nalional testing programs ,,,as another noteworthy parallel denlopment. Probably the best known .?f these programs is that of the College Entrance Examination Board ~t;EEB). Established at thc turn of the ce_ll'~' to reduce duplication in the exa"tnining of entering college freshmen, this program has undergone profound changes ill its testing procedures and in the number and nature ?f partie-ipa.ting col1eges-c·hangcs that reflect inten'ening developments 111both testIng and cducation. In 1947, the testing functions of the CEEB were llIerged with those of the Carnegie Corporation and the American Council on Education to form Educational Testing Service (ETS). In subscq.t1cnt ~'ears, ETS has assumed responsibility for a growing number of testlllg programs on behalf of universities, professional schools, government agencies, and other institutions. \[ention should also he made of the American Collegc Testing Program established in 1959 to scrccn applicants to colleges not included i~ thc CEEB program, and of several national testing programs for the selection of highl\' talented students for scholarship awards. . . Achievem.ent tests are used not only for educational purposes but also III the se]Pchon of applicants for industrial and government jobs. \fention has already been made of the systematic use of ci\'i\ sen'jce examinations in the Chinese empire, dating from 111.5 .B.c. In modern times, selection of go\'~rnI~lent emplo:-e~s by examination was introduced in European countnes 111the late eIghteenth and eark nineteenth centuries. The l!llited States Chi! Service Commission in~talled competitive examinations as a regular procedure in 1883 (Kanuck, 19.56). Test construction techniques developed during and prior to World "'a~ I were introduded into tll<:'examination program of the United States Ch-il Service with the appointment of L. J. O'Rourke as director of the newlv established research dh'ision in 1922. ' . As more and more psychologists trained in psychometrics participated m the construction of standardized achievement tests, the technical aspects of achievement tests increasingly came to resemble those of intelligence and aptitude tests. Procedur~s for cons,trllcting and evaluating all ~hese tcsts have much in common. The incre~s!ng effOlts to prepare achIevement tests that would measure the attainment of broad educational goals, as contrasted to the recall of factualiminutiae also made the content of achievement tests resemble more -cioselv th~t of intellige~lce tests. Today the difference between these two 'types of tests is dueHy one of degree of specificity of content and extent to which the test presupposes a designated course of prior instruCtion.
J' IIIIC/ /(111,\ {///(/
Another area of psy<:holo~ical testing is concerned with the aH('ctive or nonint('lIectnal aspects of b('ha\'io!'. Tests d('signed for this purpose are commonly known as personality tests. although some psychologists prefer to lISt' the term personalit~, in a hroader sense, to refer to the cntirc individual. Intellectual as well as nonintellectual traits ,,"ould thus be included under this heading, In the terminology of psychologit·al testing, howcver, the designation "personality test" most often refers to measures of such characteristics as emotional adjustment, interpersonal relations, moth·ation, interests, and attitudes. An earl~' precursor of personaJit~' testing may be r('cognizcd in Kra,:pelin's use of the free association test with abnormal patients. In thIS test the subject is gh'en specially selectcd stimulus words and is required to r('spond to each with the first word that comes to mind, Kraepelin ( 1892) also employed this technique to study the psychological effects of fatigue, hunger, and drugs and concluded that all these agents increase the relati\'{~ frequenc~' of superficial associations, Sommer (1894), also writing: during the last decade of the nineteenth century, suggested that the free association test might be used to differentiate between the various forms of mental disorder. The fre(' association technique has subscqllenth' becn utilized for a vari('ty of testing purpos('s and is still curr('nth- en\plcn'ed, \Iention should also be made of the 'York of Galton, Pear~on: and C;lttell in the dpyelopment of standardized questionnaire and ratin~-,~'ale tl'chniqn('s. Although origin~l1y devised for other purposes. these proc-edmes \wre e\'entual1~' employed by othNs in constructing some of the most common types of current personality tests. The protntype of tht, personalit\' qnpstionnaire, or self-report inventory, is the Per~(lnal Data Sheet developed by \Voodworth durin~ \"orId \Var I (DuBois. 1970; Symonds. 19:31,eh. 5; Goldlwrg, 19(1). This test was designed as a rough screening device for identifying seriously ~urotic men \\'110 would be' unfit for military service. The inventor\' conslst~d of a number of questions dealing with common neurotic sy~pt01'!lS, ,~'hich the individual answered about himself. A total score was o\5t~ined by counting the number of symptoms reported, The Personal Data ~heet was )lot completed carly enough to permit its operational use .J)efore the war cnded. Immediatel" after the war, however, civilian forms were prepared, including a special form for use with children. The \Voodworth Personal Data Sheet, moreover, served as a model for most subsequent emotional adjustment inventories. In some of these questionnaires, an attempt was made to subdivide emotional adjustment into more specific forms. such as home adjustment, school adjustment, and vocational adjustment. Other tests concentrated more intensively on a narrower area
(higill.,
of
J'sydl(l'(/~i('111 1'<'S!iIlt!.
19
of bc-!Ja>ior 01' Wl'I'(' <:olll:erncd with mOl'(' dbtindly social r('~pons('s, such as dOl1lmalll'C-sublllission in interpersonal ('ontacts. A later development \\'as th<: constmction of tests for quantifying the expression of interests and athtude's, These tests, too, W('H' based l'ssentialh' on
u~
.
,
Psychological testing is in a state of rapid chan~e. There are shifting oriel;tations, a constant stream of new tests, revisc>d forms of old tests, and additional data that mav refine or alter the interpretation of scores on existing tests. The accelerating rate of <:hange, together with ~he vast number uf available tests, makes it impracticable to sun'ey speCific tests in any single text. \lore intensive coverage of testing instruments and problems in special areas can be found in books dealing with the us~ of tests in such fields as counseling. clinical practice, personnel selection, and education. References to such publications are given in the appropriate chapters of this book. In order to keep abreast of current developments, however, anyone working with tests needs to be familiar with IlUoredirect sources of contemporary information about tests. One of the most important sources is the series of Mental !If easurements )'eaTbooks (MMY) edited hy Buros (19i2). Th('sc yearbooks cover nearly all commercially available psychological, educational, and vocational tests published in English. The coverage is especially .complete .for paper-~ndpencil tests. Eaeh yearbook includes tests publIshed dunng a speCified period, thus supplementing rather than supplanting the earlier yearbooks. The Ser,enth Mental Measurements r ear7JOok, for example, is concerned principally with tests appearing bet\\'een 1964 and 1~70. Tests. of continuing interest, however, may be reviewed r~peat('dly m StH.·cesSlyey~arhooks, as nt'w data accumulate from pertment research. The earhest publications in this series were merely bi~)liographies of tests: B~ginning in ]9,38, however, the ),earbook assumed Its ('UlTt'I\t form, wlll(:h llldudes critical reviews of most of the tests by one or more test experts, as well as a complete list of published references pertailling to each lest. .Routine information regarding poblisher, -price, forms, and age of subjects for whom the test is suitable is also regularly giv('n. A comprehensive bibliography covering all types of published tests available in English-speaking countries is provided by Te:~ts in Print (Buras, 1974). Two related sources are Reading Tests and Reviett;~ (Bums, 1968) and Personality Tests and Reviews (Buras, 11970). Both include a numbeF'~9f tests not found in any volume of the MMY, as well as master indexes'that facilitate the location of tests in the :\1\1Y. Reviews of specific tests are also published in several Ilsychological and educational journals, such as the Journal of Educational Measurement and the JOllrnal of Counseling Psyc1101ogy. Since I9iO several sourcebooks have appeared which provide information about u~published or little known instruments, largely supplementing the material listed in the MMY. A comprehensive survey of such
imtruJl1cnts {,;m hr found in A SourcelJook for .Hell/(/I 11ealtll Measures (Comn'~·. Backer, & Glaser, 197:1). Containing approximately 1,100 abstracts. this sourcehook includes tests, questionnaires, rating scales, and other
22
Context of Psyc11010gical Testing
PU?-
of manuals that meet adequate scientific standards. An enlightened lie of test users provides the firmest assurance that such standal'ds wIll be maintained and improved in the future.. . A succinct but comprehensive guide for the evaluatwn of psy~hologlcal tests is to be found in Standards for Educational arul Psyc11010glCal Tests (1974), published by the American Psychological As~ocia~ion. These standards represent a summary of recommended practices 111 test construction based on the current state of knowledge in the field. They are concerned with the information about validity, reliability, norms, and other test characteristics that ought to be reported in the manual. In their latest revision, the Standards also provide a guide for the proper use of tests and for the correct interpretation and application of test results. Relevant portions of the StQnda~ds "ill.be cited in the following chapters, in connection with the appropnate tOpICS.
CHAPTER
2
J\rat1ure arld Use of Psyclz.ological Tests
. T
introduction in Chapter 1 has already suggested some of the many uses of psychological tests, as well as the wide diversity of available tests. Although the general public may still associate psychological tests most dosely with "IQ tests" and with tests designed to detect emotional disorders, these tests represent only a small proportion of the available types of instruments. The major categories of psychological tests will be discussed and illustrated in Parts 3, 4, and 5, '\'hich cover tests of general intellectual level, traditionally called intelligence tests; tests of separate abilities, including multiple aptitude batteries, tests of special aptitudes, and achievement tests; and personality tests, concerned with measures of emotional and motivational traits, interpersonal behavior, interests, attitudes, and other noncognitive characteristics. In the face of such diversity in nature and purpose, ,~hat are tIle common differentiating characteristics of ps~'Chological tests? Ho," do psychological tests differ from other methods of gathering information about individuals? The answer is to be found in certain fundamental features of both the construction and use of tests. It is with these featm!es that the present chapter is concerned. HE HISTORICAL
BEHAVIOR SAMPLE..-A, psychological test is essentially an objective .~d standardized measure orit's'ample of behavior. Psychological tests are like tests in any other science, insofar as 0R~flh~tions are made on a small hut carefully chosen ,sample .~ . an ip~jyjil~)rs behaviQr.. In this respect, the psychologist proceeds in much·.the 'Jame way as the chemist who tests a patient's blood or a community.}swater supply by analyzing ,-et'more samples of it. If the psychologistwish¢'~ to test the extent ,iff a c1lild's vocabulary, a clerk's ability to perform arithmetic computa-
tions, or a pilot's eye-hand coordination, he ('xamim's their performance with a representatin' set of wonls, :11'ithmclie prol>lems, or motor tests. "'hetlwr or not the test adeqnately co\'(.'rs the behavior under consideration obviously depends on the number and nature of it in the samp e. or examp e, an ant 1I1letJctest consisting of only five problems, ~le including only multiplication items, would be a poor measure of the indiyidual's computational skill. A yoealmlary test composed entirely of baseball terms would hardly proYide a dependable estimate of a child's total range of vocalmlar~'. The diagnostic or 'redictiJ;c t;a7uc of a lsycholC!gical test depend~_ol! the debH,',~O which it sen'es as an indicator of a relatively broad and Measurement of the hehaYior sample directl~' !!guinea;t area·Ofb~;:. cO\'ered by the test is J:arely, if ever, the goal of psychological testing. The child's knowledge of a particular list of 50 words is not, in itself, of ,great interest. Nor is the job applicant's performance on a specific set of 20 arithmetic problems of much importune-e_ If, however, it can be demonstrated that there is a dose correspondence between the child's knO\dedge of the word list and his total l1laster~- of vocabulary, or between the applicant's score on the arithmetic problems and his computational performance on the joh. then the tests are ser\'ing their purpose, It should be noted ir.. this connectiolJ that the test items need not resemble closely the beha.vior the test is.to }[('dicr."It is only necessary tna " .- on ence be demoHstrated bet"'ecn the tm); The degrec of similarity between the test sample and the predicted behavior ma\' vary widely. At one extreme. the test mav coincide completelY with a part o'f the b;'h~or to he preclictt'cl. An e.\:Imple might be a foreign vocabulary test in whi!=·htilt:' students are examilled on 20 of the 50 nt'\\words th~y have studied; another example is provided by the ro,ld test taken prior to obtaining a driver's liccme. A lesser degree of similarity is illustrated by many vocational aptitude tests administered prior to joh ance between the training, in which there is only a mod<'rate rese tasks peIformed on the joh and those incorporat ,in the test. At the other extreme one finds projecth'e personality test!>'" eh as the Rorschach inkblot test, in which an attempt is made to predict from the subject's as~ociations to inkblots how he will rcad to other people, to ~motionally toned stimuli, and to other complex, everyday-life situations, Despite their superficial differences, all these tests consist of samples of the indi~s behavioL., And each mUst prove Its worth by" an empirically demonstrated correspondence between the subject's pcrformance on the test and in other situations. Whether the term "diagnosis" or the term "prediction" is employed in this connection also represents a minor distinction. Prediction eommonly connotes a temporal estimate, the individual's future performance on a job, for example, heing foreeast from his present test performance. In a
nls
hroader sense, ho\\"('\'er, e\-en the diagnosis of present condition, suell as mental retardation ur emutional disorder, implies a prediction of what the incIi\'idual will cIO in situations other than the present test. It is logically Simpler to consider all tests as behavior samples from which predictions regarding other JX.havior can be made. Different typps of tests can then be characterized as variants of this basic pattern. Anotlwr point that should be considered at the outset pertains to the cone-ept of Clll}(/cify. It is entirely possible, for example, to dc\'isc a test fur predicting how well an individual can learn Fre11Ch before he has even begun the study of French. Such a test would invoh-e a sample of the types of behavior required to learn the new language, but would in itself presuppose no knowledge of French. It could then be said that this test measures the indh'idual's "capacity" or "potentialitt for learning French, Such tenus should, hO"'ever, be used with caution in reference to ps~'dlOlogical tests. Onl\' in the senSe that a present behavior sample can be used as an indicator of other, future behayior can we s~ak.()f a test measuring "capacity." Ko psychological test can do more than measurelJel1"UDor. 'Vh~ethci:S\1ch behavior can serve as an effective inc!('x of other IX'hador can be determined only by empirical try-out.
STA:-;DARDIZATIO:-;, It ,,-:"iIlhe recalled that in the initial definition a ps~-chological test \\'as described as a standardized measure. Standardization implies !miformifll of ~)rQcedllre in 'hdnl11Hsfenng and SCoring the 'test If the scores obtained by different iudiyiduals are to be comparable, testin~ conditions must obYiously be the same for all. Such a requirement is only a speCial application of the need for controlled conditions in all scientific ohse-ryations. In a test situation, the single independent \'ariable is usuall~' the indh-idual being tested. In order to secure uniformity of testing conditions, the test constructor provides detailed directions for administering each newly developed h:'st. The formulation of such directions is a major part of the standardization of a new test_ Such standardization extends to the exact materials em 'plo~d, time limits, oral instructions to subjects, prc>Jiminary demonstra: ~ns, ways of handling queries from subjects. and evel,\, other ~ the testing situation. :Many other, more subtle factors may influence the subject's performance on certain tests. Thus, in giving instructions or, presenting problems orally, consideration must be given to the rate of speaking, tone of voice, inflection, pauses, and faCj~1 e}pression. In a test involving the detection of absurdities, tot eX;lnit>le, the correct an~wer may be given away by smiling or paY~jlg wh~n the crucial word th~\. ex.aminer's point of J~.read .. Stand~rdized testing p.rocedure, ~r:,~i[ \1:w, Will be dJscussed further m a later sect~g~ of-
26
COlltext Of
Psychological Testing
Nature alld Use of Psychological
Another important step in the standardization of a test is the establishment of norms, Psychological tests have no predetermined standards of pli5singor fa'inng; an individual's score is evaluated by comparing it with the scores obtained by others. As its name implies, a norm is the normal or average performance. Thus, if normal B-year-old children complete 12 out of 50 problems correctly on a particular arithmetic reasoning test, then the 8-year-old norm on this test corresponds to a score of 12, The latter is known as the raw score on the test, It may be expressed as number of correct items, time required to complete a task, number of errors, or some other objective measure appropriate to the content of the test. Such a raw score is meaninglcss until evaluated in terms of a suitable set of norms, . In the process of standardizing a test, it is administered to large, representative sample of the type of subjects for whom it is designed. This group, known as the standardization sample, serves to establish the norms. Such norms indicate not only the average performance but also the relative frequency of varying degrees of deviation above and below the awrage. It is thus possible to evaluate different degrees of superiority and inferiority. The specific ways in which such norm" may be expressed will be considered in Chapter 4. All permit the designation of the indi"idual's position with reference to the normative or standardization sample. It might also be noted that norms are established for personality tests . in esse!1tially the same way as for aptitude tests. The norm on a personality test is not necessarily the most desirable or "ideal" performance, any more than a perfect or errorless score is the norm on an aptitude test. On both types of tests, the norm corresponds to the performance of typical or average individuals. On dominance-submission tests, for example, the nonn falls at an intermediate point representing the degree of dominance or submission manifested by the average individual. Similarly. in an emotional adjustment inventory, the norm does not ordinarih· correspond to a complete absen<.'C of unfavoral;>le or maladaptive' }'esponses, since a few such responses occur in the majority of "normal" individuals in the standardization sample. It is thus apparent that psychological tests, of whatever type, are bascq'· on lmpirically established norms.
a
Reference to the definition of a psychological test with which this discussion opened will show that such a test was characterized as an objective as well as a standardized measure. In ,••.hat specific way~.are such tests objective? Some aspects of the objectivity of psychologieh'l tests have already been touched on in OBJECTIVE
MEASUREMENT
OF DIFFICULTY.
Tests
27
the discussion of standardization. Thus, the administration, scoring, and interpretation of scores are objective insofar as they are independent of the subjective judgment of the individual examiner. Anv one individual should theoretically obtain the identical score on a test r~gardless of who happens to be his examiner. This is not entirely so, of comse, since perfect standal'dization and objectivity have not been attained in practice. But at least such objectivity is the goal of test consb'uction and has been achieved to a reasonably high degree in most tests. There are other major ways in which psychological tests can be properly described as objective. The determination of the difficulty level of an item or of a whole test is based on objective, empirical procedures. 'Vhen Binet and Simon prepared their original, 1905 scale for the measurement of intelligence, they arranged the 30 items of the scale in order of increasing difficulty. Such difficulty, it will be recalled, was determined by trying out the items on 50 normal and a few mentally retarded children. The items correctly solved by the largest number of' children were, ipso facto, taken to be the easiest; those passed by relativdy few children were regarded as more difficult items. By this procedure, an empirical order of difficulty was established. This early ,:xarnple typifies the objective measurement of difficulty level, which is now common practice in psycho. logical test construction. :l'ot only the arrangement but also the selection of items for inclusion in a test can be determined by the proportion of subjects in the trial samples who pass each item. Thus, if there is a bunching of items at the easy or difficult end of the scale, some items can be discarded. Similarly, if items are sparse in celiain portions of the difficulty range, new items can be added to fill the gaps. More technical aspects of item analYsis will be considered in Chapter 8. .
. RELIABILITY. How good is this test? Does it really work? Thes£l quest~ons could-and occasionally do-result in long hours of futile discussIOn. Subjective opinions, hunches, and personal biases may lead, on the one hand, to extravagant claims regarding what a particular test can acco~plish and, on the other hand, to stubborn rejection. The only way q~estlOns sU~h ~s these can be conclusively answered is by,empirical trial. The olJ]ectlve evaluation of psychological tests involves primarilv d~tennination of the reliability and the validity of the test in specified Sltuatlons.
t?e
As used in psychometrics, the term reliability always means consistenc~', Test reliability is the consistency of scores obtain_ed;~ the same persons when retested with the identical test or with an eqRhYalent form of the test. If a child receives an IQ of 110 on Monday and an IQ of 80
when retested on Friday, it is obvious that little or 110 confidence can be put in either score. Similarly, if in olle set of 50 words an individual identifies 40 correctl~·, whereas in another, supposedly equivalent set he gets a score of only 20 right, then neither score can be taken as a dependable index of his verbal comprehension. To be sure, in both illustrations it is possible that only one of the two sC'ores is in error, but tlus could be demonstrated only by further retests. From the given data, we can conclude only that both scores cannot be right. \Vhether one or neither is an adequate estimate of the individual's ability in vocabulary cannot be established without additional information. Before a psychological test is released for general use, a thorough, objective check of its reliability should be carried out. The different types of test reliability, as well as methods of measuring each, will be considered in Chapter 5. Reliability can be checked with reference to I temporal fluctuations, the particular selection of items or behavior sample constituting the test, the role of different examiners or scorers, and other aspects of the testing situation. It is essential to specify the type of reliability and the method employed to determine it, because the same test may vary in these different aspects. The number and nature of individuals on whom reliability was checked should likewise be reported. With such information, the test user can predict whether the test will be about equally reliable for the group with 'which he expects to use it, or whether it is likelv to be more reliable or less reliable.
VALIDITY, Undoubtedly the most important question to be asked about any psychological test"concerns its validity, i.e., the degree to which the test actually measures what it purports to measure. Validity provides a direct check on how well the test fulfills its function. The determination of validity usually requires independent, external criteria of-whatever the test is nesigned to measure. For example, if a medical aptitude test ist9 be used in selecting promising applicants for medical school,. ultimatle success in medical scholYlwould be a criterion. In the process of ·y~lidating such a test, it would be administered to a large group of students at the time of their admission to medical school. Some measure of performance in medical school would eventually be obtained for each student on the basis of grades, ratings by instructors, success or failure in completing training, and the like. Such a composite measure constitutes the criterion with which each student's initial test score is to be correlated. A high correlation, or validity coefficie,,!t, would signify th~t those individuals who scored high on the- test. had been relatively successful in medical school, whereas those scoring low on the test had done poorly in medical school. A low correlation would indicate little correspondence l,,,t"'ppn tp~t ~('orp. rind criterirJn measure and hence poor validity for the
test. The validity coefficifnt enables us to determine how closel\' the criterion perfor~ance could have been predicted from the test scor~s. In a similar manner, tests designed for other purposes can be validated against appropriate criteria. A vocational aptitude test, for example, can be validated against on-the-job success of a trial group of new employees. A pilot aptitude battery can 1;>evalidated against achie\'ement in flig:lt training. Tests designed for broader f\nd more varied uses are validated against a number of criteria and their validity can be established only by the gradual accumulation of data from many different kinds of investigations. The reader may have noticed an apparent paradox in the concept of test validity. If it is necessary to follow up the subjects or in other ways to obtain independent measures of what the test is trying to predict, why not dispense v.ith the test? The answer to this riddle is to be found in the distinction between the validation l,TfOUp on the one hand anci the groups on which the test will eventually be employed for operational purposes on the other. Before the test is ready for use, its validity must be established on a representative sample of suhjects. The scores of these persons are not themselves employed for operational purposes but serve only in the process of testing the test. If the test proves valid b~' this method, it can then be used on other samples in the absence of criterion measures. It might still be argued that we would need only to wait for the criterion measure to mature, to become available, on any group in order to obtain the information that the test is trying to predict. But such a procedure would be so wasteful of time and energy as to be prohibitive in most instances. Thus, we could detennine which applicants will succeed on a job or which students will satisfactorily complete college by admitting all who apply and waiting for subsequent developments! It is the very wastefulness of this procedure-and its deleterious emotional imtests are designed to minimize. By means of pact on individuals-that tests, the person's present level of prerequisite skills, knowledge, and other relevant characteristics can be assessed with a deferminable margin of error. The more valid and reliable thef~, the smaller will be this ,margin of error. . The special problems encountered in determining the validity of different types of tests, as well as the specific criteria and statistical procedures employed, willlJ~ fhscussed in Chapters 6 and 7. One further point, however, should be coq$fdered at this time. Validitv tells us more than the degree to which the te~t is f~lfilling its funcpari.ft actually tells us what the test is measuring. By studying the validation data, we can objectively determine what the test is measuring. It would thus be more accurate to define validity as the extent to which we Jrnow what the test measures. The interpretation of test scores would undoubtedly be clearer and less ambiguous if tests were regularly named in terms of the criterion
Context of Psychological Tes/ing '~:~hl:ough which they had been validated. A tendency in this direction pe'recognized in such test labels as "~cholastic aptitude test" and sonnel classification test" in place of the vague title "intelligence
'SONS FOR CONTROLLING ,CHOLOCICAL TESTS
'y I:have
THE USE OF
a Stanford-Binet blank? ~fy nephew has to take it next week for;
i~sion to,School X and I'd like to give him ~ol1lepractice so he can pass." o improve the reading program in our school, we need a culture-free IQ ,t .that measures each child's inllate potential." st night I answered the questions in an intelligence test published in a ~gazine and I got an IQ of SO-I think psychological tests are silly."
.. 'y roommate is studying psych. She gave me a personality test and I came 1neurotic. I've been too upset to go to class ever since."
, 'ast ~'enryou gave a new personality test to our employees for research pur.;poses.We would now like to have the scores for their personnel folders." The above ·remarks are not imaginary. Each is based on a re~fincident, nd the list could easily be extended by any psychologist. SuQ't remarks 'lustrate potential misllses or misinterpretations of psychological tests in uch wavs, as to rrnder the tests worthless or to hurt the indi:,V;idual.Like ny sd~ntillc instrument or precision tool, psychological t~~s"roJ!~.LP.!:_ 9perly used to be effective. In the hands of either the unscrupulous or "we -meamng ut uninformed user, such tests can cause serious
~~~
~
. There are two principal reasons for controlling the use of psychological ests: (a) to revent general familiarity with test content, which would .' invalidate the test an ( to ensure tat e test is used ~ a qualified :> , '~\' if an individual were to merr'lbrize the correct' responses on a test o'f' color blindness, such a test w~ld no longer be a 'measure of color vision for him. Under these condItions, the test would be completely invalidated. Test content clearly has to be restricted in , order to forestall deliberate efforts to fake scores. In other cnses, however, the effect of familiarity may be less obvious, or the test may be invalidated in good faith by misinformed persons. A \ ,schoolteacher, for example, may give her class special praettee in prob.1ems closely resembling those on an intelligence test, "so that the pupils will be well prepared to take the test." Such an attitude is simply a carry"over from the usual procedure of preparing for a school examination. O'
When applied to an intelligence test, however, it is likely that such specific training 01' coaching will raise the scores on the test without appreciably affecting the broader area of beha"ior the test tries to sample. Under such conditions. the validity of the test as a predictive instl'l1ment is reduced. The need for a qualified examiner is evident in each of the three major aspects of the testing situation-selection of the test, administration and scoring, and i~terpretation of scores. Tests cannot be chos'en like lawn mowers, from a mail-order catalogue. They cannot be evaluated by name, author, or other easy marks of identification. To be sure, it requires no psychological training to consider such factors as cost, bulkiness and ease of transporting test materials, testing time required, and ease and rapidity of scoring. Information on these practica] points can '\lsually be obtained from a test catalogue and should be taken into account in planning a testing program. For the test to serve its function, however, an e"nlnation of its technical merits' in terms of such characteristics as validity reliability difficulty level, and norms is essential. Only in such a way' ~an the tes~ user determine the appropriateness of an)' test for his particular purpose and its suitability for the type of persons with whom he plans to use it. The introductory discussion of test standardization earlier in this chapter has ah'eady suggested the importance of a trained examiner. An adequate realization of the need to follow instructions precisely, as well as a thorough familiarity with the standard instructions, i~ required if the test scores obtained by different examiners are to be comparable or if anyone individual's score is to he evaluated in terms of the published norms. Careful conh-ol of testing conditions is also essential. Similarly, incorrect or inaccurate scoring may render the test score worthless. In the absence of proper checking procedures, scoring errors are far more likeh- to occur . ,\ than is generally realized. The proper interpretation of test scores requires a thorough understanding of the test, the individual, and the testing <'Onditiolls. What is being measured can be objectively determined only by reference to the specific procedures in terms of which the particular test was validated. Other information, pertaining to reliability, nature of the group on which norms were established, and the like, is likewise relevant. Some background data reg,arding the individual being tested are essential in interpreting any test score. The same score may be obtained by different persons for very different reasons. The conclusions to be drawn from such scores would therefo.re be quite dissimilar. Finally, some consideration must also be given to special factors that may have influenced a particular score, such as unusual testing conditions, temporary emotional or physical state of thl> subject, and extent of the subject's previous experience with tests.
Nature
The basic rationale of testing im·olves generalization from the behavior sample observed in the testing situation to beha"ior manifested in other, nontest situations, A test SCOl'e should help us to predict how the client will feel and act outside the clinic, how the student will achieve in college courses, and how the applicant will perform on the job. Any influences that are specific to the test situation constitute error variance and reduce test validity. It is therefore important to identify any test-related influences that may limit or impair the generalizability of test results. A whole volume could easil\' be devoted to a discussion of desirable procedures of test administration, But such a survey falls outside the scope of the present book. Moreover, it is more pra~ticable to acquire ~.such techniques within specific settings, because no one person would normally be concerned with all forms of testing, from the examination of infants to the clinical testing of psychotic patients or the administration of a mass testing program for military personnel. The present discussion will therefore deal principally with the common rationale of test administration rather than with specific questions of implementation. For detailed suggestions regarding testing procedure, see Palmer (1970), Sattler (1974), and Terman and Merrill (1960) for individual testing, and Clemans (1971) for group testing.
ADVASCE PREPARATIOS OF E."I:AMINERS. The most important requirement for good testing proc;.edure is advanc-e preparation. In testing there can he no emergencies. Special efforts must therefore be made to foresee and forestall emergencies. Only in this way can unifom1ity of procedure be ..a{ls.\wed. 'Advance preparation for the testing session takes many forms. Memorizingthe exact verbal instructions is essential in most individual testing. Even ill a group test in which the instructions are reauto the subrects, some· previous familiarity with the statements to be read prevents misreading and hesitation and permits a more natural. informal ;manner during test admillish'ation. The preparation of test materials is an9ther important preliminary step. In individual testing and especially in the administration of performance tests, such preparation invqlves the actual layout of the necessary materials to facilitate subsequent use with a minimum of search or fumbling. Materials should generally be placed on a table near the testing ta.~le so that they are within easy reach of the examiner but do not distriCt Vte subject. When apparatus is employed, frequent periodic checking and calibration may be necessary. In group testing, all test blanks, answer sheets, special pencils,· or other materials
alld
(he of PsycllOlogiclIl Tc'sls
33
needed should be carefully counted, checked, and arranged in advance of the testing day. Thorough familiarity with the specific testing procedure is another important prerequisite in both individual and group testing. For individual testing, supervised training in the administration of the particular test is usually essential. Depending upon the nature of the test and the type of subjects to be examined, such training may requi.re from a few demonstration and practice sessions to over a year of instruction. For group testing, and espeCially in large-scale projects, such preparation may include advance briefing of examiners and proctors, so that each is hilly infonned about the functions he is to perform, In general, the examiner reads the instructions, takes care of timing, and is in charge of the group in anyone testing room. The proctors hand out and collect test materials, make certain that subjects are following instructions, answer individual questions of subjects within the limitations specified in the manual, and prevent cheating.
TESTING COXDlTlOXS. Standardized procedure applies not only to verbal instructions, timing, materials, and other aspects of the tests themselves but also to the testing environment. Some attention should be iven to the selection of a . ~ flijJ.. This room should be hould wvide , venti~ .~cial~ should a so e ta -en to prevcnt mtcrrup ons unng the test. Posting a sign on the door to indicate that testing is in progress is effective, provided all personnel have learned that such a sign means no admittance under any circumstances. In the testing of large groups, locking the doors or posting an assistant outside each door may be neeessarv to-prevent the -entrance of late-comers. . It is important to realize the extent to which testing conditions may lI1fluence scores. Even apparentl~' ·minor aspects of the testing situation may appreciably alter performance. Such a factor as the use of deSKSor of chairs with desk arms, for example, proved to be significant in a group testing project with high school students, the groups using desks tending to obtain higher scores (Kelley, 1~43:Traxler & Hilkert, 1942). There is may affect also evidence to show that the Slli9ir~loyed test scores (Bell, Hoff, & Hoyt,-19t3~1~li'~1lfr-~~ab1ishment of independent test-scoring and data-processing agencies that;, provide their 0\1.'11machine-scorable answer sheets, examiners sometimes administer group tests with answer sheets other than those lIsed in the standardization sample. In the absence of empirical verification, the equivalence of these answer sheet# cannot be assumed. The Differential Aptitude Tests, for example, may be administered with any of five different answer
·
J
Context of Psychological Testing eets. On the Clerical Speed and Accuracy Test of this battery, separate s are provided for three of the five answer sheets, because they were nd to yield substantially different scores than those obtained with the reI' sheets used by the standardization sample. testing children below the fifth grade, the use of (Illy separate answer t may significantly lower test scores (Meh'opolitan Achievement Test ial Report, 19i5). At these grade levels, having the child mark the \'ers in the test booklet itself is generally preferable. any other, more subtle testing conditions have been shown to affect ormance on ability as well as personality tests. Whether the exinel' is a stranger or someone familiar to the subjects may make a 'nificant difference in test scores (Sacks, 1952; Tsudzuki, Hata, & Kuze, 57). In another study, the general manner and behavior of the exam, as illustrated by smiling, nodding, and making such comments as ood" or "fine," were shown to have a decided effect on test results "ickes, 1956). In a projective test requiring the subject to write stories 'fit given pictures, the presence of the examiner in the room tended to hibit the inclusion of strongly emotional content in the stories (Bernein, 1956). III the administration of a typing test, job applicants typed 'a significantly faster rate when tested alone than when tested in groups liHwo or more (Kirchner, 1966). Examples.could readily be multiplied. The implications are threefold. .first, follow standardized procedures to the minutest detail. It is the reonsibility of the test author and publisher to descdbe such procedures ully and clearly in the test manual. Second, record any unusual testing onditions, however minor. Third, take testing conditions into account ;hcn interpreting test results. In the intensive assessment of a person rough individual testing, an experienced examiner may occasionally dert from the standardized test procedure in OJ:der to eJi~it additional inrmation for special reasons. \Vhen he docs so, he ~ no longer inrpret the subject's responses in terms of the test norms, Under these rcumstances, the test stimuli are used only for qualitative exploration; . ld the responses should be treated in the same way as any other infor"malbehavioral observations or interview data.
In psychometrics, the term "rapport" refers to the examiner's effOl'ts o arouse the subject's interest in the test, elicit his cooperation, and nsure that he follows the standard test instructions. In ability tests, the nstructions call for careful concentration on the given tasks and for put'ng forth one's best efforts to perform well; in personality inventories, ey call for frank and honest responses to questions about one's usual
Natml.' anel USe' Of Psychological
Tests
35
behavior; in certain projective tests, they call for full reporting of associations evoked by the stimuli, without any censoring or editing of content. Still other kinds of tests may require other approaches. But in all instances, the examiner endeavors to motivate the subject to follow the mstructlOns as fullv and conscientiously as he can. The training of examiners covers techniques for the establishmcnt of rapport as well as those more directly related to test administration. In establishing rapport, as in other testing procedures, uniformity of conditions is essential for comparability of results. If a child is given a coveted prize whenever he solves a test problem correctly, his performance cannot be directly compared with the norms or with that of other children 01' who are motivated only, with the standard verbal encoura"ement 0 praise. Any deviation from standard motivating conditions for a particular test should be noted and t,aken into account in interpreting performance. Although rapport can be more fully established in individual testing, steps can also be taken in group testing to motivate the subjects and relieve their anxiety. Specific techniques for establishing rapport vary with the nature of the test and with the age and other characterbtics of the subjects. In testing preschool children, special factors to be considered include shyness with strangers, distractibility, and negativism. A friendly, cheerful, and relaxed manner on the part of the examiner helps to reassure the child. The shy, timid child needs more preliminary time to become familiar with his surroundings. For this reason it is better for the examiner not to be too demonstrative at the outset. but rather to wait until the child is ready to make the first contact. Test periods should be br~ef, and the ~asks should be varied and intrinsically interesting to the chll.d.. The testIng should be presented to the child as a game and his cunoslty aroused before each new task is introduced. A certain flexibilitv of procedure is necessary at this age level because of possible refusal~, loss of interest, and other manifestations of negativism. Children in the first two or three grades of elementary school present many of the same testing problems as the preschool child. The game approach is still the most effective way of arousing their interest in the test. The older schoolchild can usually be motivated through an appeal to his competitive spirit and his desire to do well on tests. 'Vhen testing children from educationally disadvantaged backgrounds or from different cultures, however, the examiner cannot assume they will be motiyated to excel on academic taSKSto the same extent as children in the starfdardizati~n sa~~le ..This pro~le~ and others pertaining to the testing of persons \\ lth diSSImilar expenential backgrounds will be c'Onsidered further in Chapters 3, 7, and 12. . Special. motivational problems may be encountered in testing emotionally disturbed persons, prisoners, or juvenile delinquents. Especially when examined in an institutional setting, suca persons are likely ·to ..
manifest a number of unfavorable attitudes, such as suspicion, insecurity, fl'ar, or cynical indifh'renee. Abnormal conditions in their past experiences are also likely to influence their test perforrnanee adversely. As a result of early failures and frustrations in school, for example, they may have developed feelings of hostility and inferiority toward academic tasks, \rhich the tests resemble. The experienced examiner makes special efforts to establish rappolt under these conditions. In any event, he must be sensitive t~ these special difficulties and take them into account in interpreting and explaining test performance. In testing any school-age child or adult, one should bear in mind that e\'e1')'test presents an implied threat to the individual's prestige. Some reassurance should therefore be given at the outset. It is helpful to explain, for example, that no one is expected to finish or to get all the itcms correct. The individual might otherwise experience a mounting sense of failure as 11e advances to the more difficult items or finds that he is unable to finish anv subtest within the time allowed. It is also desil:able to eliminate the element of surprise from the test situation as far as possible, because the unexpected and unknown are likely to produce al1xiet~'. :Many group tests provide a prdiminaryexplanatory statement that is read to the group by the examiner. An even better procedure is to announce the tests a few days in advance and to give each subject a printed booklet that explains the purpose and nature of the tests, offers general suggestions on how to take tests, and contains a few sample items. Such explanatory booklets are regularly available to participants in large-scale testing programs such as those conducted by the College Entrance Examination Board (1974a, 1974b). The United States Employment Service has likewise de\'eloped a booklet on how to take tests, as well as a more extensive pretesting orientation~.technique for use with culturally disadvantaged applicants unfamili~f. ,v'ith tests. \1ore general orientation booklets aie also .available, si'tc11 as l\feeting the Test (Anderson, Katz, & Shimberg, 1965), A tape recOl'ding and two booklets are combined in Test Orientatioll Procedure (TOP), designed specifically for job applicants with little prior testing experience CBennett & Doppelt, 1967), The first booklet, used together with the tape, provides general information on how to take tests; the second contains practice tests. In the absence of a tape recorder, the examiner may read the instructions from a printed script. Adult testing presents--some additional problems. Unlike the schoolchild, the adult is not so likely to work hard at a task merely because it is assigned to him. It therefore becomes more important to "sell" the purpose of the tests to the adult, although high school and college students also respond to such an appeal Cooperation of the examinee can usually ;be secured by convincing him that it is in his own interests to obtain a \,
valid score, Le., a score correctly indicating wh~lt he can do rather than overestimating or underestimating his abilities. ~Iost persons will understand that an incorrect decision, which might result from invalid test scores, would mean subsequent failure, loss of time, and frustration for them. This approach can serve not only to motivate the individual to try his best on ability tests but also to reduce faking and encourage frank reporting on personality inventories, because the examinee realizes that he himself would otherwise be the loser. It is certainly not in the best interests of the individual to be admitted to a course of study for which he is not qualified or assigned to a job he cannot perform or that he would find uncongenial.
:\lany of the practices designed to enhance rapport sen'e also to reduce test anxiety. Procedures tending to dispel surprise and strangeness from the testing situation and to reassure and encourage the subject shottld certainly help to lower anxiety. J'he examiner's own manner and a wellorganized, smccthly running testing operation will contribute toward the same goal. Individual differences in test anxiety have been studied with hoth schoolchildren and college students (Ga~dry& Spielberger, 1974;Spielberger, 19i2). Much of this research was initiated bv Sarason and his associates at Yale (Sarason, Davidson, Lighthall, "'aite, & Ruebush, 1960). The first step was to construct a questionnaire to assess the individual's test-taking attitudes. The children's form, for example, contains items such as the following: Do you worry a lot before taking a test? \\'hen the teacher sa~'s she is going to find out how much you h,we learned, does your healt begin to beat faster? While 'you are taking a test, do you usually think you are not doing wen. Of primary interest is the finding that both school achievement and intelligence test scores yielded significant negative correlations with test anxiety. Similar correlations have been found among college st1tdcn!s (1. G. Samson, 1961). Longitudinal studies likewise revealed an inverse relation between changes in anxiety level and changes in inteJligence or achievement test perfonnance (Hill & Sarason, 1966; Sarason, Hill, & Zim. bardo, 1964). ~uch findings, of course, do not indicate the direction of caUsal relationslllps. It is possible that children develop test anxiety because they per-
Context of Psydl(Jlogical Testiug form poorly on tests and haw thus experienced failure and frustration in previous test situations. In support of this interpretation is the finding that \\ithin subgroups of high scorers on intelligence tests, the negative "rrelation between anxiet~' level and test performance disappears Denny, 1966; Feldhusen & Klausmeier, 1962). On the other hand, there 5 evidence suggesting that at least some of the relationship results from he deleteLious effects of anxiety on test performance. In one study (:Waite,Sarason, Lighthall, & Davidson, 1958), high-anxious and low, 'iotlschildren equated in intelligence test scores were given repeated ials in a learning task Although initially equal in the learning test, the w-allxiousgroup improved significantly more than the high-anxious. Severalinvestigators have compared test performance under conditions esigned to evoke "anxious" and "relaxed" states. Mandler and Sarason ;;(.1952), for example, found that ego-involving instructions, such as telling subjects that everyone is expected to finish in the time allotted, had a beneficialeffect on the performance of low-anxious subjects, but a deleteriouseffect on that ofbigh-anxious subjects. Other studies have likewise foundan interaction between testing conditions and such individual char~cteristicsas anxiety level and achievement motivation (Lawrence, 1962; Palll & Eriksen, 1964). It thus appears likely that the r~latjQn between anxiety,and test performance is nonlinear, a slight amount Qf anxiety ,\lein bencficia~ while a lar e amount is detrimental. Individuals who are ',cllstomariy ow-anxious benefit from test con i,tions t lat arouse some et:>, ",hi e t lose who are customarilv hi
il tests may be unduly affected by test anxiety. In a thorough ana::4ontrol1ed investi. gationof this question, French (1962) compar~d Jhf'p,erformancc of high school students on a test given as part of the fe-gular administration of the SAT with performance on a parallel form of the test administered at ,a different time under "relaxed" conditions, The instructions on the latter , occasion specified that the test was given for 'research purposes only and scores would not be sent to any college. The results showed that performance was no poorer during the standard administration than during the relaxed administration. Moreover, the concurrent validitv of the test scores against high school course grades did not differ signifi~antly under the two conditions.
f
Comprehensive surveys of the effects of examiner and situational variables on test seores'lmve been prepared by S. B. Sarason (1954), Masling (l~60), ~foliarty (1961, 1966), Sattler and Theye (1967), Palmer (19,0), and Sattler (1970, 1974). Although some effects have been demonstrated with objective group tests, most of the data have been obtained with either projective techniques or individual intelligence tests. These extraneous factors are more likely to operate with unstructured and ambiguous stimuli, as well as "ith difficult and nO"el tasks, than with clearly defined and well-learned functions. In general, children are more susceptible to examiner and situational influences than are adults; in the examination of preschool children, the role of the examiner is especially cruCiaL. Emotionally disturbed and insecure persons of an\' age are also mClre likely to be affected by such conditions than are well-adjusted persons, There is considerable evidence that test results may vary systematically as a function of the examiner (E. Cohen, 1965; ~'Iasling, 1960). These differences may he related to personal characteristics of the examiner, such as his, age, sex, race, professional or socioeconomic status, training and expenence, personality charaderistics, and appearance. Se\'eral studies of thes~ examiner variables, however, have yielded misleading or illconcluSl\'e results because the experimental designs failed to control or isolate the influence of differcnt examiner or subject characteristics. Hence thp l:'ffeds of two or more variables ma\, be confounded. The examiner's behavior before and during test auministration has also heen s~lown to affect test results, For example, controlled investigations ha\'e YIelded significant differences in intelligence test performance as a res~lt of a "warm" versus a "cold" interpersonal relation between examllJer and examinees, or a rigid and aloof versus a natural manner on the part of the examiner (Exner, 1966; Masling, 1959). Moreover, there may be Significant interactions between examiner and examinee' charact " , h e~lstJCs,III t e sen~e that the same examiner characteristic or testing mannel may have a dIfferent effect on different examinees as a function of the examinee's Own personality characteristics. Similar interactions may occur '~ith task variables, such as the nature of th,e test, the purpose of the testing, and the instructions given to the subjects. Dyer (1973) adds even more variables to this list, calling attention to the possible inHirence of th t t· , d . ," . . c es gIVers an the test takers' diverse perceptions of the funetiglls ' and goals of testing.' St'll ' • '. I. an,other way in which an examin8r may inadvertently affect the ~x~~m~e s responses is through ~is own 'cexpectations, This is simply a P clal mstance of the self-fulfilhng prophecy (Rosenthal, 1966; Rosen-
40
Context of Psycholog.ical Testing
thaI & Rosnow, 1969). -An experiment conducted with the Rorschach will illustrate this effect (Masling, 1965). The examiners were 14 graduate student volunteers, 7 of whom were told, among other things, that experienced examinel's elicit more human than animal responses from the subjects, while the other 7 were told that experienced examiners elicit more animal than human responses. Under these conditions, the two groups of examiners obtained significantly diHerent ratios of animal to human responses from theh subjects. These differences occurred despite the fact that neither examiners nor subjects reported awareness of any influence attempt. ~foreover, tape recordings of all testing sessions revealed no evidence of verbal influence on the part of any examiner. The examiners' expectations apparently operated through subtle postural and facial cues to which the subjects responded. Apa~ from the examiner, other aspects of the testing situation may Significantly affect test performance. Military recmits, for example, are often examined shortly after induction, during a period of intense readjustment to an unfamilim' and stressful situation. In one investigation designed to test the effect of acclimatization to such a situation on test performance, 2,724 recruits were given the Navy Classification Battery during their ninth day at the ~a\'al Training Center (Gordon & Alf, 1960). When their scores were c'Ompared with those obtained by 2,180 recruits tested at the conventional time, during their third day, the 9-day group scored Significantly higher on all subtests of the battery. The examinees' activities immediately preceding the test may also affect their performance, especially when such activities produce emotional disturbance, fatigue, or other- handicapping conditions. In an investigation with third- and fourth-grade schoolchildren, there was some evidence to suggest that IQ on the Draw-a-Man Test was influenced Qrthe children's preceding classroom activity (McCarthy, 1944). On one occasion, the class had been engaged in writing a composition on "The" Best Thing That Ever Happened to Me"; on the second occasion, they had again been writing, but this time on "The Wo~sLThing That Ever'Happened to Me." The IQ's on the second test, fOllowing what may have been an emotionally depressing experience, averaged 4 or 5 points lo\ver than on the first test. These findings were corroborated in a later investigation specifically designed to determine the effect of immediately preeeding experience on the Draw-a-Man Test (Reichenberg-Hackett, 1953). In this study, children who had had a gratifying experience involving the successful solution of an interesting puzzle, followed by a reward of toys and candy, snowed more improvement in their test scores than those who had undergone neutral or less gratifying experiences. Similar results were obtained by W. E. Davis (1969a, 1969b) with college students. Perfonnance on an arithmetic reasoning test was significantly poorer when preceded by a failure experience on a verbal comprehension test than it
Natufa aile! Use
of
Psychological Tests
41
was in a control group given no preceding test and in one that had taken a standard verbal comprehension test under ordinary conditions. Several studies have been concerned with the effects of feedback regarding test scores on the individual's subsequent test performance. In a particularly well-designed investigation with seventh-grade students, Bridgeman (1974) found that "success" feedback was followed by significantly higher performance on a similar test than was "failure" feedhack in subjects who had actually performed equally well to begin with. This type of motivational feedback may operate largely through the goals the subjects set for themselves in subsequent performance and may thus represent another example of the self-fulfilling prophecy. Such general motivational feedback, however, s1)ould not be confused with corrective feedback, 'whereby the individual is informed about the specific items he missed and given remedial instruction; under these conditions, feedback is much more likely to improve the performance of initially low-scoring persons. The examples cited in this section illustrate the wide diversity of testrelated factors that may affect test scores. In the majority of well-administered testing programs, the influence of these factors is negligible for practical purposes. Nevertheless~ the skilled examiner is constantly on guard to detect the possible operation of such factors and to mipimize their influence. When circumstances do not permit the control of these conditions, the conclusions drawn from test performance should be qualified.
In evaluating the eHect of coaching or practice on test scores, a fundamental question is whether the improvement is limited to the specific items included in the test or whether it extends to the broader area of ~ehavior that the test i~gned to p;edict. The answer to this ques~ represel1ts the difference between coacmng and education. Obviously any educational experience the indiVidual undergoes, either formal or informal, in or out of school, should be reflected in his performance on tests sampling the relevant aspects of behavior. Such broad influene.es will in no way invalidate the test, since the test score presents an aar:a,tate piCture of the individual's standing in the abilities under conside~n. The difference is, of course, one of degree. Influences cannot..:..be~dassified as either. narrow or broad, but obviously vary widely in scop~~f;om those ~ffecting only a single a~lllinis~tj~n of a.,single test, throu~hJib.~se. affect~ng'p~rformance on all Items ;()fi,ca /:crtUln,type, to those mtfUencmg the mdl vidual's performance in the large .Irtai9rity of his activities. From the standpOint of effective testing, however, a workable distinction can be
COlltext of P~yc1lOlogic(/l
Testing
e. Thus, it can be stated that a test score is inmlidated only when a ':'cular experience raises it withont appreciably affecting the criterion ~Lviorthat: the test is deSigned to predict.
:";{CHIKC. 'the effects of coaching on test scores have been widely ingated. Many of these studies were conducted by British psycholo,with special reference to the effects of practice and coaching on the brinerly used in assigning ll-year-old children to different types of 'Ilrv;,schools (Yates et aI., 195:3-1954). As might be expected, the ~~ovement depends on the ability and earlier educational; 'ences of'the examinees, the nature of the tests, and the amount and 'of coaching provided. Individuals with deficient educational backunds are more likely to benefit from special coaching than are those 'ihave had superior educational opportunities and are already pre, to do well on the tests. It is obvious, too, that the closer the re,blance between test content and coaching material, the greater will the improvement in test scores. On the other hand, the more closely truction is restricted to specific test content, the less likely is improve:nt to extend to criterion performance. "n America, the College Entrance Examination Board has been conhed about the spread of ill-advised commercial coaching courses for lege applicants. To clarify the issues, the College Board conducted veral well-controlled experiments to determine the effects of coaching 'its Scholastic Aptitude Test and surveyed the results of similar studies other, independent investigators (Angoff, 19711>;Conege Entrance 'amination Board, 1968). These studies covered a variety of coaching ethods and included students in both public and private high schools; e investigation was conducted with black students in 15 urban and '"ral high schools in Tennessee. The conclusion from all"these studies is ':at intensive drill on items similar to those on the SAT is unlikelY to 'oduce appreciably greater gains than occur students are rete~ted 'th the SAT after a year of regular high schot;il instruction. On the basis of such research, the Trustees of the College Board issued .formal statement about coaching, in which the fonowing points were ade, among others (College Entrance Examination Board, 1968, p.8-9):
and is taught. Rather, this particular Scholastic Aptitude Test is a measure of abilities that seem to grow slowly and stubb(lrnl~'. profoundly influcllced by conditions at home and at school over thc years, but not responding to hasty attempts to relive a young lifetime. \in'S
It should also be noted that in its test construction procedures, the Col. lege Board im'estigates the susceptibility of new item types to coaching (:\ngoH, 1971b; Pike & Evans, 1972). Item types on which perfo.rma1lce can be appreciably raised by short-term drill or instruction of a narrowly limited nature are not included in the operational forms of the tests..
ot
wrJ/i
e results of the coaching studies which ha,'e thus far been completed inte that average increases of less than 10 points on a 600 point scale can ,expected. It is not reasonable to believe that admissions decisions can be ected by such small changes in scores. This is especially true since the tests merely supplementary to the school record and other evidence taken into . unt b'): admissions officers. . . , As the College Board uses the term, apitude is not something flxed and impervious to influence by the way the child
PRACTICE.The effects of sheer repetition, or practice, on test performance are similar to the effects of coaching, but usuaIl~' less pronounced. It should be noted that practice, as well as coaching, may alter the nature of the test, since the subjects may emplo~' different work methods in solving the same problems. Moreover, certain types of items may be much easier when encountered a second time. An example is 'provided by problems requiring insightful solutions which, once attained, can be applied directly in solving the same or similar problems in a retest. Scores on such tests, whether derived from a repetition of the identical test or from a parallel form, should therefore be carefully scrutinized. A number of studies have been concerned ~,'ith the effects of the identical repetition of intelligence tests over periods ranging from a few days to se,'eral years (see Quereshi, ] 968). Both adults and children, and both normal and mentally retarded persons have been employed. The studies have covered individual as well as group tests. All agree in showing significant mean gains on retests. Nor is improvement necessarily limited to the initial repetitions. \Vhether gains persist or level off in successive administrations seems to depend on the difficulty of the test and the abilit~· level of the subjects. The implications of sucll findings are il- \ lustrated by the results obtained in annual retests of .3,500 schoolchildren with a Yariety of intelligence tests (Dearborn & Rothnev, 1941). When the same test was readministered in successive years, th~ median IQ of the group rose from 102 to 113, but it dropped to 104 when another test w~s substituted. Becaus~ of the retest gains, the meaning of an IQ obtamed on an initial and later trial proved to be quite different. For example, .a~ ~Q of 100 fell approximately at the average o£'lhe distribution on the Im~lal trial, -but in the lowest quarter On a retest~S\ldl iQ's, though numencally identical and derived from the same te~ 1l;!ightthus signify normal ability in the one instance and inferior ability#},(,the other. G~ins in score are also found on retesting with pili:dIel -forms <1j the same tes~, although such gains tend in general to be .srh.a4Ier.Significant m~a,n gams have been reported when altema"f~ forins ofa 'test were adrnullstered in immediate succession or after intervals ranging from orie
Context of Psychological Tesring
b three years (Angoff, 1971b; Droege, 1966; Peel, 1951, 1952). .r results have been obtained with normal and intellectually gifted )children, high school and college students, and employee samples. a "onthe distribution of gains to be expected on a retest with a parallel should be provided in test manuals and allowance for such gains . ~dbe made when interpreting test scores. )17 SOPHJSTICATIO~. The general problem o(test sophistication should '"be considered in this connection. The individual who has had ex'vl! prior experience in taking psychological tests enjoys a certain adJage in test performance over one who is taking his first test (Heim & , IIace,194~1950; Millman, Bishop, & Ebel, 1965; Rodger, 1936). Part Ithis advantage stems from having overcome an initial feeling of angeness, as well as from haVing developed more self-confidence and "etter test"taking attitudes. Part is the result of a certain amount of overlap in the type of content and functions covered by many tests. SpeCific ,"familiaritywith common item types and practice in the use of objective "answer sheets may also improve performance slightly. It is particularly important to take test sophistication into account when comparing the scores obtained by children from different types of schools, where the extent of test-taking experience may have varied Widely. Short orientation and practice sessions, as described em'lier in this chapter, can be quite effective in equalizing test sophistication (Wahlstrom & Boersman,
1968).
CHAPTER
3
Social a1ld Etltical 11JljJZicatioTls of Testi1lg xORDER to prevent the misuse of psychological tests, it has become necessary to erect a number of safeguards around both the tests themselves and the test scores. The distribution and use of psychological tests constitutes a major area in Ethical Standards of Psychologists, the code of professional ethics officially adopted by the American Psychological Association and reproduced in Appendix A. Principles 13, 14, and 15 are specifically directed to testing, being concerned with Test Security, Test Interpretation, and Test Publication. Other principles that, 'although broader in scope, are highly relevant to testing include 6 (ConfideIitiality), 7 (Client Welfare), and 9 (Impersonal Services). Some of the matters discussed in the Ethical Standards are closely related to points covered in the Standards for Educational and Psychological Tests (1974), cited in Chapter 1. For a fuller ,and richer understanding of the principles set forth in the Ethical Standards, the reader should consult two companion publications, the Casebook on Ethical Standards of PsycllOlogists (1967) and Ethical Principles in tIle Conduct of Researc11 with Human Participants (1973). Both report specific incidents to illustrate each prinCiple. Special attention is given to marginal situations in which there may be a conflict of values, as between the advancement of science for human betterment and the protection of the rights and welfare of individuals.
I
The requirement that tests be used only by appropriately qualified examiners is one step toward protecting !he indiy!~ual againE: the im~oper use of tests. Qf course, the necessary qualiB,c~tions vary with the type of test. Thus, a relatively long pe.ri!'d of int~nsive training and s~pervised experience is required for the proper use of individual intelligence tests and most personality tests, whereas a mini~um of specialized psychological training is needed in the case of educational achievement 45
46
COllfext of Psycl1010gicaf Testing
or vocational proficiency tests. It should also be noted that students who take tests in class for instructional purposes are not usually equipped to administer the tests to others or to interpret the scores properly. The well-trained examiner chooses tests that are a )ro riate for 0 the particular purpose for whie 1 e is teshn an t examme. e IS a so cognizant of the available research literature on the clioseiitest and able to evaluate its technical merits with reC1 o ard to such character,istics as norms, reliability, and validity. In administering the test, he is sensitive to the many conditions that such as those 1 ustrate 10 apter 2. He draws conclusions or ~ makes recommendations only after considering the test score (or scores) in the light of other pertinent information about the individual. Above all, lie shpuld be sufficiently knowledgeable about the science of human behavior to guard against unwarranted inferences in his interpretations of test scores. When tests are administered' by psychological technicians or assistants, or by persons in other professions, it is essential that an adequately qualified psychologist be available, at least as a consultant, to provide the needed perspective for a proper interpretation of test performance. Misconceptions about the nature and purpose of tests and misinterpretations of test results underlie Illany of the popular criticisms of psychological tests. In part, these difficulties arise from inadequate communication between· psychometricians and their various publicseducators, parents, legislators, job' applicants, and so forth. Probably th~ most common examples center on unfounded inferences kdfrtIQs. Not alT IU1sconcephons· about tests, howcyer, can bc attrib_R!;~ to inadequate communication between psychologists and laymeD.)~'c.:hological testing itself has tended to become dissociated from~;.the· mainstream of behavioral science (Anastasi, 1967). The growing.Fdrnplexity of the science of psychology has inevitably becn accompani~,dby increasingspecialization among psychologists. In this process, psychometricians have concentrated more and more on the technical refinements of test construction and have tended to lose conta:tt wit'rr developments in other relevant specialties, such as learning, child development, individual diffe;ences, and behavior genetics. Thus, the technical aspects of test construction have tended to outstrip the psychological sophistication with which test results are interpreted. Test scores can be properly interpreted only in the light of all available knowledge regarding the behavior that the tests are designed to measure. Who is a qualified psychologist? Obviously, with the diversification of the field and the consequent specialization of training, no psychologist is equally qualified in all areas. In recognition of this fact, the Ethical Standards specify: "The psychologist recognizes the boundaries of his competence and the limitations of his techniques and does not offer
Social alief Etllicalll1lplications
of Testing
47
selyices or use techniques that fail to meet profeSSional standards established in particular fields" (Appendix A, Principle 2c). A useful distinction is that between a psychologist working in an institutional setting, such as a school system, university, clinic, or government agency, and one ractitioner engaged in independent practice. B~cause the in de endent is less subject to judC1ment and eva ua on l' wle eable collen es t lan lS 1e lIlS Itntional s choloC1ist he needs to meet hi her standards ? - pro esslOna qualifications. The same would be true of a psychologist responSIble for the supervision of other i·nstitntional psychologists or one who serves as an expert consultant to institutional personnel. A Significant step, both in upgrading professional standards and in helping the public to identify qualified psychologists, was the enactment of state licensing and certification laws for psychologists. Nearly all states now have such laws. Although the terms '1icensing" and "certification" are often used interchangeably, in psychology certification typically refers to legal protection of the title "psychologist," whereas licensing controls the practice of psychology. Licensing laws thus need to include a definition of the practice of psychology. In either type of law, the requirements are generally a PhO in psychology, a specified amount of snpervised experience, and satisfactory performance on a qualifying examination. Violations of the APA ethics code constitute grounds for revoking a celtiRcate or license. Although most states began with the simpler certification laws, there has been continuing movement toward licensing. At a more advanced level, speCialty certification within psychology is provided by the American Board of Professional Psychology (ABPP). ReeJuiring a high level of training and experience within deSignated specialties, ABPP grants diplomas in such areas as clinical, counseling, industrial and organizational, and school psychology. The Biographical Director~' of the APA contains a list of current diplomates in each specialty, which can also be obtained directly from ABPP. The principal f~nction of ABPP is to provide information regarding qualified psychologIsts. As a privately constituted board within the profession, ABPP does ~)()thave the enforcement authority available to the agencies administermg toe state licensing and certification laws.
.The. p~rchase of tests is generally restricted to persoJl~ ,who meet certam z:nlmmal qualifications. The catalogues of major testp~1>lishers specify reqUlr~ments that must be met by purchasers, Usually ~pdividuals with a mast~r s degree in psychology or its equivalent qu~l.i~~' -SO'rtle publishers claSSIfytheir tests into levels with reference to user qt;al~fi~~ions, ranging from educational achievement and vocational proficiency tests, through
'Context of Psychological Testing , , 'entories to such clinical instrultelligence tests and mterest In\ t 'ersonalit tests, Distincs individual intelligence tests al ldmOhsPers alld a~thorized instid' 'idua 1 [lUre as e' alsohma db'e ofetween In ,1\ t . Graduate students who may appropnate tes s, , h Pure asers " must have t e . , f I ignment or for research , . articular test or ~ c ass a~s h "ehology instructor, who as" order countersigned by t elf ps~ , 'b'l' f' th oller use of the test. , f h a dual objective: secunty sponsl 1 Ity 01 e'pr, to restrict the distn~uboll o· ~ests ;~: Ethical Standards state: ' .1 d prevenhon of mIsuse, 1 , t atena san ' , I' 't d to persons \\1,'th professional mteres s to such deVices IS ImI e , , 1 13)' "Test scores like test ' d h' "( Pnnclp e, , ~ll safeguar t elr use who arc ualifled to interpret and q als, are rele::sed ~nl~ to perso~:sshould be noted that although test m properly (Prmciple 14)" I t these obJ'cctives, the conk ' , efforts to Imp emen 'b'l' utors ma 'e SllleCIe , '1 limited, The major responsl 1 Ity Yare able to exert IS neeessan y h ' d' 'dual uscr or institution f 'd in t e 111 IVi proper use 0 tests resl es h t MA degree in psychology ~ed,It is evident, ~or exampleA~;p a~i 'lorna-do not necessarily P articular test or that his en a PhD, state hc~nse, a~ld a ' hat the indi\'idualls quah~ed ~o u;e ti ;: of the results obtained is relevant to the proper mtel pre a 0 at test. 'bilihr concern.s the Il1arketing of psvcho, . . l' er professIOna lcsponsl '} h Id - t be released preI d blishers Tests s Oll no , I' be made regardincr the tests by aut lOrs an pu ' ' 1 N" h Id anv c aUllS b V for
Social alld Ethical Implicatiolls of Tes/ing
either naIve credulity or indiscriminate lic toward aU psychological testing,
49
resistance on the part of the pub-
Another unprofessional practice is testing by mail, An individual's performance on eithel' aptitude or personalit~· tests cannot be properly assessed by mailing test forms to him nnd lla\'ing him return them by mail for scoring and interpretation, Not only does this procedure provide no control of testing conditions but usually it nlso involves tIle interpretation of test scores in the absence of other pertinent information about the individual. Under these conditions, test results may be Worse than useless,
A question arising particularly in connection with personality tests is that of invasion of privacy, Insofar as some tests of emotional, motivational, or attitudinal traits are necessarily disguised, the subject may reveal characteristics in the COurse of such a test without realiZing that he is so dOing, Although there are few available tests whose appr~1ts subtle enough to fall into this category, the possibility of developing s'i1~1.r indirect testing procedures i~~ a grave responsibility on the pi. choIogist who uses them. F~~se61 ijf'te§..ting cliee:tii\'ene~,~. De,.. necessary to keep the examinee"in'1gnQ.f~~ the speCific ~.):h his l'esponses on any Oue test are to be int~fpreted, Xe\'er~~ •.a.1Jt'r_ son should not be subjected to any testing program under false pretenses, Of primary importance in this connection is the obligation to have a dear understanding with the examinee regarding the use that will be made of llis test results, The- Jellowing statement contained in Ethical Standards of Psychologists (Principle 7d) is especially germane to this problem: The psychologist who asks that an individual reveal personal information in the COurseof interviewing, testing, or evaluation, or who allows such infonnation to be divulged to him, does s9 only after making certain that the r:esponsible person is fully aware oflhe purposes of the intervjew, testing, or evaluation and of the ways in which the information may be used, Although concerns about the invasion of privacy have .been expressed most commonly about perspnalit)' tests, they logi<:ally apply to any type of test. Certainly any itlteJligence, aptitude, or achievement test may reveal limitations in skills and knowledge that an individual would rather 1Totdisclose. Moreover, any observation of an individual's behavi@r-'tt'~ in an interview, casual conversation, or, other personal '~llcoul1ter-m:lM' yield information about him that he wouldpr~fer to c.qnCe.E.l1 and that I¢ may reveal unWittingly. The fact that psycI11;)Jogicaltests have often been.
Il/('xl (If Psychological Testing
lit in discussions of the invasion of privacy probably reflects . misconceptions about tests. If all tests were recognized as .of behavior samples, with 110 mysterious powers to penetrate havior,popular fears and suspicion would be lessened. 'Id also bc noted that all behavior research, whether employing het-observational procedures, presents the possibility of invasion '. Yet,as scientists, psychologists are committed to the goal of g,.knowledge about human behavior. Principle 1a in Ethical s of Psychologists (Appendix A) clearly spells out the psycholoViction"that socieh' v.·ill be best served when he investigates judgment indicate~ investigation is needed." Several other printhe other hand, are concerned with the protection of privacy 'the{velfare of research subjects (see, e.g., 7d, 8a, 16). Conflicts may thus arise, which must be resolved in individual cases. amplesof such confl.ict resolutions can be found in the previously ical Principles in the Conduct of Research tcit11 Human Pars (1973). problem is obviously not simple; and it has been the subject of "e delibemtion by psychologists and other professionals. In a retitled Privacy and Be7IGvioral Research (1967), prepared for the f Science and Technology, the right to privacy is defined as "the the individual to decide for himself how much he will share with histhoughts, his feelings, and the facts of his personal life" (p. 2). fllrthercharacterized as "a right that is essential to insure dignity reedomof sf>lf.determination"-(p. 2). To safeguard personal prijno universal rules can be formulated; only general guidelines £illl rovided.In the application of these guidelines to specific cases, th~~~ substitute for the ethical awareness and professional respons~i{9 Ie individual psychologist. Solutions must be worked out in ter~ p£ :particularcircumstances. :'nerelevant factor is the purpose for which the testing is conducted'ther for individual counseling, institutional decisions regarding~~lecand classification, or research. In clinical or counseling sit1,j.tions, the _ t is usually willing to reveal himself in order to obtain h~]p with his ,oblems.The clinician or examiner does not invade privacy'where he is eelyadmitted. Even under these conditions, however, the client should tie warned that in the course of the testing or interviewing he may reveal :informationabout himself without realizing that he is so doing; or he Irony disclose feelings of which he himself is unawar - When tes ng IS con uded for institutional purposes, the lfiaffiinee Isbouldbe fully informed as to the use that will be made of his test scores. , It is also desirable, however, to explain to the examinee that correct assessment will benefit him, since it is not to his advantage to be placed
in a position where he will fail or which he will find uncongenial. The results of tests administered in a clinical or counseling situation, of course, should not be made available for instihltional purposes, unless the examinee gives his consent. When tests are given for research purposes, anonymity should be preserved as fully as possible and the procedures for ensuring such anonymity should be explained in advance to the subjects. Anonymity does not, however, solve the problem of protecting privacy in all research contexts. Some subjects may resent the disclosure of facts they consider personal, even when complete confidentiality of responses is assmed. In most cases, however, cooperation of subjects may be elicited if they are convinced that the information is needed for the research in question and if they _ have sufficient confidence in the integrity and competence of the investigator. All research OIl human behavior, whether or not it utilizes tests, may present conflicts of values. Freedom of inquiry, which is essential to the progress of science, must be balanced against the protection of the individual. The investigator must be alert to the values involved and must carefully weigh alternative solutions (see Ethical Principles, 1973; Privacy and Be1lGvioral Researc11, 1967; Ruebhausen & Brim, 1966). Whatever the purposes of testin tlle rotection f riva two Key concepts: re evanc consent. The information that t e m iVl ua is asked to reveal must be relevant to the stated purposes of the testing. An important implication of this principle is that an practicable effOlts should be made to ascertain the validity of tests for the particular diagnostic or predictive purpose for which they are used. An instrument that is demonstrably valid for a given purpose is one that provides relevant information. It also behooves the examiner to make sure that test scores are correctly interpreted. An individual is less likely to feel that his privacy is being ~aded by a test assessing his readiness for a particular educational progrlfm than by a test allegedly measuring his "innate intelligence." The concept.,£.f informed consellt also requires clarification; and its application in individual cases mav call for the exercise of considerable judgment (Ethical Principles, 1973;,Ruebhausen & Brim, 1966). The examinee should certainly be infoJ'l!le~.about the purpose of testing, the kinds of data sought, and the use tha1;:wifi be made of his scores. It is not implied, however, tliat he be shown the test items in advance or told how specific responses will be scored. Nor should the test items be shown to a parent, in the case of a minor. Suc~ infonnation would usually invalidate the test. Not only would the giving of this information seriously impair the usefuhless of an ability test, boutit would alsotcm.d Jo distort responses on many personality tests. For ~xaQJple, if an indi®~,~l is told in advance that a self-report inventory-will be scored v.ith adorpinance
Social and Ethical Implications
of Psychological T('sting . fl d by stereotyped (and often ,p'J)se~are likely to bbeIn thu~n:ait or by a false or distorted , as'he may have a ou t IS .
.
'th regard to pae the Russell
ng of children, special qU,es~ons anse "':1
tfite COeelle~~i~~: ~~:(i~;~~~U~~iS~~:~r:i:;:~;n~;:;d~di::I7:rc , . ' f P '1 Recor s. 11 re ereo ,.and DissenunatlOl1 0 tip' . d' "d al consent, nt, the Gujdelines differentiate b;tween l~t:~~o:al consent, 'hild, his'tiparents, or both, an . ~r~~e resentatives, such 'arents: legally elected ~r .appoll1t~. . p the Guidelines board. 'While avoiding rigId preSC;lpti~n:h type of instru, and achie",~mcnt tests as examp es °b em' t, at the " , I nt should e su Cleo, ,!lich representation a conse .. . " ", t' cite . 11 I , e, personality ~ss~ssm~~i~:lilles is the inclusion of sample helpfu eature. o. ~ e~~ tten consent. There is also a selected .forms,for obtammo ' 1 t of school record keeping, , on the ethical and ~ega alsPdec~ that protect the indid 'penmenta eSlgns rocedur~~ a~o pe:rucipate and that adequately safeguard his t ,to eCme. . f 1 data resent a challenge 'tP d the establishHevielding scientifically meanmg u , '. . W'th oper rappor an h b of refusals to c,hologist's ipgenUlty.. 1 pr , 1 t however t e num er titudes of mutua' respec, . 'bl ' tity The technical difmay be reduced to a neghgl e quan ' h'; b avoided. ,bi;sed sampling and voluntee~ error, may : USe;t; tllat this gg rom both national and stateWide .SUlvley~'t: ,·, nd in the , h . f g educatlona ,ou comes a rch (Holi:zn~~n, 1971; Womer, be achieved, bot III t':s III '~itiv~area of pers~~allty ;~:~ath(' number of respondents 'who ,',' "on of privacy or ere Is-also some eVI ence . . t enresents an mvaSI . a personahty llwen ory r 1" .'. 'S" nt'ly reduced when 15 slgm ca ' ff nsive ''der some of th e.ltems 0 e " : ex lanation of h.Q.YLitemL :preceded by a Simple. and ~orthrJ ~:d..(Fink & Butcher, 1972). ted and I 0\ ores WI I be mterpre_ , .1:'~,' h ,lid' 't hould be' adde~~~"t sue an the personality standpoint of test va Ity, 1 Sf'" 'on did not affect the mean profile 0 scores on - , '
a
IDENTIALITY ,
. . which it is related, the problem of t,~e~rotectlOn ~f p~lVacYiftf:ceted. The fundamental question is: tiahty of test ata ISmu {ts? Several considerations influence the all hav~ access. to t~t resAmu ~ng them are the security of test conin particular situations.
53
of Testing
tent, the hazards of misunderstanding test scores, and the need of various persons to know the results. There has been a growing awareness of the right of the individual himself to have access to the findings in his test re ort. He should also lave e opportum to comment on e contents of the report and if necessary to clarify or correct factual information. Counselors are now trying more and more to involve the client as an active participant in his O\\'n assessment. For these purposes, test results should be presented in a form that is readily understandable, free from technical jargon or labels, and oriented toward the immediate objective of the testing. Proper safeguards must be observed against misuse and misinterpretation of test findings (see Ethical Standards. Principle 14). -In the case 'of minors, one must also consider the parents' right of access to the child's test record. This presents a possible conflict with the child's own right to privacy, especially in the case of older children. In a searching analysis of the problem, Ruebhausen and Brim (1966, pp. 4314,32) wrote: uShould not a child, even before the age of full legal responsibility, be accorded the dignity of a private personality? Considerations of healthy personal growth, buttressed with reasons of ethics, seem to command that this be done." The previously mentioned Guidelines (Russell Sage Foundation, 1970, p. 27) recommend that uwhen a student reaches the age of eighteen and no longer is attending high school, or is married (whether age eighteen or not)," he should have the right to deny parental access to his records, However, this recommendation is followed by the caution that school authorities check local state laws for possible legal difficulties in implementing such a policy. Apart from these- possjble exceptjons, the question is not whether to commUDlcute test results to arents of a minor but how to do so. Parents 1 norma y have a legal right to information- a out eir child; and it is usually desirable for them to have such information. In some cases, moreover, a child's academic or emotional difficulties may arise in part from parent-child relations. Under these conditions, the counselor's contact WIth die parents IS of prime importance, both to fill in background data and to elicit parental coope.ration. of test records have usuall~ dealt Discussions of ~he ~n6dentiality with accessibility to a thIrd person, other than the in~hjdilal tese~d (or parent of a minor) and the examiner (Ethical Stando,r.ds, Principle 6; Russell Sage Foundation, 1970). The underlying principle is that such records should not be released without the knowl~~~. an..d. conseiitOf • the individual.' ., 'Vhen tests are administered in an institutional context, as in a school system, court, or employment setting, the indi~dual should be .infonne~ at the time of testing regarding the purpose 6f~!he test, how th~ results
-
_._~--_._ _.-._--
...•..
-- ..
~,:~'
Social alld Ethical Implications
'ntext of psychological
Testing
55
the c:lpacity to record faithfully, to maintain permanently, to retrieve promptly, and to communicate both Widely and instantly.
'd
nd their availabilih' to institutional personnel who h~v~ a ISC ,ad f th UncJ:e,r'these conditions, nO further penms~lOn e nee or em. . hi 'h' t1 institutiOn, .ti results are made avalla e Wit III Ie e d at tlIe me 1 r uested by outsiders, 'nt situation exists when test resu ts are eq t It from " 'm lover or a college requests tes resu s "~.R:::~~t~~:s: i~st~nc~s, ind~v~d~l~~e~o;:~:~t~o:;:~~:~e~;dt~: urposes. The previously equired, T~e same r~qUlre%~,nres:~ch and coullsehng contexts, or d' 1971 P 42) contain a sample uidelines (Russell Sage Folun :tlOn"n de~ri~lg the transmission, of iformfor the use of schoo sys ems I , ta. , f . d'n institutions. On er pr,oblem pertains to the l'ete~tlO~l? recor s I vcr' valuable, be ,hand, longi1tudinal rec~r~s a~:o l:~~I~::~~:t~~~ing ani'counseling y for researc I purposes u . advanta es resuppose proper son. As is so often the cas~, th;se t1 othe; haKd the availability . interpretation •.of test resu ts, n m::uses as inl~rrect inferences rleords opens t~e way f~~ s~ch for otber than the original 'solete data atld.~unauthollze 1 acbcessd for example to cite an IQ , , b anifest v a sur , .gpurpose, I ~ wou Id em: d b a child in the third grade reading achle\'t>ment sco~e, obtalOe II Ye Too much may have hapn evaluating him for admISSion to co eg 'k h ·1' and ""'lated , I" 'ears to ma e suc eaI' ,.,.. d to llim in t Ie mtervemng ) d etained fo'l"many , f I S' '1 Iv when recor s are r Iml ar .' b ed for purposes that the individscores meaning u. rs,t11ereis dan!!:er that tbey ma): edu~nd would not have approved. (or his parents) never suspecte 'd t' d either for le, when recor s are re ame , f h 'd'" d al or for aca I1revent suc I1 mIsuses, , " I 'the interest 0 t e m 1'111 u late longltudma use m them should be subject to unusual¥i table research purPloseCs,a,cdcej:setso (Russell Sal1e foundation, 1970:W' , t troIs In t Ie w e In I:> d t ngen can . d 1 . 'fi d into three categories-with regar· 0 t2), sch~ol recol' s. are c aSSli~in factor in this classification is the 'I" retenti~n, ~. major det~~~ilih~ of the data; anot\l.er is rdevance to ree of objectIVity and ven a 'J 1 I Id be ..s-e for any type of . 1 b' ti f the schoo. t wou ,,"", . e educationa 0 Jec ves ,0 '1 . l' 't policies regardit.g the destruc.stitution to fonnulate SHm ar exp lCl d' . . . 'b'1't f personal recor s. :t!on, retention, and acceSSI I I Y a 't nd accessibility of test results '", The' pro bl ems 0f mam, . tenance secun y, a . 'fi d bv the develop-
of TCStillg
i
.~and uf all other ~ersonal da~:n~avlen b~~; ;:~~e eta the Guidelines . inent of computenzed, aata . 5-6) Ruebhausen wrote; , , (Russell Sage Foundation, 1970, pp, . d a new dimension into the issues of pnvacy. h tr t allies of privacy were the inModernscience has mtl'Oduce ' 1e among t e s ongcs , . d the healing compaSSion Therewas a t Ime W 1 n , h f II'b'n" f hiS memorv an efficiencyof man, tea 1 1 I • ,0 f' t' 'd' the warmth of human reeol, d b th the passmg 0 tme an ' lhatat'compame,. 0 ,'." .., ""II" ,_,,"'.\fnrlrrn sciellcehas !!ivenus
The unprecedented advances in storing, processing, and retrieving data made possible by computers can be of inestimable service both in research and in the more immediate handling of social problems, The potential dangel"s of invasion of privacy and violation of con~dentiality need to be faced squarely, constructively, and imaginatively, Rather than fearing the centralization and efficiency of complex computer systems, we should explore the possibility that these very characteristics may permit more effecth'e procedures for protecting the security of individual records. An example of what can be accomplished with adequate facilities is provided by the Link system de\'eloped by the American Council of Education (Astin & Boruch, 1970), In a longitudinal research program on the effects of different types of college environments, questionnaires were administered annually to several hundred thousand college freshmen, To permit the collection of follow-up data on the same persons while preventing the identiflcation of individual responses by anyone at any future time, a three-file system of computer tapes was devised, The first tape, containing each student's responses marked with an arbitrary identincation number, is readily accessible for research purposes. The second tape, containing only the students' names and addresses with the same identification numbers, was originally housed in a locked vault and used only to print labels for follow-up mailings. After the preparation of these tapes, the original questionnaires were destroyed. This two-file system repl'esents the traditional security system. It still did not provide complete protection, since some staff members would have access to both files. ~'Ioreover, such files a-re subject to judicial and legislative subpoena. For these reasons, a third me was prepared. Known as the Link file, it contained only the original identification numbers and a neW set of random numbers which were substituted for the original identification ~umbers in the name and address file. The Link file was dcposited at a computer facilit), in a foreign country, with the agreement that the file would never bC;le)eased to anyone, inclu~jpg the American Council on Education. Follow-u.p data t~p!s are sent tq the f{)reign facility, which substitutes one set of code numbers f~the other. With the .decoding files and the research data files under: the control of different organizations, no one can identify {he responses of illdividuals ~ the data files. Such elaborate precautions roi'the protection of conlidentiality obviously would not be feasible except in a!aJge-scale computerized data bank. The procedure could be simplified sQmewhat if the lin\ing faCility'· were located in a domestic agency given,:adequate protection against subpoena.
Social and "Etl1icalIIll1"ications of Testing
i$tshave given much thought to the comm~nication of test "formthat will be meaningful and useful. It IS clear that the should not be transmitted routinely, but should be accomnterpretive explanations by a professionally trained person. imicating scores to parents. for example, a recommended to arrange a group meeting at which a counselor or school '\explains the purpose and nature of the tests, the sort of th'tt"t mav reasonably be drawn from the results, and the of the d~ta. Written'reports about their own children may ributed to the parents, and arrangements made for personal ';vithany parents wishing to discuss the ~epol'ts further .. ~ehow they afe transmitted, however, an Important condItIon resu1tsshould be prcsented in terms of descriptive performrather than isolated numerical scores. This is especiall}' tnu::.. nee test· which are more likely to be misinter reted than are 't tes ,ll1icatingresults to teachers, school administrators, emplo'yers, approprig.te persons, similar safeguard~ shoul~ b~ proVided. Is of performance and qualitati\·e descnptot~ns 111 Sllnple terms preferred over specific numerical. scores, cxc,:pt when comg with adequately trained professlOnals .. Ev~n well-educated ye been known to confuse percentiles WIth Q~~centa~e scor~s, with lQ's, norms with standards, and int~Fts~ ratlOgs With 'ores.But a.more serious misinte )fetation )ertams to the conrawn from test SCOl'es,even w en their te.c:nnical meaning is that mderstood. A familiar example is the popuhyassumption !cates a fixed characteristic of the individual wl)ich pTedeis lifetime level of intellectual achievemen~. , ,litcommunication it is desirable to take .i.W:oaccount the char- . of the person who is to receive the i~fomlation. This. applies o at person's general educatIOn 1~:imowledge about psynd testing. but also to his anticipated eIllotional response to the on. In the case of a parent or teacher, for. example, personal I' involvement with the child may interfere with a calm and 'cceptance of factual information. . . ut by no means least is the problem of commumcatlOg test re';e individual himself, whether child or adult. The same gene.ral .'s against misinterpretation apply here as in ~mmuni~tm~ ird party. The person's emotional reaction to the mforrnatlOn lS ly important. of course, when he is learnin? about hfs 0'1\'11 assets .,... :.. ~.. 'H1".~ ,,,, ;nr1;vir'll1:1l is !!iven hiS own test results, not I
57
onl~. s~ould the data be interpreted by a properly qualified person, but faclli~Ies shoul.d also be available for counseling anyone who may become cmOti01~any dIsturbed by such information. For example, a college student mIght become seriously' discouraged when he leams of his poor performance on a scholastic aptitude test. A gifted schoolchild might develop habits of laziness and shiftlessness, or he might become uncooperahve a~ld unm.anageable, if he discovers that he is much brighter than any of Ius asso.clates. A severe personality disorder may be precipitated when a ~aladlust('d individual is given his score on a personality test. Such de~nmental effects may, of course, occur regardless of the correctness or lllcorrectness of the score itself. Even when a test has been accurately administer:d and scored and properly interpreted, a knowledge of such a score WIthout the opportunity to discuss it further ~nay be harmful to the individual. Counseling psychologists h~e been especially concerned with the dev~lo ment of effective wavs of transmittin test inform' to-their-_ c IC11t5 see, e.g., Goldman, 1971. Ch. 14-16). Although the details of ..-tfu~ pr.ocess ~re be}'o~d the, scope of ?~present discussion, two major gll1del~nes are of particular mterest. FI~ test-reporting is to be \'iewed~ as an mtegral part of the counselin rocess and incor orated into the o a counse or-c lent relationshi . Se d, insofar as ossible, test results shou e reported as answers to specific !:lucstions raised bv the CQun~. An Important consideration in counseling relates to the' counselee's ~cceptance o~ the information presented to him. The counseling situation IS such thaf If the individual rejects any information, for whatever reasons, then that information is likely to be totally wasted.
T~ SETfINC. ~he decades since 1950 have witnessed an increasing publIc concern With the rights of minorities,' a concern that is reflected in the enactment of civil rights legislation at both federal and state levels. In conn~t~on with mechanisms for improving educational and vocational opportumhes ~f such groups, psychological testing has been a major focus of att:nbon. Th~ psychological literature of the 1960s and early 197?s co~tams many dI~cussions of the topic, whose impact ran.ges from clanflcabo~ ~o obfuscation. Among the more clarifying contributions are several po.slbon papers by professional associ,tit>ns (see, e.g., American Psychological Association, 1969; Cleary, Humphreys, Kendrick, & \Ves-
Ie tlthou~h ~omen repre)'lnt a statistical majorltyjn the nati~~al population. ga I.y,~c~upalJonallY'in in otlu~r ways.they have s~ed Jllany of the problems the term "minority" is use(i "fu tnis section it will be of mmoTlhes. Hence w understood to includj) men. ' I
I
I II
1
II
Social and Etllicallmplications . 'onlcxt
of Ps!}clIOlogica1Testing
Tl::
'5' Deutsch Fishman, Kogan, North, & Whiteman, 1964; '1Jl~use of t~sts 1972). A brief but cogent paper b~ F~augh
Iso helps to cle~r away some preval~nt S~ll;C~So~;:; ~~I~~~ural 'of the concern centers on the lowenng 0 es sc . d . t reoE ns that ma)' have affected the devel~p;ne~t lofc~;:~~e:;;ti: otivation, attitudes, and other psyc ~ O~IC: for the problem ou members. Some of the propose so u Ions . al mi~nlrstandings about tIle nature anddfllnfction of ps~chdol'Vll?j~~ls . . I b kgroun s 0 groups or 10 iflerencesin the expenentia ac hI' 1 test ~itably manifested in test performanlce. Ev:rytPsbychaoVl~o~C~ts in. 1 I f as Cll ture alIec s e , res a beh:wlOl' samp e. nso ar If 1 ut aU cultural will and should be detected by tests. .we ~ e. 0 as a measure I1tialsHom a test, we may th.ereb Ylower Its ;ah~?t case the test behavior domain it was deslgnc d to assess. n 'fail to provide the kind of information needed to correct the very 'ionsthat impaired performance. . 1 citron the ause the testing of minorities repr~sent\a sP:~~~l ~~; :heoretical .er problem of cross-cultural te.stmg, t e U full) in Cha ter 12. naleand testh~g procedures ar: ~1~~~:~e~i:'?7s giv:n in Ch~pter 7, t h ter our interest is chnicalanalysIs of the concep 0 h In t e presen c ap , , .h l'd't llnnectlOl1Wit test va I I y. ., ., f inDrity groUp wily in the basic issues and SOCialImplications 0 m
·ng.
~~d
FACTORS. In testing culturally di"h·elt·seffPerst °bno~h i:e~~ . . b cultural factors t a a ec rtant to differentiate etween . t . t d to the test It is . I' d th hDse in uence is res nc e ·terionbe laVlor an ose w d ~ Ex~mples of such atter, tSst-related actors that. re l\~e va 1 .; ion to erEorm variable; ,~_ to~sinclude previous experience m ~akmg tests, mo~;t. r ~veJlon tests, rappDrt with the exammer, an~ an y 0 tet ~_-i
,
toreduce
.~:e~c:;
~prl;;e~st~t~e:~ also~n~~e:~:s:e;: :~~~e;e~7c ~:::o::~, ~:: unrelated to cntenon per£orm~n tu' of obl'ects unfamiliar in a particular -ample the use of names or piC res . d h di ex l' T ld obviously represent a test-restncte an cap. cultura mlleu wou h' k' d not depend upon fami!. Ability to carry out. quantitative t m mg oes
of Testing
59
iarity with such objects. On the other hand, if the development of arithmetic ability itself is more strongly fostered in one culture than in another, scores on an arithmetic test should not eliminate or conceal such a difference. Another, more subtle way in which specific test content may spuriously affect performance is through the examinee's emotional and attitudinal responses. Stories or pictures portraying typical suburban middle-class family scenes, for example, may alienate a child reared in a low-income inner-city home. Exclusive representation of the physical features of a single racial type in test illustrations may have a similar effect on members of an ethnic minority. In the same vein, women's organizatiDlls have objected to the perpetuation of sex stereotypes in test content, as in the portrayal of male doctors or executives and female nurses or secretaries. Certain words, too, may have acquired connotations that are offensive to minority groups. As one test publisher aptly expressed it, "Until fairly recently, most standardized tests were constructed by white middle-class people, who sometimes clumsily violate the feelings of the test-taker without even knDwing it. In a way, one cDuld say that we have been not so mueh culture biased as we-have been 'culture blind'" (Fitzgibbon, 1972, pp. 2--3). The major test publishers now make special efforts to weed out inappropriate test cDntent. Their Dwn test construction staffs have becDme sensitized to pDtentially offensive, culturally restricted, or stereotyped material. Members of different ethnic groups participate either as regular staff members or as consultants. And the reviewing of test content with reference to possible minority implications is a regular step in the process of test construction. An example Df the application Df these procedures in item construction and revision is provided by the 1970 edition of the Metropolitan Achievement Tests (Fitzgibbon, 1972; HarcDurt Brace Jovanovich,1972).
INTERPRETATION AND USE OF TEST SCORES. By far the most important coflsiderations in the testing of culturally diverse groups-as in all testing -,;..,pertain to the interpretation of test scores. The most frequent misgivings regarding the use Df tests with minority group m~w:bers ste~ from misinterpretations of scores. If a minority examinee Qn~l:li~sa low score on an aptitude test or a deviant score on a personality):est, it is essential tQ.investigate why he did so. FDr example, an infel~i'St:ore on an arithmetic test could result from low test-taking motivation, poor reading ability, or inadequate knowledge of arithmetic, among other reasons. Some thought should also be given to the type of nQCWsto be employed in evaluating individual scores. Depending on the purpose of the testing, the appropriate norms may be general nDrms~.!2gl;oUP.Jlotms based Qn
-
.
.
Social alld Et!lical171lplicatiolls of Testing
61
an IQ would thus serve to perpetuate their handicap. It is largely because implications of permanent status have become attached tq.Jhe IQ that in 1964 the use of group intelligenGe-testS-..M:asdiscontinued in the l\ew York City public schools (H. B. Cilbeli, 1966; Loretan, 1966). That it proved necessary to discard the tests in order to eliminate the misconceptions, about the fixity of the IQ is a revealing commentary on the tenacity of the misconceptions. It should also be noted that the use of individual intelligence tests like the Stanford-Binet, which are administered and interpreted by trained examiners and school psychologists, was not eliminated. It was the mass testing and routine use of IQs by relatively unsophisticated persons that was considered hazardous. According to a popular misconception, the IQ is an index of innate intellectual potential and represents a fixed property of the organism. As will be seen in Chapter 12, this view is neither theoretically defensible nor supported by empirical data. \Vhen properly intcrrireted, intelligence test scores should not foster a l'igid categorizing ~f persons. On the conhary, intelligence tests-and any other test-may be regarded as a map on which the individual's present position can be located. When combined with information about his experiential background, test scores should facilitate effective planning for the optimal development of the individual.
OBJECTIVITY OF TESTS. "'hen social stereot:'pes and prejudice may distort interpersonal evaluations, tests provide a safeguard against favoritism and arbitrary or capricious decisions. Commenting on the use of tests in schools, Gardner (1961, pp. 4&-49) wrote: "The tests couldn't see whether the youngster was in rags or in tweeds, and they couldn't hean the accents of the slum. The tests revealed intellectual gifts at every level of the population." In the same vein, the Guidelines for Testitlg Minority Group Children (Deutsch et at, 1964, p. 139) contain the follOWingobservation:
Many bright, non-conforming pupils, with backgrounds different from those of their teachers, make favorable showings on achievement tests, in contrast to their low classroom marks. These are very often chffaren whose cultural handicaps are most evident in their overt social and interpersonal behavior. Without the intervention of standardized tests, many such children would he stigmatized by the adverse subjective ratings of teachers who tend to reward can· formist behavior of middle-class character. \Vith regard to personnel selection, the contr!!>ution:,of t~sts was aptly characterized in the following words by John Macy, Jr.,'Chairman of and Public Policy, the United States Civil Service Commission (7.f~~!f,rg 1965, p. 883) :""'.
,¥:,
Social and Etlticallmplications ntcxt of Psychological Testing " ., f pIc that are related to job perh' h' the basis for entrv sityto measure charactenS!lCS 0 peo , is at the very root of the merit system, ~v~u:s over the veal'S, th~ ~areerservices of ~hel~ederalt ~o\t'he:::l~pmen't and application of .. .. h s had a vita mteres m d bt that the widesprea d pu bl'Ie eTVIcea gicaltesting methods. I ha\'~ ~o ou d res has in large part been " in the objectivity of ~ur 111 nn gp;~ce ~: the' practicality, and the "by the public's perception 0 f t he alrne., . -.'ofthe appraisal methods they must submit to. ". • 101 ee Selection Procedures, prepared by the :GUldeltnes on Emp y. ., (1970) as an aid in the ". I t 0 portumty CommiSSIOn mp oymen P b' 'th the following state'entation of the Civil Rights Act, rgm WI purpose:
I h belief that properly validated and elin,esin this part ar~ based o~ ~e: can significantly contribute to the fzedemployee selection proce u I I'CI'es as required bv Title ' ' . t personne po I ' , , entation of no~ d Iscnmma or; . llv developed tests, when used in (is also recogmzed that pro esslon~ ;~sessment and complemented by 'ction with other tools of perso~n~fi tl,'d in the development and " f ' b d' may sign! can 'Ii al d programs 0]0 eSlgn, d . deed aid in the utilization an tenanceof an efficient work force an , In , servationof human resources generally, , b 'sused in testing culturally disadvantaged nsummar)' .'. tests can e ,Iml ' When properly used,'h owever, th e)' . ns-as 111 testmg aD.yon~ ese, ting irrelevant and unfair discrim, e an important fun~tlOn 111 pre~te~ive index of the extent of cultural . 'ti' The\' also prOVIde a quanti ~ .. lOaon, . d'al programs • nandicapas a necessar~' first step In reme 1<
be of states enacted legislation and estlt ••• Anum. r ., (FEPC) to implement i,t..:,. dF . E 10 ment Practices CommiSSions. -1'im\'!\. "e aIr mp y f h legal mechanisms at the federal l~;l~~' nor to the development 0 suc lIotts have been made to pat1iI0ngthe states that did so 7t~r, sfme;e\ The most pertinent federal tern th~ re?ulatio~s after the e u~tE:olo '~ent Opportunity Act (Title legislatIOnIS provld.ed by the ~q 1964 ~ ?ts subsequent amendments).> 'n of the Civil Rl?hts Act o. a~ ;nfottement is vested in the sponsibility for Implementation an ., (EEOC) When charges , 0 rtunity C ommlSSlon . qual Employment ppo. h plal'nt and if it finds the charges , " h EEOC' shgates t e com , -arefiled, t e lllve t th 'tuation through conferences and first to correc e Sl . '6 d'" to be lush e , u1.es d f '1 EEOC may proceed to r If these proce ures al, voluntary com~ lance. d d . t orders and finally bring action in hold hearings, ISsue cease an eSlS , AL REGULATIONS.
, e.
al developmentssince midcentury, including rt decisions, can be found in Fincher legislativeactions, executive orders, an cou .
1
'A brief summary of ~he major e~ d
(1973).
of Testing
63
the federal courts. In states having an approved FEPC, the Commission will defer to the local agency and will give its Bndings and conclusions "substantial weight." The Office of Federal Contract Compliance (OFCC) has the authority to monitor the use of tests for employment purposes by government contractors. Colleges and universities are among the institutions concerned with OFCC regulations, because of their many research and training grants from such federal sources as the Department of Health, Education, and Welfare. Both EEOC and OFCC have drawn up guidelines regarding employee testing and other selection procedures, which are virtulillly identical in substance. A copy of the EEOC Guidelines on Employee Selection Procedures is reproduced in Appendix B, together with a 1974 amendment of the OFCC guidelines clarifying acceptable procedures for reporting test validity,3 Some major provisions in the EEOC Guidelines should be noted, The Equal Employment Opportunity Act prohibits discrimination by employers, trade unions, or employment agencies on the basis of race, color, religion, sex, or national origin, It is recognized that properly conducted testing programs not only are acceptable under this Act but can also contribute to the "implementation of nondiscriminatory personnel policies." Moreover, the same regulations specified for tests are also applied to all other formal and informal selection procedures, such as educational or work-history requirements, interviews, and application forms (Sections 2 and 13), \Vhen the use of a test (or other selection procedure) results in a significantly higher rejection rate for minority candidates than for nonminority candidates, its utility must be justified by evidence of validity for the job in question. In defining acceptable procedures for establishing validity, the Guidelines make explicit reference to the Standards for Educational and Psychological Tests (1974) prepared by the American PsycholOgical Association. A major portion of the Guidelines covers minimum requirements for acceptable validation (Sections 5 to 9). The reader may find it profitable to review these requirements after reading the more detailed technical discussion of validity in Chapters 6 and 7 of this book. It will be seen that the requirements are generally in line with good psychometric practice. In the final section, dealing with affirmative action, the Guidelines point out that even when selection procedures have been satisfactorily 3 In 1973, in the interest of simplIficationand improved coordination,the preparation of a set of uniform guidelines was undertaken by the Equal Employment Opportunity Coordinating Council, consisting of representatives of E ,the U.S, Department of Justice, the u.s. Civil Service Commission,the U.S'c,rtlJlent of Labor, and the U.S. Commissionon Civil Rights. No'uniform versioD,o<... et. 1u!s yet been adopted. " '•.
Context
of Psychological
Testing
'ted, if disproportionate rejection rates result for minorities, steps e.takento reduce this discrepancy as much as possible. Affirmative '~impliesthat an organization does more than merely avoiding dis'. ry practicCli,.Psychologically, affirmative action programs may ded as eHorts to compensate for the residual effects of past social ~s.Such effects may include deficiencies in aptitudes, job skills, ~,motivation, and other job-related behavior. They may also be '~iniH~erson'sreluctance to apply for a job not traditionally open " ndidates, or in his inexperience in job-seeking procedures. ~mative actions in meeting these problems include remedia most likely to reach minorities;, explicitly enminority candidates to apply and following other recruiting esignedto counteract past stereotypes; and, when practicable, special training programs fOI the acquisition of prerequisite
knowledge.
PART
Primipus of Psychological listing
2
CHAPTER
4
NornlS a'nd the 11lterjJretation of Test Scores NTHE absence of additional interpretive data, a raw score on any psychological test is meaningless. To say that an individual has correctly solved 15 problems on an arithmetic reasoning test, or identified 34 words in a vocabulary test, or successfully assembled a mechanical object in 57 seconds conveys little or no information about his standing in any of these functions. Nor do the familiar percentage scores provide a satisfactory solution to the problem of interpreting test scores. A score of 65 percent correct on one vocabulary test, for' example, might be equivalent to 30 percent corred on another, and to 80 percent correct on a third. The difficulty level of the items making up each test will, of course, determine the meaning of the score. Like aU raw scores, percentage scores can he interpreted only in terms of a dearly defined and uniform frame of reference. Scores on psychological tests are mOst commonly interpreted by reference to norms which represent the test performance of the standardization sample. The norms are thus empirically established by determining what a representative group of persons actually do on the test. Any individual's raw score is then referred to the distribution of scores obtained by the standardization sample, to discover where he falls in that distribution. Does his score coincide with the average performance of the standardization group? Is he slightly below average? Or does he fall near the upper end of the distribution? In order to determine more precisely the individual's exact position with reference to the standardization sample, the raw score is converted into some relative measure. These derived scores are designed to serve a dual purpose. First, they indicate the individual's t~lativ.e standing in the normative sample and thus permit an evaluation of his'performance in reference to other persons. Second, they provide comparable measures that permit a direct comparison of the individual's performance on different tests. For example, if an individual has a raw score of 40 on a vocabulary test and a:raw score of 22 on an arithmetic reasoning test, we
I
67
il1lcsof Psychological
Tcstillg
'nownothing about his relative performance on the two tests. in vocabulary or in arithmetic, or equally good in both? Since '.9ndifferent tests are usually expressed in different units, a ,a)'isollof such scores is impossible, The difficulty level of the est would also affect such a comparison between raw scores. ,~s, on the other hand, can be expressed in the same units "to the same or to closely similar normative samples for . The individual's relath'e performance in many different ,thusbe compared. ariousways in which raw scores may be converted to fulfill p.vesstate'd above. Fundamentally, however, derived scores )0 one of two major ways: (1) developmental level atrelative position within a specified group. These types of ~r with some of their common variants, will be considered ::tions of this chapter. But first it ,vill be necessary to ex'elementary statistical concepts that underlie the develop'zation of norms. The following section is included simply .meaningof certain common statistical measures. Simplified .examples are given onl~; for this purpose and not to pro'~ statistical methods. For computational details and speto be ~llowed in the practical application of tl1ese techer is refeHed to any recent textbook on psychological or
s
atistics.
ject of statistical method is to organize and summarize )~ in order to facilitate their understanding. A list of 1,000 be an overwhelming sight. In that form, it conveys littlestep in bringing order into such a chaos of Iaw data is to es into a frequency distribution, as illustrated in Table l. 'on is prepared by grouping the scores into convenient d tallying each score in the appropriate interval. When .n entered, the tallies are counted to find the frequency, es, in each class im"erval. The sums of these frequencies 'e total number of cases in the group, Table 1 shows the ,~ollegestudents in a code-learning test in which one set ds, or nonsense syllables, was to be substituted for an, ~cores, giving number of correct syllables substituted Inute trial, ranged from 8 to 52. They have been grouped '1s of 4 points, from 52-55 at the top of the distribution Ie frequency column reveals that two persons scored
TABLE 1
Frequency Distribution of Scores of 1 000 C II Stud on a Code-Learning Test ' 0 ege ents (Data
-
from Anastasi,
1934, p. 34)
Class Interval 52-55 48-51 44-47 40-43 36-S9 32-35 28-31 24-27 20-23 16-19
12-15 8-11
Frequency 1
1
20 73 156 328 244 136 28 8 3 2
1,000 •. ~-:-na-=
fa
~~~ws:e~n~and 11, three b~tween 12 and 15, eight ,between 16 and 19, f The information provided b presented graphicallv in the f y af r~~ue~lcy. distribution can also be the data of Table 1 'l'n gra h,orm ° a lstnbubon curve. Figure 1 shows f on the b ase rme, or h'onzontal axis, p lC orm. are the scores grouped int I' frequencies, or number of o. c ass/1~ervals: .~n the vertical axis are the graph has been plotted I' teases a m gwlthm each class interval. The be' . n wo ways both fo In the histogram, the hei ht of the :x.l rms 109 m common use. terval corresponds to the g b umn erected over each class incan think of each individ n~mt erd~f persons scoring in that interval. We ua 1s an mg on another's shoulders to form the column In the fre is indi~ated by a ~o th~ number of persons in each interval across from the appro n~atacef m t e center of the class interval and , , ,p erequency The s c' . Jomed by straight I' . u ceSSlVe pomts are then meso ' Except for minor irregularities th di 'b . . resembles the bell-shaped normdl e stn ution por~ayed in Figure 1 ~erfect normal curve is reproduce;~:~i A mathem.atically dete~jned, lmportant mathematical TO erti ' , . gu:e 3, This type of curve has of statistical a~alyses FoP thP es and prOVIdesthe basis for many kinds . represent purpo h tures will be noted E ti n h se, owever, only a few feath " . ssen a y t e curve . d' number of ca 1 " m lcatesat'J4~ largest ses custer In the center of the range and thattlie nu;ri15er
q;~i:~YY~~'
Norms and tile Interpretation of Test Scores
71
Principles of Pbycl1010gical Testing
ps off gradually
in both directions as the extremes are approached. .curve is bilaterally symmetrical, with a single peak in the center. st distributions of human traj,ts, from height and weight to aptitudes personality characteristics, approximate the normal curve. In genI,the larger the group, the more closely will the distribution resemble theoretical normal curve.
340 320 300
280
-
Frequency polygon
---
Histogram
260 240 ~ 220
i3
200
'0180 •• 160 140 :l 120 100 80 60 40 20
i
~he most ~bvious and faniiliar way of reporting variability is in terms of e range etween the highest and lowest score The ran e h . cxtrem I d d . g, owever IS . . e y cru c an unstable, for it is determined by onl two scores' A smgle unu~ually high 01' low score would thus markedly Iffect its size' A . :ore precIse method of measuring variability is based on the d'ff etwee~ eac~ individual's score and the me;n of the ou 1 erence
r~
Table 2 in w~t:~ P01~t it will be helpful to look at the exam~Ie 10 c t ~ va~ous measures under consideration have been computed on str:~~~' alu~ a s~an group was chosen in order to simplify the demon• ,< tough 111 actual practice we would rarely perform these co T hI mputations on so fe' ' ard statistical sym~o~~~~t s~o~: ~ervetS adlsfotO introduce certain standf e no e or uture reference Original d . n . raw scores are conventionally designated by a capital X used to refer to deviations of each score from the ' an a sma x IS letter I means "sum of" It 'n b group mean. The Greek . th d f . Wi e seen that the first column in Table 2 ata or the computation 'f 0 mean and median. The mean is g lves , th e d" 40 , erne lan IS 405" fall'mg ml'd way b etween 40 and 41-five cases J
TABLE
2
~
Illustration of Central Tendency and Variabilit)· ••
""JI
fi!.=z:r--
Diff. Squared
--I
12- 16- 20-
15 19 23
24- 28- 32- 3627 31 35 39 scores
(:1:2 )
40- 44- 48- 5243 47 51 55
Flc.1. Distribution Curves: Frequenc\: polygon and Histogram.
50% of {:~
(Data from Table 1.)
cases
A group of scores can also be described in terms of some measure.:of central tendency. Such a measure provides a single, most typical or repJi~sentative score to characterize the performance of the entire grouf:- 'The most familiar of these measures is the average, more technically known as the mean (M). As is well known, this is found by adding all scores and dividing the sum by the number of cases (N). Another measure of central tendency is the mode, or most frequent score. In a frequency distribution, the mode is the midpoint of the class ihterval with the highest frequency. Thus, in Table 1, the mode falls midway between 32 and 35, being 33.5. It will be noted that this score corresponds to the highest point on the distribution curve in Figure 1. A third measure of central tendency is the median, or middlemost score when all scores have been arranged in order of size. The median is the point that bisects the distribution, half the cases falling above it and half below. Further description of a set of test scores is given by measures of varia, "', ..• 1. ~"'t "f ;..,rl;"i"'l1~ 1 flifkrences around the central tendency. r
~ •••
~~1 ~! J
___ ~X
9
+20
~~
Medi,n ~ 40.5 ~~:, ~
64 49
{E
=H
1 1
o -20
4
=~J
3_2
= 400
~
Ixl = 40
~X 400 M=N=1O=40 AD = }; ixj
. V anance = SD or u
=
_
40_
N - 10}~ 4 ~x' 244·
0"
~~2
= -N = -10 -- 24 .40
= v'24.40 = 4.9
:£x'
=
16 36 64 244
.,;Principles of Psychological Test ing 99.72'1
'eIcent) are above the median and five below. There is little point in a mode in such a small group, since the cases do not show c1eartering on anyone score. Technically, however, 41 would repremode, because t",o persons obtained this score, while all other ccur only once. and column sho\\'s how far each score deviates above or below of 40. The sum of these deviations will always equal zero, be.EOsitive and negative deviations around the m~an nec~ssarily. or cancel each other out ( + 20 - 20 0). If we Ignore slgns, of e Ci,\1l average the absolute deviations, thus obtaining a measure th'eaverage deviation (AD). The symbol Ix\ ill the AD formula that absolute values were summed, without regard to sign. Alf ~mne descriptive value, the AD is not suitable for use in furthema'tical analyses because of the arbitrary discarding of signs.
t
Lorge SD
---Small SD
Scores
Frequenc\'Distributions ...\'ith the Same Mean b~t Different Variahility. . h more serviceable measure of variability is the standard devw:mbolized by either SD or u), in which the negative signs are 'ely eliminated by squaring each deviation. This p~ has owed in the last column of Table 2. The sum of thiS column
:by the number
of cases
("iN
X2
)
68.26'1
1 I I I
I I
I I I
I I
=
--
95.44'1
I
I I I
-30' FIC.
-leT
Mean
+leT
+20'
3. Percentage Distribution of Cases in a NOlmal Curve.
diffe~ent tests in terms of norms, as will be shown in the section on stan~ard scores. The interpretation of the SD is especi~lly clear-cut when apphed to a normal or approximately normal distribution curve. In such a distribution, there is an exact relationship between the SD and the proportion of cases, as shown in Figure 3. On the baseline of this normal curvc have been marked distances representing one, two, and three standard deviations above and below the mean. For instance, in the example given in Table 2, the mean would correspond to a score of 40, +1u to 44.9 (40 + 4.9), +20' to 49.8 (40 + 2 X 4,9), and so on. The percentage of cases that fall between the mean and + lu in a normal curve is 34.13. Because the curve is symmetrical, 34.13 percent of the cases are likewise found between the mean and -1u, so that between + 1u and - 1(1 on both sides of the mean there are 68.26 percent of the cases. Nearly all the cases (99.72 percent) fall within ±3u from the mean. These relationships are particularly relevant in the interpreta.tion of standard scores and percentilcs, to be discussed in later sections.
is known as the variance, or mean
eviatiol1, andc~ymbo1ized by u'. The variance has proved ~x'useful in sorting out the contributions of different factors to mdifferences in test performance. For the present purposes, howchief concern is with the SD, which is the square root of the as shown in Table 2. This measure is commonly employed in .'g the variability of different groups. In F.igur.e 2,. for e~a~~le, distributions having the same mean but dlflenng In vanabllity. ribution with wider individual differences yields a larger SD "one with narrower individual differences. Sf) also provides the basis for expressing an individual's scores on
One way in which meaning can be attached to test scores is to indicate how far along the normal developmental path the individual has progressed. T~us a~ 8-year-old who performs as well as the average 10-yearold on an mtelhgence test may be described, as having a mental age of 10; a mentally retarded adult who performs at the saifre level would likewise be assigned ~n MA of 10. ~n a different context. 11 i~.urth-grade child may be cba.ractenzed as reacbmg the sixth-grade nonn An a reading test and the t~l~d-grade n~rm in an. ar~thmetic test. Other d~velopm~tal systems uti!tze more hIghly quahtative deSCriptions of be.JU~yi9I.in ~ r
Norms and the Interpretation
'Prillcil,lesof PSljchological Testing unctionsranging from sensorimotor activities to concept formation. -I'erexp~essed, scores based on developmental norms tend. to be oinetricallvcrude and do not lend themselves well to precise statreah~e~t. Nevertheless, they have considerable appeal for de\ve purposes, especially in the intensive clinical study of individuals or certain research purposeS. 'l'l;TAL ACE. In Chapter 1 it was noted that the tenn "mental ~ge" s;ddelv popularized through the various translations and adaptatiOns the Billet-Simon scales, although Binet himself had employed the re nelitral term "mental levcl." In age scales such as the Binet and 'revisionsjitemsare grouped into year le,·els. For example, those items ssedbv the majority of 7-vear-olds in the standardization sample are ~jacedi~ the 7-year level, tilose passed by the m~j~rity of 8-year-olds ~e assignedto the 8-year level, and so fOlth. A child s score on the test ',,~11then correspond to the highest year level that he can succe5sful~y 'omplete.In actual practice, the indh'idual's performance shows a certal~ '~mountof scatter. In other words, the subject fails some tests below h1s mental age level and passes some above it. For this reason, it is c~stomar}'to compute the basal age, i.e., the highest age at and below w~lCh all testsare passed. Partial credits, in months, are then ~d?ed to thiS basal ,'agefor all tests passed at hi~e:;p~r ~evels The chIld s mental age o~ months of credit the test ISthe sum of the ba~:gp ;lvitbe:dditjonaJ
earned at higher age level§.:. . ' ~tal age norms have also been employed wl~h ~ests that are l:ot dldivedinto year levels. In such a case, the subJect s raw scor~ 1S first determined. Such a score may be the total number of correct Items on the whole test; or it may be based on time, on number of~p"(lrs, or on by somecombination of sU~'h measures. The mean raw scores.t;,t)Q~nined the children in each year group within the standardiza~tQn' sample constitute the age norms for such a test. The mean raw seore of the 8-~ea~old children, for example, would represent the 8-year nonn. If an ll1d~-i vidual's raw score is equal to the mean 8-year-old raw SCOre,then hiS mental age on the test is 8 years. All raw scores on such a test can be transformed in a similar manner by reference to the age nonns. It should be noted that the mental age unit does not remain constant with age, but tends to shrin~ with advancing years. For example, a child who is one year retarded at age 4 will be approximately three. years. retarded at age·12. One year of mental growth from ages 3.to 4 IS eqUIValent to three years of growth from ages 9 to 12. Since mtellectual development progresses more rapidly at the earlier ages and gradually decreases as the individual approaches his mature limit, the mental age unit shrinks correspondingly with age. This relationship may be more
of Test Scores
75
readily ~isualized if ••w~ think ~~ the in.dividual's height as being expressed 10 tem1S of heIght age. The dIfference in inches between a height age of 3 and 4.years would be greater tha~ that betw~en a height age of 10 and 11. OWll1gto the progressive shrinkage of the MA unit, one year of acceleration or retardation at, let us sav, age 5 represents a larger deviation from the norm than does one vear 'of acceleration or retardation at age 10, .
GRADE EQUIVALENTS. Scores on educational achievement tests are often interpreted in terms of grade equivalents. This practice is understandable becaus.e,the t<:stsare employed within an academic setting. To describe a pupil s ~chlevement as equivalent to seventh-grade performance in spelhng, eIghth-grade in reading, and fifth-grade in arithmetic has the same popular appeal as the use of mental age in the traditional intelligence tests. ~rade ~orms are found by computing the mean raw score obtained by chIldren In each grade. Thus, if the average number of problems solved c~ITectly on .an arithmetic tes~ by the fourth graders in the standardizahon sample 1S23, th~n a raw score of 23 corresponds to a grade equivalent of 4. IntermedIate grade equivalents, representing fractions of a gr~de, a~e usually found by interpolation, although they can also be obtamed directly by testing children at different times within the school year. Because the school year covers ten months, successive months can be expressed as decimals. For example, 4.0 refers to average perfonnance at the beginning of the fourth grade (September testing), 4.5 refers to average performance at the middle of the grade (Febmary testing), and so forth. Despite their popularity, grade norms have several shortcomings. First, the content of instruction varies somewhat from grade to grade. Hence, grade norms are appropriate only for common subjects taught througho~t the grade le~els covered by the test. They are not generally apph cable at the hIgh school level, where many subjects may be studied for only one or two. years. Even Vlith subjects taugkt in each grade, however, the emphas1s placed on different subjects may vary from grade ~o grade, and ~rogress may therefore be more rapid in oJ1e subject than III ~other dUrIng a particular grade. In other words, grade-units are obv~ously unequal and these inequalities occur irregqllirly in different ,; . subjects. Grade norms are also subject to misinterpretation uni~s ,the test user keeps fi~ly in mind the manner in which they were ·deri~ed. For exam~le, .If a fourth-grade child obtains a grade eq.~ivalent of 6~9in arithmetic, I.t does ~ot mean that he has mastered thfi aritn,w.etic processes taught In the SIxth grade. He undoubtedly obtained'hjs sc6r~ largely by
Norms arid the ITltcrprc:tafioTl
.Principles of Psyc11010gicaJ Testing . " . I Id • >~t . ce 'I·nfouI,th grade arithmetic. It certam y COU not lOrpenorman - • . d 'h fc I. med that he has the prerequi~ites for seventh-gra e ant me I ~ adc norms tend to be incorrectly regarded as performan~l A sixth-grade teacher, for example: may assume tha.t all class should fall a! or close to tl~e sixth-grade ,n?rm In ac rade ests This misconception is certamly not surpnsmg when g h iare ~sed Yet individual differences within any onc grade ar~ suc ·.,:therange' of achJevement test scores will inevitably exten over
h~!:e~
;df.
pal grades, 1 t developmental norms derives Another approac 1 0 1 b t' f behavior , hI' E Ipirica 0 serva Ion 0 research in chIld psyc 0 og~, . n . 1 d t the description of be'pment in infants and young chlldl;n e. 0 1 omotion sensory typical of successive ages in ,SUC uncti~ns as OCt forma~ion. An
DINAL SCALES.
?
.' inati0t, .lingui~~c dc~~~~~;~~:t:~n~f a~ese~lo:~e£ his associates at p eAxame1913s et ~l. 1940; Gesell & Amatruda, 1947; H~lver( mes" , h d I h th apprOXImate e h ff 1933) The Gesell Developmental Sc e U es s 0''0 r lopm~ntallevel in months that the child has attained in eadc 0 °aul d ptive lan<1uage an person .areas of behavior, namely, motor, a ~ h'ld' 'behaVior with h 1 Tliese levels are "found by companng tIe CIS k a ran ing from 4 weeks to 38 mont s. g . d tl uential patterning of typlCalof eight ey at>es, sell and his co-workers emphaSize Ie .seq. f'f''t d xtenslVe eVidence 0 um or1111 , behavior development. Th ey CIe e. . f behavior of developmental sequences and an orderly pdrogressllolllb~ect piaced fons towar a sma 0 ] h hOld' Iges.For example, tee I s reac I , . visual ont of him exhibit a characteristic chronologIcal sequen:e I~ d in ion and in hand and finger movements. Use of th~ entire an 'de attempts at palmar prehension OCC~Il'S ~t a~ ear~er i~h;: t~:: he thumb in opposition to the palm; thIS t)~e 0 pre en~, t pincerowedb use of the thumb and index finger In a more e c~en . . Y f the ob'ect Such sequential patterning was hkewlse ob-
l~:~e~
0
J
•
0
0
0
~g~
cg~~;wOalking,st!ir ~limbing, and ~ost ~f th; s~~~~:~l~:o~':~:~~;k t of the first few years, The scales eve ope ~ 'c6nstant . do I' the sense that developmental stages follow In a . e~:~~~hl~tage presupposing m~stery of prerequisite behaVIOr char-
of Test Scores
77
Since the 19605, there has been a sharp upsurge of interest in the developmental theories of the Swiss child psychologist, Jean Piaget (see Flavell, 1963; Ginsburg & Opper, 1969; Green, Ford, & Flamer, 1971). Piaget's research has focused on the development of cognitive processes from infancy to the midteens. He is concerned with specific concepts rather than broad abilities. An example of such a concept, or schema, is object permanence, whereby the child is aware of the identity and continuing existence of objects when they are seen from different angles or are out of sight. Another widely studied concept is conservation, or the recognition that an attribute remains constant over changes in perceptual appearance, as when the same quantity of liquid is poured into differently shaped containers, or when rods of the same length are placed in different spatial arrangements. Piagetian tasks have been used widely in research by developmental psychologists and some have been organized into standardized scales, to be discussed in Chapters 10 and 14 (Goldschmid & Bentler, 1968b; Loretan, 1966; Pinard & Laurendeau, 1964; Uzgiris & Hunt, 1975). In accordance with Pia get's approach, these instruments are ordinal scales, in which the attainment of one stage is contingent upon completion of the earlier stages in the development of the concept. The tasks are designed to reveal the dominant aspects of each developmental stage; only later are empitical data gathered regarding the ages at which each stage is typically reached, In this respect, the procedure differs from that followed in constructing age scales, in which items are selected in the first place on the basis of their differentiating between successive ages. In summary, ordinal scales are designed to identify the stage reached by the child in the development of specific behavior functions. Although sc.'Oresmay he reported in terms of approximate age levels, such scores are secondary to a qualitative description of the child's characteristic behavior. The ordinality of such scales refers to the uniform progression of development through successive stages. Insofar as these scales typically provide information about what the child is actually able to do (e.g., climbs stairs without assistance; recognizes identity in quantity of liquid when poured into differently shaped containers), they share important features with the criterion-referenced tests to be discussed in a later section of this chapter.
a~teJ'isticof earlier stages.' ,
•• . I I" differs from that in statistics, in which an k l' f individuals wjthout '. Thisusageof the term ordma sca ~ " .' I that permlt~ a ran -oruenn~ 0 .al scale IS simp y one . . between them' in the statistical sense; o~1 . dge about amount of dilI~r~nce les Ordinal sillIes of child development arecontra.stedto equal-umt mterva ~:m~~ scale or simplex, in which successuallydeSignedon theI ~o~~;so:u:c:ss at lower levels (Guttman, 1944). An :pprformanceat one 1 eve mlp I o
i
an
Nearly all standardized tests now provide some foryn of within~group norms. With such norms, the individual's performa,~~,. is evaluated in ;t.~·
extension of Guttman's analysis to Include nonlinear hi~archies i,~ilescribc:d by Bart . and Airasian (1974), with special reference to Piagetillrr··~al.~".~
__________________________
••••••••••••
Norms and tile Interpretation
Principles of Psychological
Testing
msof the performance of the most nearly comparable standardization up, as when comparing a child's raW score with that of ~hi~dren of e same chronological age or in the same school grade. Wlthm-group reshave a uniform and clearl\' defined quantitative meaning and can appropriately employed in m~st types of statistical analysis.
Percentile scores are expressed in terms of the percentage persons in the standardization sample who fall be~ow a given raw reoFor exampk, if 28 percent of the persons obtam fewer than 15 bblemscorrect on an arithmetic reasoning test, then a raw score of
PERCEKnLES.
of Test
Scores
79
whereas raw score differences near the ends of the distribution are greatly shrunk. This distortion of distances between scores can be seen in Figure 4. In a normal curve, it will be recalled, cases cluster closely at the center and s~atter more widely as the extremes are approached. Consequently, any glYen percentage of cases near the center covers a shorter distance on the baseline than the same percentage near the ends of the distribution. In Figure 4, this discrepancy in the gaps between percentile ranks (PH) can readily be seen if we compare the dj$tance between a PR of 40 and a PH of 50 with that between a PR oero and a PR of 20. Even more stdking is the discrepancy between these distances and that between a PH of 10 and PR of 1. (In a mathematically derived normal curve, zero percentile is not reached until infinity and hence cannot be shown on the graph. ) Mdn
Q1
Q3
1
99
20130405 06070180
.' 'dual's standing. e 50th percentile (P;;(I) corresponds to the medlan, already dlsd as a measure of central tendency. Percentiles above 50 represent e-average performance; those below 50 signify inferior p~rforman:e. '.25th and 75th percentile are known as the first and thlrd quartile hits (Ql and Q3), because they cut off the lowest and highest quarters the distribution. Like the median, they provide convenient landmarks Qrdescribing a distribution of scores and comparing it with other dis-
i J
i I I :
I
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i
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\
:
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ributions. . Percentiles should not be confused with the familiar percehtage scores. he latter are raw scores, expressed in terms of the percentage of correct /items;percentiles are derived scores, expressed in terms of perce~ltage of }
-30-
~m FIC.
-10-
M
+10-
+20-
+30-
~
~
~
98
99.9
4. Percentile Ranks in a NOlmal Distribution.
The same relationship can be seen from the opposite direction if we examine the percentile ranks corresponding to equal u-distances from the mean ~f a. normal curve. These percentile ranks are given under the graph m Flgure 4. Thus, the percentile difference i;letween the mean and + lIT .is 34 (84 - 50). That between + I.,. and +~is only 14 (98 - 84). . It IS apparent that percentiles show each indiyf
·1
Norms and the Interprdation of Test Scores
81
.";pfillciIJles of Psychological Testing
of differences between standard scores derived by such a linear transformation corresponds exactly to that between the ;aw scores. All-properties of the original distribution of raw scores are duplicated in the distribution of these standard scores. For this reason, any computations that can be carried out with the original raw scores can also be carried out with linear standard scores, withollt any distortion of results. Linearly derived standard scores are often desilTnatedsimpl\' as "standb . ard scores" or "z scores." To compute a :; score, we find the difference between the individual's raw score and the mean of the normative group and then divide this difference by the SD of the normative group. Table 3 shows the computation of z scores for two individuals, one of whom falls 1 SD above the group mean, the other .40 SD below the mean. Any raw score that is exactly equal to the mean is equivalent to a z smre of zero. It is apparent that such a procedure will yield derived scores that have a negative sign for all subjects falling below the mean. .Moreover, because the total range of most groups extends no farther than about 3 SD's above and below the mean, such standard scores will have to be reported to at least one decimal place in order to provide sufficient differentiation among individuals. John Mary
Ellen
Edgar
Jane
Dick
Bill
Debby
~h-A Normal"PercentileChart. Percentiles are spaced so as to ~orrespond
~~Idistancesin a normal distribution. Compare the sc~re. distance ~e" hn and Mary with that between EIIen and Edgar; w!.thm both pal:s, entile difference is 5 points. Jane and Dick differ by 10 percentile as do Bill and Debby.
3 Computation of Standard Scores
TABLE
X-M SD JOHN'S SCORE
"'canbe used to plot the scores of different persons. on the same r thescoresof the same person on different tests. In elther case, the illinterscoredifference will be correctly represented~ Many aptitude achievementbatteries now utilize this technique in their score pro'whichshow the individual's performance in each test. An example ~eIndividualReport Form of the Differential Aptitude Tests, reprod in Figure 13 (Ch. 5).
t
. "AXDARD SCORES. Current tests are making increasing use of standard. . scoreswhichare the most satisfactory type of derived score ftom most ~oints'of view. Standard scores express the individual's distance from meanin terms of the standard deviation of the distribution. Standardscores mav be obtained by either linear or nonlinear transationsof the origi~al raw scores.Whe~ found by a l.in.eartransforma; theyretain the exact numerical r~labons of the ongmal raw scores, . usethey are computed by subtracting a constant from each raw score thendividing the result by another con~tant The relative magnitude ",
X\=65 65 - 60 Zl=
BILL'S SCORE
X:=58 58 - 60
5
= +1.00 Both the abovE'conditions, viz., the occurrence of negative values and of decimals, tend to produce awkward numbers that are confusing and difficult to use for both computational and reporting purposes. For this reason, some further linear transformation is u~u,:lly applied, simply to put the scores into a more convenient form. ,For. ~x~lnple, the scores on the Scholastic Aptitude Test (SAT) of the College Entrance Examination Board are standard scores adjusted to a mean ot;~:, and an SD of 100. Thus a standard score of -Ion this test would b: . ressed as 400 (500 - 100 = 4(0). Similarly, a standard score of + l.S ou1ltcorrespond to 650 (500 + 1.5 X 100 = 650). To con"er~ an origi~$ll!tandard score to the new scale, it is Simplynecessary to multiply the standard score by the
Principles of P~Y;'IO'ogical Testing
'ed SD (100) and add it to or subtract it from the desired mean ). Any other convenient values can be arbitrarily chosen for the ,mean and SD. Scores 011 the separate subtests of the Wechsler Inence Scales, for instance, are converted to a distribution with a 1 of 10 and an SD of 3. All such measures are examples of linearly sformed standard scores. 'twill be recalled that one of the reasons for transforming raw scores o any derived scale is to render scores on different tests comparable. e linearlv derived standard scores discussed in the preceding section " be cO~lparable only when found from distributions that have apximately the same form. Under such conditions, a score corresponding ~.I SD above the mean, for example, signines that the individual occuies the same position in relation to both groups. His score exceeds aproximately t1J.e.same percentage of persons in both distributions, and is percentage can be determined if the form of the distribution is 'known.If, howeyer;"one distribution is mal'kedly skewed and the other "normal,a z score of +1.00 might exceed only 50 percent of the cases in ,negroup but would exceed 84 percent in the other. In order to achieve comparability of scores from dissimilarly shaped ,distl-ibutions,nonlinear transformations may be employed to fit the scores to any specified type of distribution curve. The mental age and percentile scores described in earlier sections represent nonlinear transformations, but they are subject to other limitations already discussed. Although under certain circumstances another type of distribution may be more appropriate, the normal curve is usually employed for this purpose. One of the chief reasons for this chotee is that most raw score distributions approximate the normal CUJ;V-e more closely than they do any other type of curve. Moreover, physical me1tsures such as height and weight, which use equal-unit scales derived. thl:"'t'fugh physical operations, generaU,y yield normal ~istributions., Anoth'1f"frnportan: advantage .of the ~or.~al :~rve is that It has many useful mathematical properties, whlchl""faclhtate further computations. NQrmalized standard scores are standard scores expressed in terms of a distribution that has been transformed to fit a normal curve. Such scoreS can be computed by reference to tables giving the percentage of cases falling at different SD distances from the mean of a normal curve. Firsf, the percentage of persons in the standardization sample falling at or above each raw score is found. This percentage is then located in the normal curve frequency table, and the con-esponding normalized stand2 Partly for this reason and partly as a result of other theoretical considerations. it has frequently been argued that, by normaliZingraw scores. an e(lual-unit scale could be developcd for psycholo~ical measurement similar to the equal-twit sL-dlesof physical measurement. This, however, is a debatable point that involves certain questionable assumptions.
ard score is obtained. Normalized standard scores are expressed in the same form as linearly derived standard scores, viz., with a mean of zero and an SD of 1. Thus, a normalized score of zero indicates that the individual falls at the mean of a normal curve, excelling 50 percent of the group. A score of -I means thafhe surpasses approximately 16 percent of the group; and a s(:ore of + I, that he surpasses 84 percent. These percentages correspond to a distance of 1 SD below and 1 SD above the mean of a normal curve, respectively, as can be seen by reference to the bottom line of Figure 4. Like linearly derived standard scores, normalized standard scores can be put into any convenient form. If the normalized standard score is multiplied by 10 and added to or subtracted from 50, it is converted into a T score, a type of score first proposed by McCall (1922). On this scale, a score of 50 corresponds to the mean, a score of 60 to 1 SD above the mean, and so forth. Another well-known transformation is represented by the stanine scale, developed by the United States Air Force during World War II. This scale provides a single-digit system of scores with a mean of 5 and an SD of approximately 2.3 The name stanine (a contraction of "standard nine") is based on the fact that the scores run from 1 to 9. The restriction of ~cores to single-digit numbers has certain computational advantages, for each score requires only a Single column on computer punched cards. TABLE
4
Normal Curve Percentages for Use in Stanine Conversion
Percentage Stanine
Raw scores can readily be co~verted to stanines by arranging the original scores:in order of size and ~,~fn assigning stanines in accordance with the normal curve percentages"re,produced in Table 4. For example, if tlJ.e group consists of exactly I()() persons, the 4 lowest-scoring persons receive a stanine score of 1, the next 7 a score of 2, the next 12 a score of 3, and so on. When the group contains more or fewer than l00~cases, the number corresponding to each deSignated percentage is first computed, and these numbers of cases are then given the appropriate stanines. "'c 3 Kaiser (1958) proposed a modification of the staninl!'scale thaq~volves slight (;han~es in the percentages and yields an SD of exactly 2, thus being e~Werto handle quantitatively. Other variants are the C scale (Guilford & ltruchter, :1,.913" Ch. 19), consisting of 11 units and also yielding an SD of 2, and tl.!~~lO-Uilitstefl scale, with 5 units above and 5 below the mean (Canfield, 1951}.'\: ".
-"
Co
Prillciplcs of Psycl1010gical Testing
us,out of 200 cases, 8 would be assigned a stanine of 1 (4 percent of = 8). With 150 cases, 6 would receive a stanine of 1 (4 percent of == 6). For any group containing from 10 to 100 cases, Bartlett and ,erton (1966) have prepared a table whereby ranks can be directly rted to stanines. Because of their practical as well as theoretical rimtages,stanines are being used increasingly, especially with aptitude achievement tests. Ithough nOlmalized standard scores are the most satisfactory type of .refor the majority of purposes, there are nevertheless certain techal objections to normalizing all distributions routinely. Such a trans:)ation should be carried out only when the sample is large and repIltative and when there is reason to believe that the deviation from in~litvresults from defects in the test rather than from characteristics he sample or from other factors affecting the behavior under conration/it should also be noted that whpn-the original distribution of scores approximates normality, the linearly derived standard scores the normalized standard scores will be very similar. Although the :ods of deriving these two types of scores are quite different, the tiltingscores will be nearly identical under such conditions. ObViously, .!proeessof normaliZing a distribution that is already virtually normal r produce little or no change. Whenever feasible, it is generally more 'rable to obtain a normal distribution of raw scores by proper adjust,t of the llifficulty' level of test items rather than ~by subsequently alizing a markedly nonnormal distribution. With an approximately al distributiou of raw scores, the linearl\' derived standard scores ,servethe same purposes as normalized st;ndard scores.
In an effort to convert ~1A scores into a ~6rm of the individual's relative status, the ratio IQ (Intelligence Jient) was introduced in early intelligence tests. Such aIJ.,IQ was ply the ratio of mental age to chronological age, multiplied by 100 to 'pate decimals (IQ 100 X MAjCA). Obviously, if a child's ~IA Is his CA, his IQ will be exactly 100. An IQ of 100 thus represents '\i.\ or average performance. IQ's below 100 indicate retardation, above 100, acceleration. " apparent logical simplicity of the traditional ratio IQ, however, proved deceptive. A major technical difficulty is that, unless the f the IQ distribution remains approximately constant with age, will not be comparable at different age levels. An IQ of 115 at age r example, may indicate the same degree of superiority as an IQ at age 12, since both may fall at a distance of 1 SD from th~ . of their respective age distributions. In actual practice, it prm'e,&' . ifficult to constmc:t tests that met the psychometric requiremeritS' .~ DEVIAT10JlO IQ.
J
=
Norms and the Interpretation
of Test Scores
85
for comparability of ratio IQ's throughout their age range. Chiefly for this reason, the ratio IQ has been largely replaced by the so-called deviation IQ, which is actually another variant of the familiar standard score. The deviation IQ is a standard score with a mean of 100 and an SD that approximates the SD of the Stanford-Binet IQ distribution. Although the SD of the Stanford-Binet ratio IQ (last used in the 1937 edition) was not exactly constant at all ages, it fluctuated around a median value slightly greater than 16. Hence, if an SD close to 16 is chosen in reporting standard scores on a newly developed test, the resulting scores can be interpreted in the same way as Stanford-Binet ratio IQ's. Since Stanford-Binet IQ's have been in use for many years, testers and clinicians have become accustomed to interpreting and classifying test performance in terms of such IQ levels. They have learned what to expect from individuals with IQ's of 40, 70, 90, 130, and so forth. There are therefore certain practical advantages in the use of a derived scale that corresponds to the familiar distribution of Stanford-Binet IQ's. Such a correspondence of score units can be achieved by the selection of numerical values for the mean and SD that agree closely with those in the Stanford-Binet distribution. It should be added that the use of the term "IQ" to designate such standard scores may seem to be somewhat misleading. Such IQ's are not derived by the same methods employed in finding traditional ratio IQ's. They are not ratios of mental ages and chronological ages. The justification lies in the general familiarity of the term "IQ," and in the fact that such scores can be interpreted as IQ's provided that their SD is approximately equal to that of previously known IQ's. Among the first tests to express scores in terms of deviation IQ's were the \Vechsler Intelligence Scales. In these tests, the mean is 100 and the SD 15. Deviation IQ's are also used in a number of current group tests of intelligence and in the latest revision of the Stanford-Binet itself. \Vith the increasing use of deviation IQ's, it is important to remember that deviation IQ's from different tests are comparable only when they employ the same or closely similar values for the SD. This value should, always be reported in the manual and carefully noted by the test user. If a test maker chooses a different value for the SD in making up his deviation IQ scale, the meaning of any given IQ on his test will be quite different from its meaning on other tests. These discrepancies are illustrated in Table 5, which shows the percentage of cases}i1normal distriblltions with SD SD's from 12 to 18 who would obtain IQ's at different l~els.These values have actually been employed in the IQ scales ofp*lJli~hed tests. Table 5 shows, for example, that an IQ of 70 cuts off the lo\v(j:..st3.1 percent when the SD is 16 (as in the Stanford-Binet); but it _",;;y cut off. as few as 0.7 percent (SD = 12) or as many as 5.1 percen .' = 18) . An IQ of 70 has been used traditionally as a cutoff point fpl' . ying
5 tage of Cases at Each IQ Interval and Different Standard Deviations
in Normal
Distributions
with Mean In
5:
co v
esyTest Department, Ha~court Brace Jovanovich, Inc.)
'0
.8 E
. : 1Q1ilterval s',b .
\Rh
130 above 120-129 ··:110-119 100-109 90- 9~ 80- 89 70- 79 . Below70 Total
SD= 12
0.7 4.3
15.2 29.S} 59.6 29.8
SD = 14
3.1
5.1
7.5
8.5
15.8
15.4
26.1}52.2
4.3
6.3
0.7
1.6
100.0
0.13% 0.13% -40-
21.°l
;;::}47.2
21.0) 420.
15.8 7.5 3.1
15.4 8.5 5.1
100.0
z'"
= 18
1.6
15.2
=
SO
6.3 16.0 26.1 16.0
100.0
SD = 16
I 100,0
-,'1II9tA~;r.r
... ).~~"""""~
mental retardation. The same discrepancies, of course, apply to IQ's of 130 and above, which might be used in selecting children for special programs for the intellectually gifted. The IQ range between 90 and lIO, generally described as normal, IJlay include as few as 42 percent or as many as 59,6 percent of the popula-tion, depending on the ~est chosen. To be sure, test publishers are making efforts to adopt the umform SD of 16 in new tests and in new editions of earlier tests. There are still enough variations among cuaently available tests, however, to make the checking of the SD imperative.
z score
I -4
Tscore
L 10
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Stanine
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! 55
CEEB score
Deviation IQ (SD =15)
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6
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7
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+4<1
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+2
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400
2
Percentile
Mean Test score
4%
8
90 95
!l9
6. Relationships among OiHerent Types of Test Scores in a Normal
Distribution.
INTERRELATIONSHIPS OF WITHIN-GROUP SCORES,At this stage in our dis; cussian of derived scores, the reader may have become aware of a rapprochement among the various types. of scores. Percentiles ~ave gradually been taking on at least a graphIC rese~b~a~ce t? norma}ijzed standard scores. Linear standard scores arc mdlstingmshable from normalized standard scores if the original distribution of raw scores closely approximates the normal curve. Finally, standard s(:ores have. become IQ's and vice versa. In connection with the last point, a ree,xamm~tion of the meaning of a ratio IQ on such a test as the Stanford-.Bmet WIll show that these IQ's can themselves be interpreted as standard scores. If we know that the distribution of Stanford-Binet ratio IQ's had a mean of 11") ronrl ~n qT) of :mnroximatelv 16. we can conclude that an IQ of 1I6
falls at a distance of 1 SD above the mean and represents a standard score of + 1.00. Similarly, an IQ of 132 corresponds to a standard score of +2.00, an IQ of 76 to a standard score of -1.50, and so forth. Moreover, a Stanford-Binet ratio IQ of lI6 corresponds to.~Percertile rank of approximately 84, because in a normal curve 84 plirc~1it of-the cases fall helo. +1.00 SD (Figure 4). . ,. In Figure 6 are summarized the relaHbnships that exist in a normal distribution among the types of scores so far discussed in .this chapter. These include z scores, College Entrance Examination Bqp,rcd (CEEB) scores, Wechsler deviation IQ's (SD = 15), T SCOres,stanines, and percentil~s. Ratio IQ's on any test will coincide with th~g_iven deviation iQ scale-If they are normally distributed and have an S1). of 15. Any other
90
Principles of Psychological Testing ally distributed IQ could be added to the chart, provided we know 'SD. If the SD is 20, for instance, then an IQ of 120 corresponds to '1 SD, an IQ of 80 to -1 SD, and so on. In conclusion, the exact form in which scores are reported is dictated gelyby convenience, familiarity, and ease of developing nonns. Standscores in any form (including the deviation IQ) have generally placed other types of scores because of c.-ertain advantages they offer 'th regard to test construction and statistical treatment of data .. ~ost pes of within-group derived scores, however, are fundamentally s1m1lar _. carefully derived and properly interpreted. When certain statistical conditions are met, each of these scores can be readily translated into ...any of the others.
ISTERTEST COMPARISONS, An IQ, or allY other score, should always be accompanied by the name of the test on which it was obtained. Test ~corescannot be properly interpreted in the abstract; they must be ree ferred to particular tests. If the school records show that Bill Jones re. ceived an IQ of 94 and Tom Brown an IQ of 110, such IQ's cannot be accepted at face value without further information. The positions of these two students might have been reversed by exchanging the particular tests that eq,ch was given in his respective school. Similarly, an individual's relative standing in di~erent functions may be grossly misrepresented through lack of comparability of test norms. Let us s~ppose that a student has been given a verbal comprehension test and a spatial aptitude test to determine his relative standing in the two fields. If the verbal abilitv test was standardized on a random sample on a of high school students, while the spatial tes~ was standardized selected group of boys attending elective shop courses, the examiner might erroneously conclude that the individual is much more able along verbal than along spatial lines, when the reverse may actually be the case. Still another example involves longitudinal comparisl?,ns of a single individual's test performance over time. If a schoolchild's cumulative record shows IQ's of 118, 115, and 101 at the fourth, fifth, and sixth grades, the first question to ask before interpreting these changes is, "What tests did he take on these three occasions?" The apparent decline may reflect no more than the differences among the tests. In that case, he would have obtained these scores even if the three tests had been administered within a week of each other. There are three principal reasons to account for systematic variations among the scores obtained by the same individual on different tests. First,
Norms and the Interpretation
of Test Scores
89
tests may differ in content despite their similar labels. So-called intelligence tests rrovide many illustrations of this confusion. Although common]y descnbed by the same blanket term, one of these tests may include only v~rba] content, another may tap predominantly spatial aptitudes, and still another may cover verbal, numerical, and spatia] content in about equal proportions. Second, the scale units may not be comparable. As explained earlier in this chapter, if IQ's onone test have an SD of 12 and IQ's on another have an SD of 18, then an individual who received an IQ of 112 on the first test is most likely to receive an IQ of 118 on the secon~. !hird, the composition of the s~dardi;;;ation sa'!!Ples used in establIshmg nonns for different tests may vary. ObViously, the same indi~idu~l will appear to have performed better when compared with an mfenor group than when compared with a superior group. Lack of comparability of either test content or scale units can usually be detected by reference to the test itself or to the test manual. Differences in the respective normative samples, howeyer, are more likely to be overlooked. Such differences probably account for many otherwise unexplained discrepancies in test results.
THE NORMATIVE SAMPLE.• Any norm, however expressed, is restricted to the particular normative population from which it was derived, The test user should never lose sight of the way in which norms are established. Psychological test norms are in no sense absolute, univer;!U,or penn~ne~t. They JIle~ely represent the test performance of the subi.~15 consti~tmg the~i\r..~ardization sample. In choosing such a sample·, af1 eff?rt IS usual.lr~de t(t'Qbtain a representative cross sectiol\Hlf.the populatIon for which th~.it~st is designed. . In st~tistjca] terminology, a distinction is made between sample and populatIOn. Th: former refers to the group of individuals actually teste (i. Th~ latter des1gn~tes the larger, but similarly constituted, group froin which the sample 1Sdrawn. For example, if we wish to establish nonns of test performance for the population of 10-year-old, urban, public schoo] boys, ~ve migh~ test a carefully chosen sample of 500 10-year-oJd boys attendmg PUb~IC schools in several American cities. The sample would be checked w1th reference to geographical distribution, socioeconomic level, ethnic (,'omposition, and other relevant characteristics to ensure that it was truly representative of the defined population. In the development and application of test norms, considerable attention should be. given to the standardization sample. It is,,apparent that the sample on wh1ch the norms are based should be large enough to provide stable values., Another, similarly chosen sample of th•.•same population should not yIeld nonns that diverge appreciably frorp tfl.ose obtained.
"Prillciplesof Psychological Testing , with a large sampling error would obviollsly be of little yalue in ~erpretationof test scores. uallyimportant is the requirement that the sample be representative ',population under consideration. Subtle selective factors that might . the sample unrepresentative should be carefully investigated. A ber of such selective factors are illustrated in institutional samples. ausesuch samples are usually large and readily available for testing oses,they offer an alluring field for the accumulation of normative . The special limitations of these samples, however, should be careyanalyzed. Testing subjects in school, for example, will yield an in'singlysuperior selection of cases in the sllccessive grades, owing to e progressive dropping out of the less able pupils. Nor does such iffiinationi?,ffectdifferent subgroups equally. For example, the rate of ctiveelimination from school is greater for boys than for girls, and /~greater in lower than in higher socioeconomic levels. S~I~ctivefactors likewise operate in other institutional samples, such .prisoners,patients in mental hospitals, or institutionalized mental redates.Because of many special factors that determine institutionaliza'n itseH,such groups are not representative of the entire population of riminals,psychotics, or mental retardates. For example, mental retardtes with physical handicaps are more likely to be institutionalized than re the physically fit. Similarly, the relative proportion of severely rearded persons will be much greater in institutiunal samples than in the total population. Closely related to the question of representativeness of sample is the needfor defining the specific population to which the norms apply. Obvious]y,one way of ensuring that a sample is representative is to restrict the population to fit the ~ecifications of the available sample. For ex. ample, if the population i$ defined to include only 14-year-old schoolchDdrenrather than all 14-year-old children, then a school sample would be representative. Ideally, of course, the desired population should be definedin advance in terms of the objectives of the test. Then a suitable sample should be assembled. Practical obstacles in obtaining subjects, however, may make this goal unattainable. In such a case, it is far better to redefine the population more narrowly than to report norms on an ideal population which is not adequately represented by the standardization sample. In actual practice, very fe''''' tests are standardized on such broad populations as is pORularly assumed. No test provides norms for the human species! And it is doubtful whether any tests give truly adequate norms for such broadly defined populations as "adult American men," "lO-year-old American children," and the like. Consequently, the samples obtained by different test constructors often tend to be unrepresentative of their alleged populations and biased in different ways. Hence, the rr
NATION~L ANCHOR NORMS. One solution for the lack of comparability of n~rms IS to use an anchor test to work out eqUivalency tables for scores ?n dl~erent tests. Such tables are designed to show what score in Test A IS e~Ulvalent to ~ach score in TestB. This can be done by the equipercent,ze m.ethod, m which scores are considered equivalent when ther have equal percentiles in a given group. For example, if the 80th pel:' centile in the same group corresponds to an IQ of lI5 on Test A and to an IQ of 120 on Test B, then Test.A-IQ 115 is considered to be equivalent to Test-B-IQ 120. This approach has been followed to a limited extent by so~e test publishers, who have prepared equivalency tables for a few of theIr Own tests (see, e.g., Lennon, 1966a). More ambitious proposals have been made from time to time for cali. brat~n~ each new test against a single anchor test, which has itself been admllllstered to a highly representative, national normative sample (Len~on, 1966b). No single anchor test, of course. could be used in establishmg norms for all tests, regardless of content. "'hat is required is a batterY of anchor tests, all administered to the same national sample. Each ne,~' ~est could then be checked aKainst the most nearlY similar anchor test 111 the battery. .
The data gathered in Project TALENT (Flanagan et a!', 1964) so far come closest to providing such an anchor batten' for a high school popula~ion. Using a r~ndo~ sample of about 5 per~nt of the high schools in tIllS country, th~ lllVeStIga.torsadministered a two-day battery of specially cons~ructed aphtude, achIevement, interest, and temperament tests to appr~:llnately 400,000 students in grades 9 through 12. Even with the avail~bihty of anchor data such as these, however, it must be recognized tItat l~dependen~ly dev.eloped tests ·can ~ever be regarded as completely interchangeable. At best, the use of natIOnal anchor norms would appreciably reduce the lack of comparability among tests, but it would not elimi. nate it. Th~ Pro!ec~ TALENT battery has been employed to calibrate several test battenes III use by the Navy and Air Force (Dailey, Shaycoft, & Orr, 1962: ~haycoft, Neyman, & Dailey, 1962). The general procedure is to admllllster both the Project TALENT battery and the tests to be calibra~ed to the same sample. Through correlational analysis, a ,composite of Project TALENT tests is identified that is most n~ya,dycomparable to each test to be norme?. By means of the equipercentile method, tables are then prepared g1Vlllg the corresponding scores On the Project T~LENT composite and on the particular test. For several other battenes, data have been gathered to identify the Project TA.Lf:NT com4 F~r an excellent analysis of some of the technical difficulties involved in efforts to achIeve score comparability with different tests, see Angolf (i~~. 1966, 1971a). "~-
,~
Principles of Psychological Testing
..positecorresponding to each test in the battery (Cool~y, 1965; Cooley & Miller,1965). These batteries include the General AptItude Test Battery 'ofthe United States Employment Service, the Differential Aptitude Tests, .andthe Flanagan Aptitude Classification Tesfs . .Ofparticular interest is The Anchor Test Study conducted by the EducationalTesting Service under the auspices of the U:S. Office of E~uqation(Jaeger, 197.3). This study represents a systematIc effort to proVIde comparable and tI'uly representative national norms for the seve~ most 'dely used reading achievement tests for. elementa~ schoolchIldren. hrough an unusually \vell-controlled ~xpenmental desl.gn, o.ver 300,000 fourth-,fifth-, and sixth-grade schoolchIldren were exammed 111 50 states. The anchor test consisted of the reading comprehension and vocabulary btests of the Metropolitan Achievement Test, for which new norms cre established in one phase of the-project. In the equating phase of the "d)', each child took the reading comprehension an~ voca?ula~ subests from two of the seven batteries, each battery bemg paned In turn with every other battery. Some groups took parallel forms of t~~ t\.•.•o sub:testsfrom the same battery. In still other groups, all the pamngs were 'duplicated in reverse sequence, in order to control for order. of administration. From statistical analyses of all these data, score eqUivalency "tablesfor the seven tests were prepared by the equipercentile method. A manual for interpreting scores is provided for use by school systems and . other interested persons (Loret, Seder, Bianchini, & Vale. 1974).
SPECIFIC NORMS. Another approach to the nonequivalence of existing norms-and probably a more realistic one for most tests-is to standardize tests on more narrowly defined populations, so chosen as to suit the specificpurposes of each test. In such ca.ses. the limits of the normative ; population should be clearly reported wIth the norms. :hus, the n?rms " might be said to apply to "employed clerical worke~',s 111 large busll1~sS '. organizations" or to "first-year enginee~ing students. For many test~ng <. purposes. highly specific norms are deSirable. Eve~ w~e~ representatIve . norms are available for a broadly defined populatIon. It IS often helpful .tohave separately reported subgroup norms. This is true whenever recog-; .•nizable subgroups yield appreciably different scores on a particular ~est. The subgroups may be formed with respect to ag~, grade, type.of curnc~. lum, sex, geographical region, urban or rural envIronment, soclOeCOnO~T1lc 'level and manv other factors. The use to be made of the test determmes the ~pe of differentiation that is most relevant. as well as whether general or specific norms are more appropriate. , Mention should also be made of local norms, often developed by the test users themselves within a particular setting. The groups employed in r11'ridnrt s11ehnorms are even more narrow I)· defined than the subgroups
Norms alld the Intcrpretation of Tcst Scores
93
considered a?ove. Thus, an employer may accumulate norms on applicants for a gIVen type of job within his company. A college admissions office may develop norms on its own student population. Or a single elementa~y school may evaluate the performance of individual pupils in terms of Its own sco:e distribution. These local norms are more appropriate than broad nahonal norms for many testing purposes, such as the prediction of subsequent job performance or college achievement, the comparison of a child's relative achievement in different subjects, or the measurement of an individual's progress o\-er time.
• FIXED REFERENCE GROUP. Although most derived scores are computed m such a way as to provide an immediate normative interpretation of test perfom~ance, there. ~re some notable exceptions. One type of nonnormative scale utIlIzes a fixed reference group in order to ensure compar~bility and continuity of scores, without providing normative evaluation of performance. \Vith such a scale, normative interpretation requires reference to independently collected norms from a suitable population. Local' or other specific norms are often used for this purpose. One of the clearest examples of scaling in terms of a fixed reference group is provided by the score scale of the College Board Scholastic Aptitude Test (Angoff, 1962, 1971b). Between 1926 (when this test was first a~ministered) and 1941, SAT scores were expressed on a normative scale, 111 t~r.ms o~ the mean and SD of the candidates taking the test at each adm~mstration. As the number and variety of College Board member colleges l~lcreased and the composition of the candidate population changed, It was concluded that scale continuity should be maintained. Otherwise, an individual's score would depend on the characteristics ot the group tes~ed .dUring a particular year. An even more urgent reason for scale continu~ty ~temmed from the observation that students taking the. SA~ at certam .hmes of the year performed mOre poorly than those ~akll1g It at other bmes, Qwing to the differential operation of selective f~ctors. After 1941, therefore, all SAT scores were expressed in terms of the ~ean and SD of the approximately 11,000 candidates who took the test m 1941. These candidates constitute the fixed reference group employed in scaling all subsequent forms of the test. Thus, a score of 500 on any form of the SAT corresponds to the mean of the 1941 sample' a score of 600 falls 1 SD above that mean, and so forth. ' , To permit translation of raw scores on any {prm of the SAT into these ~x~d-refere~ce-group scores, a short anc~or test (9r set of common items) IS lI:c1uded 111 each fonn. Each new form is thereby linked to one or two ~arher forms. which in turn are linked with other forms by"g chin of Items extend!ng back to the 1941 form. These nonnormative SAT scores can then be mterpreted by comparison with any appropriate distribution
Norms and the Intcrpretat,ion of Test Scores
"94
Princil)les of Psychological
Testing
of scores; such as that of a particular college, a type of college, a r~gi?n, etc. These specific norms are. more useful in making colle.ge adml~slon decisions than would be annu~l norms based on ~he entire. candidate o ulation. Any changes in the candidate populatlOn o.ver time, more~v~r,can be detected only with a fixed-score scale. It will be noted that the principal difference beh":een the fixed-reference-group scales u~der consideration and the previously discussed. scales ~ased on natlOn~1 anchor norms is that the latter require the chOIce of a. smgle group that IS broadl representative and appropriate for normative purposes. Apart from the practical difficulties in obtaining such a group and the need to update the norms, it is likely that for many testing purposes such broad norms are not required. . Scales built from a fixed reference group are analogous m one respect to scales employed in physical measurement. In this connection, Angoff (1962}pp. 32--33) writes: There is hardly a person here who knows the precise origina~ definition of ~he I gth of the foot used in the measurement of height or distance, or which it was whose foot was originally agreed upon as the standard; on t~e other hand, there is no one here who does not know how to. evalm~te lengt s and distances in terms of this unit. Our ignora~ce of the precise on.gmal me~n. g or derivation of the foot does not lessen Its usefulness to us In a~y "ay. ~~susefulness derives from the fact that it remains the same ~ver time and allows us to familiarize ourselves with it. Needless to say, .preclsely th~ same considerations applv to other units of measurement-the mch, the mile, th: de ree of Fahrel1h~it, and so on. In the field ofpsych?l.ogical measureme.nt It . g. 'lar]y reasonable to say that the original defimtlOn of the scale IS or IS Slml . . h . t ce of a should be' of no consequence. ~Vhat is of consequence IS t e ~am enan . . t nt scale--which in the case of a multiple-form testmg program, IS cons a·, d 1 .. f s pIe achieved bv rigorous form-to-form equati~g-an . t 1e provlSl~n 0 up.,. or'nlative data to aid in interpretation and III the formation of specific men t alY n , . d't' .. nt decisions, data which would be revised from time to time as con I lOllSwalla .
~:g
COMPUTER UTILIZATION IN THE INTERPRETATION OF TEST SCORES Computers have already made a Sig~i~cant.impact ,upon eve? phase of testing, from test construction to admlmstrahon, sconng, reportmg, and interpretation. The obvious uses of computers-and those develop~d earliest-represent simply an unprecedented increase in the spe~d WIth which traditional data analyses and scoring processes can be earned out. 'mportant however are the adoption of new procedures and F ar more 1 " .' h' h ld the exploration of new approaches to psychological testmg w lC wo~ have been impossible without the fle:dbility, speed, and d~ta-processl~g ('~n:lhiliti('s of computPTS. As Baker (1971, p. 227) SUCCinctlyputs It,
95
computer capabilities should serve "to free one's thinking from the constraints of the past." Various testing innovations resulting from computer utilization will be discussed under appropriate topics throughout the book. In the present connection, we shan examine some applications of computers in the interpretation of test scores. At the simplest level, most current tests, and especially those designed for group administration, are now adapted for computer scoring (Baker, 1971). Several test publishers, as well as independent test-scoring organizations, are equipped to provide such scoring services to test users. Although separate answer sheets are commonly used for this purpose, optical scanning equipment available at some scoring centers permits the reading of responses directly from test booklets. Many innovative possibilities, such as diagnostic scoring and path analysis (recording a student's progress at various stages of learning) have barely been explored. At a somewhat more complex level, certain tests now provide facilities for computer interpretation of test scores. In such cases, the computer program associates prepared verbal statements with particular patterns of test responses. This approach has been pursued with both personality and aptitude tests. For example, with the ~1innesota Multiphasic Personality Inventory (MMPI), to be discussed in Chapter 17, test users may obtain computer printouts of diagnostic and interpretive stl;\tements about the subject's personality tendencies and emotional condition, together with the numerical scores. Similarly, the Differential Aptitude Tests (see Ch. 13) proVide a Career Planning Report, which includes a profile of scores on the separate subtests as well as an interpretive computer printout. The latter contains verbal statements that combine the test data with information on interests and goals given by the student on a Career Planning Questionnaire. These statements are typical of what a counselor would say to the student in going over his test results in an individual conference (Super, 1973). .. Individualized interpretation of test scores at a still more complex level is illustrated by interactive computer systems, in which the individual is in direct contact with the computer by means of response stations and in effect engages in a dialogue with the computer (J. A. Harris, 1973; Holtzman, 1970; M. R. Katz, 1974; Super, 1970). This technique has been investigated with regard to educational and vocational planning and decision making. In such a situation, test scores are usually incorporated in the computer data base, together with other inforn:tation ,,tovided by the student or client. Essentially, the computer com~thes all the available information about the individual with storedt-t' ",bout educational programs and occupations; and it utilizes all re,lev;tnt' facts and relations in answering the individual's questions and aiding him in reaching de-, cisions. Examples of such interactive computer systems, ii!' various stages
Norms and the Interpretation . PrillcijJles of Psychological
Testing
. 1 d IBM's Education and Career Exerationaldevelopment, mc~T;' s S 'stem for Interactive Guidance !:ionSystem (ECES). a~d fi ld I show good acceptance of ation (SIGI). Prehmmary e na s. nts (Harris 1973). systemsby high school stud~nts and1 thel roPfart~edata utilized in t an mtegra par t I) I der to present instructional t results aIso repres~n titer-assisted instructwn (CAd .~ n or t le\'el of attainment, the , . t ch stu ent s curren d I ate the student's responses to 1 appropnate 0 ea 'ermust r.epeated~' s~or.ea~ hi~::~onse history, the student may 'Pg matenal. On t e aSlSo. I . to further practice at the present edto more ad.vanced m:te~:r~~~ he receives instruction in more ,r to a reme~l~l branc . w . nostic anal sis of errors may lead correcr the specific learning taryprereqUIsItematenal. .Dlag ,instructionalprogram desIgned to ltiesidentified in individual cases. f 'ble variant of computer ' t' ally more eaSl ss costly an d opera Ion d ';nstruction (CMI-see . . computer-manage , ion in 1earmng IS , 1 I mer does not interact directly leton,1974). In suc~ syst~~~~t::me:ter is to assist the teacher in
i.
,~~~~u~~:'nT~e i~~~vi~ualize~ il~struct~~n~f~:~~;U~~~'~eu::;~~ 'tionpackages or more ~onventlOn:l t~: rather formidable mass of 'utionof the computer IS to proces f f each student in a '1 d' g the per ormance 0 , ceumulateddal y regar m. 1 d' dl'fferent activity and to 'I I Y be InvOve In a ' ;,omW lere eac I, ma ..' xt instructional step for each these data in prescnbmg the ne -, 'ded by the l' t' of computers are PIOVI ,J,. Examplesof thi,Sapp lCan~~iduallY Prescribed Instruction-see Jsityof Pittsburgh s IPI (1 ) d' Pro)'ect PLAN (Planning for 1968 an .. & GIaser, 1969', Glaser . I n" 1 d b the Amencan i~gin Accordance with Needs) deve ope SYh Brudner & I 1971' Flanagan anner, , s for Researc~e~t ;~~~ninclud~s a progr~m of self-knowled?e, !lr,1975). Pro) d t' al planning 'as well as instruction aualdevelopment, an occupa Ion , "entaryand high school subjects.
'
, h testing that has aroused a surge of USES.~n appro~c t~ enerally desi
of
Test Scores
97
domain-, and objective-referenced. These terms are sometimes employed as synonyms for criterion-referenced and sometimes with slightly differ~nt connotations. "Criterion-referenced," however, seems to have gained ascendancy, although it is not the most appropriate term. Typically, criterion-referenced testing uses as its interpretive frame of reference a specified content domain rather than a specified population of persons. In this respect, it has been contrasted with the usual normreferenced testing, in which an individual's score is interpreted by comparing it with the scores obtained by others on the same test. In criterionreferenced testing, for example, an examinee's test performance may be reported in terms of the specific kinds of arithmetic operations he has mastered, the estimated size of his vocabulary, the difficulty level of reading matter he can comprehend (from comic books to literary classics), or the chances of his achieving a designated performance level on an external criterion (educational or vocational). Thus far, criterion-referenced testing has found its major applications in several recent innovations in education. Prominent among these are computer-assisted, computer-managed, and other individualized, selfpaced instructional systems. In all ,these systems, testing is closely integrated with instruction, being introduced before, during, and after completion of each instructional unit to check on prerequisite skills, diagnose possible leaming difficulties, and prescribe subsequent instructional procedures. The previously cited Project PLAN and IPI are examples of such programs. From another angle, criterion-referenced tests are useful in broad surveys of educational accomplishment, such as the National Assessment of Educational Progress (\Vomer, 1970), and in meeting demands for educational accountability (Gronlund, 1974). From still another angle, testing for the attainment of minimum requirements, as in qualifying for a driver's license or a pilof s license, illustrates criterion-referenced testing. Finally, familiarity with the concepts of criterion-referenced testing can contribute to the improvement of the traditional, informal tests prepared by teachers for classroom use. Gronlund (1973) provides a helpful guide for this purpose, as well as ~ simple and well-balanced introduction to criterion-referenced testing. A brief but excellent 'discussion of the chief limitations of criterion-referenced tests is given by Ebel (1972b).
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CONTENTMEANING. The major distinguishing feature of criterionreferenced testing (however defined and whether designated by this term or by one of its synonyms) is its interpretation of test performance in terms of content meaning. The focus is clearly on u;hat the person can do and what he kno'.\'s, not on how he compares with others. A funda-
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Norms and tIle Interpretation
rinciplrs of Psychological T ('sting equirement in constructing this type of test is a. clearly defined . f knowledge or skills to be assesscd by the test. If scores. on such e to have communicable meaning, the content domam to be ~lust be widely recognized as important. The selected domain subdivided into small units defined in performance terms. llciHQIlUI context these units correspond to behaviorally defined 6nal~.bjectives, 'such as "multiplies three-digit by two-digit •.or "identifies the misspelled word in which the final e is re,hen addl~g -ing." In the programs prepared for in?ividualized ion; these objectives run to several hundred for a smgle school .~Afterthe instructional objectives have been fonnulated, items are d to sample each objective. This procedure is admittedly difficult , e -consuming. \Vithout such careful specification and control of ..t, however, the results of criterion-referenced testing could derite into an idiosyncratic and uninterpretable jumble. ,en strictly applied, criterion-referenced testing is best adapted for ng basic skills (as in reading and arithmetic) at elem~ntary le~e1s. heseareas, insh'uctional objectives can also be arranged m an ordmal archy, the acquisition of more elementary skills being prerequisite :the acquisition of higher-level skills.6 It is impr~eticab~e a?d probably ndesirable, however, to formulate highly speCIfic obJectIves for advancedlevels of howl edge in less highly structured subjects. At these ',ievels,both thc content and sequence of learning are likely to be much 'moreflexible. On the other hand, in its emphasis on content meaning in the interpretation of test scores, criterion-referenced testing may exert a salutary effecton testing in general. The interpretation of intelligence test scores, _,for example, would benefit from this approach. To describe a child's " intelligence test performance in terms of the specific intelJech~al skills and knowledge it represents might help to counteract the confuSIOns a~d misconceptions that have become attached .to the IQ. VVhen stated I~ these general terms, however, the critenon-referenced approa~h IS equivalent to interpreting test sCOTesin t~e light of the demonstra~ed validity of the particular test, rather than m terms of vague underlymg entities. Such an interpretation can certainly be combined with n?rmreferenced scores. MASTERY TESTING. A second major feature almost always found in criterion-referenced testing is the procedure of testing for mastery. Essentiany, this procedure yields an all-or-none score, indicating that the
6ldeaUy, such tests follow the simplex model of a Guttman scale (see Popham & 1T1Isck,] 9(9), as do the PiaF:etian ordinal scales discussed earlier in this chapter.
of Test Scores
99
indiVidual. has ~r has not attained the preestablished level of mastery . When basic skIlls are tested, nearly complete mastery is generally expected (e.g., 80--85% correct items). A three-way distinction may also be employed, including mastery, nonmastery, and an intermediate doubtful, or "review" interval. ' In connection with individualized instru('tion, some educators have argued that, given enough time and suitable instructional methods nearly ~veryone can achieve complete mastery of the chosen instructio~al obJ:etives. Individ~al differences would thus be manifested in learning hme rather than In final achievement as in traditional educational testing (Bloom, 1968; J. B. C~rroll, 1963, 1970; Cooley & Glaser, 1969; Gagne, 1965). It follows t.hat In mastery testing, individual differences in perfo~m~nce are of httle or no interest. Hence as generally constructed cnter~on-refer~nced tests minimize indh'idual differences. For example: they lnclude items passed or failed by all or nearly all examinees although such. ite~ns are usually excluded from no~n-referenced t~sts.' Mas:er~ t.estin? IS r~gularly. employed in the previously cited programs fo~ l~dlvlduahzed mstructIon. It is also characteristic of published cr~tenon-referenced tes~ for basic skills, suitable for elementary school. Exam~le~ of such tes~ mclude the Prescriptive Reading Inventory and Pres~np~lve Mathem~tlCsJnventory (California Test Bureau), The Skills M:omtor~ng System in Reading and in Study Skills (Harcourt Brace o\'anovlch) '. and ~iagnosis: An Instructi onal Aid Series in Reading and In Mathematics (ScLCnceResearch Associates). Beyond basic skills, mastery testing is inapplicable or insufficient. In more. ad~'~nced and less structured subjects, achievement is open-ended. The ll1dlvJ~ual m~~ progress almost without limit in such functions as understandmg, cnbcal thinking, appreciation, and originality. Moreover, content ~vel:a~e m~y p~oc~ed in many different directions, depending upon .the mdl~I~~al s abllibes, interests, and goals, as well as local instructional . unr . factllties. Under these conditions ' complete ma St ery IS rea lStiCan.d unnecessary. Hence norm-referenced evaluation is generally enlployed In such cases to assess degree of attainment. Some published tcsts are so constructed as to permit both norm-referenced and criterionrefe~enced applications. An example is the 1973 Edition of the Stanford AchIevement Test. While providing appropriate norms at each level this batt~ry ~eets three important requirements of criterion-referenced ;ests: speclflc~tlO~ of ~etailed instructional objectives, adequate coverage of each obJective WIth appropriate items, and wide range of item difficulty, It should be noted that criterion-referenced testing is neither as ne~'
!
. : As a resl~lt.of this reduction in variability, the usual methods for findin tdtlJio ~,hty and \'al,d'.ty are,inapplkahle to most criterion-referenced tests. Further sum of these pomts Willbe found in Chapters 5, S, and 8.
irSCIlIl.
Norms and the Interpretation
rinciples of Psychological
Testing
-/
clearly divorced from norm-referenced testing as some of its ts imply. Evaluating an individual's test performance in absolute ch as by letter grades or percentage of correct items, is certainly , er than normative interpretations, More precise attempts to test performance in terms of content meaning also antedate the lion of the term :'criterion-referenced testing" (Ebel, 1962; il,l962-see also Anastasi, 1968, pp. 69-70), Other examples may _ in early product scales for assessing the quality of handwriting, _tions, or drawings by matching the individual's work sample f a set of standard specimens. Ebel (1972b) observes, furtherthe sense of all-orthat the concept of mastery in education-in earning of specific units-achie\"ed considerable popularity in the and 19305and was later abandoned. om1ativeframework is implicit in all testing, regardless of how , are expressed, (Angoff, 1974). The very choice of content or to be measured is influenced by the examiner's knowledge of what e expected from human organisms at a particular developmental or ctional stage. Such a choice presupposes information about what persons have done in similar situations, Moreover, by imposing rm cutoff scores on an ability continuum, mastery testing does not 'by eliminate individual differences, To describe an individual's level ding comprehension as "the ability to understand the content of • ~ett;York Times" still'leaves room for a wide range of indi\'idual erencesin degree of understanding. f
TABLES.Test scores may also be interpreted in terms of eeted criterion performance, as in a training program or on a job, s usage of the term "criterion" follows standard psychometric prac, as when a test is said to be validated against a particular criterion Ch, 2), Strictly speaking, the term "criterion-referenced testing" uld refer to this type of performance interpretation, while the other proaches discussed in this section can be more precisely described as tent,referenced. This terminology, in fact, is used in the APA test PECTANCY
ndards (1974). n expectancy table gives the probability of different criterion outroesfor persons who obtain each test score. For example, if a student tains a score of 530 on the CEEB Scholastic Aptitude Test, what are e chances that hislreshman grade-point average in a specific college ill fall in the A, B, C, D, or F category? This type of information can e obtained by examining tbe bivariate distribution of predictor scores SAT) plotted against criterion status (freshman grade-point average), 'f the number of cases in each cell of sueh a bivariate distribution is Changedto a percentage, the result is an expectancy table, such as the
at Test
Scores
'II 101 one I ustrated in Table 6 Tl d . 171 high school boys en 'II dl~ ata for thIs table were obtained from ' ro e m courses in Am' h' Ictor was the Verbal R' encan Istor)', The pred easomng test of the D'ff t' I . administered earl . th I eren la Aphtude Tests y m e course. The crite . 'd The correlation between test d ~lOn."as en -of-course grades. scores an crltenon was ,66. I
TABLE
6
. Expectancy Table Showing Relation betwe f en DAT lerbal Reasoning Test and Course Grades in America H' t n IS ory or 171 Boys in Crade 11 (Adapted from Fifth Edition Manual for . . th~. DIfferential Aptitude Tests, Forms Sand T, p. ll~. Reproduced by permission Corporation, New York, N.Y. All right~~~;:~~~~,~ 1973, 1974 by The Psychological
~'-=-== -r----=--r:--.:.:---Percentage Receiving Each Criterion Crade Test Score
40 & above 30-39 20-29 Below 20
--=
~umber of Cases
Below 70
70-79
80-89
15
46 36
6
39
22 39
43 46
12 30
63
21
52
17
90
&
above
63
17 5
The first column of Tahle 6 shows h .' . class intervals' the numb f t d t e test SCOles, dlVlded into four " ' er 0 s u ents whose f 11' . IS gIven in the second column The r " scores. a. mto each mterval table indicate the pe t' f emall1l1lg entnes m each row of the 'th' h rcen age 0 cases who received each grade at th d f h WI III eac . test-score interval ~e ;e:b e course. ~hus, of the 46 students wi~h scores of 40 or above celved grades of 70-79 22 al Reasomng test, 15 percent re' percent grades of 80-89 d 63 gra d es of 90 or above At th th ' an percent e 0 er e~treme, of the 46 students scoring below 20 on the test '30 ' percent receIved gr d b I 7 etween 70 and 79 a d 17 a es e ow 0, 52 percent b limitations of the a~ai~ble dPtercent between 80 and 89. Within the estimates of the probabilit ~ha~tthese. p~rcentages. represent the best criterion grade. For exam 'f an mdlVldual WIll receive a given ':e n~w t~udent receives a test score of 34 (i.e" in the 30--39 inte~,:i/ of his obtaining a grade of 90 ~ _" ou . conclude that the probability 17 r of his obtaining a grade betwee ~~ove . out of 100; the probability ~n 9 IS S9'~ of 100, and so on. In many practical situation n. cess" and "failure" in a 'ob ' s, cntena can be dicliotomized. into "sucthese conditions, an e~ e~;::;,se cof study, or othe.r undertak~ng. Under probability of success oP fa"I y hart can be prepared, showing the r I ure corresponding t 'h . ' h 0 eac . score mterval. F Igure 7 is an -example f selection battery developeod ~\h a~.ex:ectanc~ chart. Based on a pilot y e Ir orcc, thIS expectancy en,lirt shows.
0: ?
lS8
CHAPTER No. of
Reliability
Men
9
21,474
8
19,444
7
32,129
6
39,398
5
34,975
••
'23,699
3
11,209
2
2,139
5
refers to the consistency of scores obtained by the same persons when reexamined with the same test on different occasions, or with different sets of equivalent items, or under othel: variable examining conditions. This concept of reliability underlies the computation of the error of measurement of a single score, whereby we can predict the range of fluctuation likely to occur in a single individual's score as a result of irrelevant, chance factors. The concept of test reliability has been used to cover several aspects of score consistency. In its broadest sense, test reliability indicates the extent to which individual differences in test scores are attributable to "true" differences in the characteristics under consideration and the extent to which they are attributable to chance errors. To put it in more technical terms, measures of test reliability make it possible to estimate what proportion of the total variance of test scores is error variance. The crux of the matter, however, lies in the definition of error variance. Factors that might be considered error variance for one purpose would be classified under true variance for another. For example, if we are interested in measuring fluctuations of mood, then the day-by. day changes in scores on a test of cheerfulness-depression would be relevant to the purpose of the test and would hence be part of the true variance of the scores. If, on the other hand, the test is designed to measure more permanent personality characteristics, the same daily fluctuations would fall under the heading of error variance. Essentially, any condition that is irrelevant to the purpose of the test represents error variance. Thus, when the examiner tries to maintain uniform testing conditions by controlling the testing environment, instructions, time limits, rapport, and other similar factors, he is reducing error variance and making the test scores more reliable. Despi~e optimum testing conditions, however, no test is a perfectly reliablei~strument. Hence, every test should be accompanied by a statemellt of its reliability. Such a measure of reliability characterizes the test when administered under standard conditions and given to subjects simil!lT to those constituting the normative sample. The characteristicsof thiss~mple should therefore be specified, together with the type of reliability that was measured.
R
LIABILlTY
904
, R l' bet "een Performance 7 Expectancv Chart ShowlI1g e atlon \, . . , d E1' ' fan from Primary Flight Trall1JUg. IectionBattery an IIDlllaI
G. •
',(From Flanagan, 1947, p, 58.)
~ . ,'thin each stanine on the battery who the pertentage of men scormg 'It b seen that 77 percent . l' W ht trammg can e ,failedto camp :t: pnmary. 19 f 1were eiiminated in the course of train.ofthe men recelVlDg a stamne 0 . 9 f. 'led to complete the " 1I 1 4 t of those at stamne aJ, lng. W Ii c on y percen es the ercentage of failures training satisfactorily. Between these ex.trcm ., . Po the basis of this . 1 the succeSSl'\'e stamnes. n ' , decreases consIstent y over ". f Ie that approximately r , expectancy chart, it ~uld be predlcte , °t e:amPco~e of 4 win fail and 'I t d t who obtain a s an me s 40 percent 0f pI 0 ea e s '1 1t 'marv flight train;tpproximately 60 percent wil1:.atisf~ctor:':b~~~i~ye o~~~cces~ and failure m t eh~ receive each stanine. Thus, an ing. Similar statements .reia: d could be ma.de about. m lVI ua s 60'40 or 3:2 chance of completing individual wIth a stamne o.f 4 has . . . a criterion-referenced interpreprimary flight training. Besldebs provldmthg t both expectancy tables and . f t t es it can e seen a d' 1 'd f the validitv of a test in pre Icttatlol1 0 es scor., expectancy charts give a genera 1 ea 0 , ing a given criterion.
"I ..
d
1
:v
iud/Iles of Psychological Testing could,of course, be as many varieties of test reliability as there 'lions affecting test scores, since any such conditions might be _for a certain purpose and would thus be classified as error varie types of reliability computed in actual practice, however, are few. In this chapter, the principal techniques for measuring the . of test scores will be examined, together with the sources of iance identified by each, Since all types of reliability are con-with the degree of consistency or agreement between two in deBy derived sets of scores, they can all be expressed in terms of a lion coefficient, Accordingly, the next section will consider some ;basic characteristics of conelation caefficients, in order to clarify use and interpretation, More technical discussion of correlation, as as more detailed specifications of computing procedures, can be d:in any elementary textbook of educational or psychological statissuch as Guilford and Fruchter (1973).
9
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9
,
I
OJ
:g 60-69
m
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OF CORRELATION. Essentiallv, a correlation coefficient (T) ex~ssesthe d'egree of correspondence, '01' relationship, between two sets ;scores,Thus, if the top-scoring individual in variable 1also obtains the score in variable 2, the second-best individual in variable 1 is second ..~stin variable 2, and so on down to the poorest individual in the group, ncn there would be a perfect correlation between variables 1 and 2. uch a correlation would ha\'e a value of + 1.00, A hypothetical illustration of a perfect positive correlation is shown in igure 8. This figure presents a scatter diag~\lm, or hivariate distributiOflt, ch tally mark in this diagram indicate~~~e score of one individual in th vllriable 1 (horizontal axis) and vain.\:B1e: 2 (vertical axis). It will be noted that all of the 100 cases in thee grolJ.l) are distributed along ~~ diagonal running from the lower left- to,'theupper right-hand corner of .,'the diagram. Such a distribution indicates a perfect positive correlation (+ 1.00), since it shows that each individual occupies the same relative , ,position in both variables. The closer the bivariate distribution of scares approaches this diagonal, the higher will be the positive correlation. Figure 9 illustrates a perfect negative correlation ( -1.00 ). In this case, there is a complete reversal of scores from one variable to the other. The best individual in variable 1is the poorest in variable 2 and vice versa, this reversal being consistently maintained throughout the distribution. It will be noted that, in this scatter diagram, all individuals fall on the diagonal extending from the upper left- to the lower right-hand comer. This diagonal runs in the reverse direction from that in Figure 8. "- .... ,,1,,.;,,~;."l;,,~t,,~ ('()mnlete "bsence of rdationship, such as
~
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: i
0. MO.O.
()o..
0
i"'P'? 0
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i ,
Score on Variable J
Bivariate D' t'b' f ISn utlOn or a Hypothetical Correlation of +1.00. might occur by chance, If each individ l' 'f' tl.a s n~me were pulled at random out of a hat to determine his were repeated for variabl~ C) pOSI IOn m vanable 1, and if the process Under these conditions l't -, alzderbo~r near~zero correlation would result. , WOu e ImpOSSIblet d' , 0 pre, Ict an 1l1dividual's relative standing in variable 2 from k 1. The top-~oring subJ'ect I'n "bl a1 n~whledge of IllS score in variablE! , valla I" mlg t scar I' I I In variable 2. Some individual 'h b h e ug I, ow, or average ~oth variables, or below ave;a~e~l~gb~th~ ~hance ~core above average in In one variable and below in the oth .' 'Uers might ~all above average average in one and at th ' .er, sh others 11lIght be above the d f , e avel acre 111 the second would be no regularit}, in the relate: h' f ' an so orth. There "d I TI Ie coefficients found in a t I'lOns Ip rom one in d'1\I ua to another. extremes, having some value 'h~ ~1 p~actIce generally fall between these lations between measures of t an zero but lower than 1.00. CorrefrequentlY low When a a I,lIes are nearly ;rlways positive, aIthoug'h " negative conel t' . b' such variables, it usually results f th a IOn IS a tamed between two rom e way in which the scores are expressed, For example 1'£ t' , Ime scores are correla't d 'th I Th ,e;. WI amount scores, a negative correlation wl'11 prob bl u '~f -h b' , , a y resu t. an anthmetic computation t t' d s, '1. cae su lect s score:()n f , es IS recor ed as the xi' b qmred to complete all itenls h"l h' ',pm er a secondsre· , W Ie IS Score on an 'th . ,~, an mehc reasoning test represents the number of bl ' pro ems correctly soh d . 1ahon . ~" a negative correcan be expected In su I h . CIa case, t e poorest (i.e.", slowest) individ-
~1,t'
CHAPTER No. of
Reliability
Men
9
21,474
S
19,444
7
32,129
6
39,398
5
34,975
4
'23,699
3
11,209
2
2,139
5
refers to the consistency of scores obtained by the same persons when reexamined with the same test on different occasions, or with diHerent sets of equivalent items, or under othel: variable examining conditions. This concept of reliability underlies the computation of the error of measurement of a single score, whereby we can predict the range of fluctuation likely to occur in a single individual's score as a result of irrelevant, chance factors. The concept of test reliability has been used to cover several aspects of score consistency. In its broadest sense, test reliability indicates the extent to which individual diHerences in test scores are attributable to "true" differences in the characteristics under consideration and the extent to which they are attributable to chance errors. To put it in more technical terms, measures of test reliability make it possible to estimate what proportion of the total variance of test scores is error variance. The crux of the matter, however, lies in the definition of error variance, Factors that might be considered error variance for one purpose would be classified under true variance for another. For example, if we are interested in measuring fluctuations of mood, then the day-by-day changes in scores on a test of cheerfulness-depression would be relevant to the purpose of the test and would hence be part of the true variance of the scores. If, on the other hand, the test is designed to measure more permanent personality characteristics, the same daily fluctuations would fall under the heading of error variance. Essentially, any condition that is irrelevant to the purpose of the test represents error variance. Thus, when the examiner tries to maintain uniform testing conditions by controlling the testing environment, instructions, time limits, rapport, and other similar factors, he is reducing error variance and making the test scores more reliable. Despite optimum testing conditions, however, no test is a perfectly reliable instrument. Hence, every test should be accompanied by a statement of its reliability. Such a measure of reliability characterizes the test when administered under standard conditions and given to subjects similllr to those constituting the normative sample. The characteristics of thiss~mple should therefore be specified, together with the type of reliabIlity that was measured.
R
LIABILITY
904
. R el'atIon bet \\'ee ., Performance Ch t Showmg IG,7. Expectancy aT p.' . Flight Training. ejectionBattery and Elimination from I1maly n
.{FromFlanagan, 1947, p. 58.)
: . ,thin each stanine on the battery who ,the percentage of men scormg \\ I . . . It b seen that 77 percent , J' fI' ht trammg can e ailed to comp :t: pnmary. Ig f 1were eiiminated in the course of train. 9 f 'led to complete the of the men receIVing a stamne 0 '1 I 4 t of those at stamne al ing, W 111 C on y percen es the ercentage of failures h'aining satisfactorily, Between these ex.trcm ", Po the basis of this . 1 the succeSSl'\'e stanmes. n decreases consistent y over '. f I that approximately r expectancy chart, it ~uld be predlCt,e , °t e~amPcoe~eof 4 will fail and . flight train40 percent 0f pI'J0 t ca d e t s who obtam a s amne 1s itpproximately 60 percent wil1;atis~~~tor~'~b~~~i~ye~f and failure ing, Similar statements re~a~ m~ hp i each stanine. Thus, an could be made about. indlvldua s w 6~.~~c:rv;:2 chance of completing . individual. with a. s~amne o.f 4 has ~idin' a criterion-referenced interpreg primary fhght trammg. Besldebs pro th t both expectancy tables and . f t t scores it can e seen a d' .' I 'd f the validitv of a test in pre lcttatlon 0 es expectancy charts glVe a genera 1 ea 0 ing a given criterion.
d
l:~:::~
J
iflciplesof Psychological Testing
"~ould, of course, be as many varieties of test reliability as there ,jtionsaffecting test scores, since any such conditions might be for a certain purpose and would thus be classified as error varie types of reliability computed in actual practice, however, are few. In this chapter, the principal techniques for measuring the 'f}'of test scores will be examined, together with the sources of illiance identified by each. Since all types of reliability are con,with the degree of consistency or agreement between two inde'flyderived sets of scores, they can all be expressed in tcrms of a 'on coefficient. Accordingly, the next section will consider some basic characteristics of correlation cBefficients, in order to clarify use and interpretation. ?\fore technical discussion of correlation, as ·as more detailed specifications of computing procedures, can be ,in any elementary textbook of educational or psychological statis; such as Guilford and Fruchter (1973),
9
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,
I Essentially, a correlation coefficient (T) exses the d'egree of correspondence, or relotions1Jip, between two sets cores.Thus, if the top-scoring individual in variable 1 also obtains the op score in variable 2, the second-best individual in v-ariable 1is second ~stin variable 2, and so on down to the poorest individual in the group, 'brll there would be a perfect correlation between variables 1 and 2. uch a correlation would ha\'e a value of + 1.00. A hypothetical illustration of a perfect positive correlation is shown in igure 8. This figure presents a scatter diag~ll.m, or bivariate distrihutiOl/,. ach tally mark in this diagram illdicated~e score of one individual in 'oth variable 1 (horizontal axis) and vUllable: 2 (vertical axis). It will be noted that all of the 100 cases in thee groBl) are distributed along "diagonal running from the lower left- t~,'the"upper right-hand corner of :the diagram. Such a distribution indicates a perfect positive correlation , (+1.00), since it shows that each individual occupies the same relative position in both variables. The closer the bivariate distribution of scares approaches this diagonal, the higher will be the positive correlation, Figure 9 illustrates a perfect negative correlation ( -1.00), In this case, there is a complete reversal of scores from one variable to the other, The best individual in variable 1is the poorest in variable 2 and vice versa, this reversal being consistently maintained throughout the distribution. It will he noted that, in this scatter diagram, all individuals fall on the diagonal extending from the upper left- to the lower right-hand comer, This diagonal runs in the reverse direction from that in Figure 8. ,,1..•;,,~ ;."l;r·~tr'~ ('omnlete flbsellce of rdationship, such as
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EA!\'ING OF CORRELATION.
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FIG. 8, Bivariate Distr'b t' f I U IOn or a Hypothetical Correlation of +1.00. might OCcur by chance If each ind' 'd I' out of a hat to determ'ine hi 1I.as n~me \"ere pulled at random , s pOsitIOn In vanahle 1 a d 'f th ' n I e process were repeated for variable" Under these conditions it -, alzderbo~r near~zero correlation would result. , \Vou e ImpOSSible to d' t d relative standing in variable 2 from k pre. IC an in ividual's ~. The top-sl!Oring Subject in variable a 1 ~~w~edge of l~,s SCore in variable In variable 2. Some individ I 'h b g t Score 11lgh,low, or average both vadables or below av:;'l s n~,gbt hY chhance score above average in . ' age In ot . ot ers mightf II b 111 one variable and below in the oth .' '11 .a a Ove average " .er, sh others mIght be above the average in one and at th f h ld b e a\el:lge III the second and .e no regularity in the relationshi from '.. ,. so art, There wou The coefficients fOund in t I ~ one mdl\ Idual to another. extremes, having some value ~~ ~'l .p~achce generally fall between these lations between measures of t an zero but lower than 1,00. CorreI,lies are nearly a-lways positive, althoug'h frequentlv low When a ,. negative con-el t' . b' such variables, it usually results from th a IOn.IS 0 .tamed between two e way III which the scores are expressed. For example if time , ' SCores are correlated with negat.lYc correlation will probabl ' result. Th ';~:'~' , am.ou~t scores, a d d us, 1f~!ch sublect s score'On an anthmetic computation te t .) . d S IS recor e as the dumb f d '~er a secon sre· qUire to complete all items wh'l h' I e IS Score on an arith t' t es t represents the number of' hI '''.' me IC reasoning ' pro ems correctly sol\!cd Ia t'Ion can be expected. In SUell 'h . :,<:,' a negatIve cone,a case, t e poorest (I.e., slowest) individ-
.1:1
a~1.t
Reliability
I
\
./ill I
./iIt./ill
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60-69 -
I
11II11II1
o u Vl
m. Table 7 not the quickest, rf. of the ~terr~latIon coeffiCient more clearly
\
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i Jlltl/tf .IIII./iII
Ii > 50-59 ~ 040-049
I
\ 11IIJIlt JIlt 1/1
.9
tive. .. 'll bWhen 1 some prod uc t s are posItive and some negative the correlation e c ose to zero. ' W1 In actual practice it's t standard score befo' ~ d~o n~cessary to convert each raw scorc to a can be mad . re n mg t e cross-products, since this conversion , he once for all after the cross-products have been added There are manydemonst. s ortcuts foar .computmg.the . . The method Pearson correlation coefficient.
\
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0-
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1
'?
'?
but it illustrates the than other methods
l~
Pears~~ I:~;~:~~t:~~::i\~hor::uts. Table 7 shows the computation of a to each child's nam ~1e IC and reading scores of 10 children. Next reading test (Y) T~ are. hiS s~ores in the arithmetic test (X) and the the res ective c~l e sums an . means of the 10 scores are given under each aJthm ti umn;- The thU'? column shows the deviation (x) of the deviatio~ ero~1 thed~nthmetic mean; and the fourth column, deviations are squareda~n ~~: ;::g /~ore fr~m the reading mean. These squares are used in . x wo co umns, and the sums of the and reading scores ~~~K:t:::!t~h~ ~and~~d /~viations of the arithmetic dividing each x and y by'ts . 0 eSdc~le m Chapter 4. Rather than 1 correspon mg u to find standard scores, we
(yS~o~;
.11/I11I
\
0-
107
r;-
Score on Variable 1
Ic.9. Bivariate Distribution for a Hypothetical Correlation of -1.00.
7
TABLE
Computation of Pearson Product-Moment Correlation Coefficient
. 'ualwillhave the numerically highest score on the first test, while the best individualwill have the highest score on the second. Correlation coefficients may be computed in variom ways, depending on the nature of the data. The. most common is the Pearson ProductMoment Correlation Coefficient. This correlation coefficient takes into a.ceountnot only the person's position in the group, but also the amount of his deviation above or below the group mean. It will be recalled that . wheneach individual's standing is expressed in}erms of standard scores, personsfalling above the average receive positive standard scores, while thosebelow the average receive negative scores. Thus, an individual who is superior in both variables to be corre1al:ed,:would have two positive standard scores; one inferior in both woul~ have two negative standard scores.If, now, we multiply each individ\i&r" tandard score in variable I by his standard score in variable 2, all.at . products will be positive, provided that each individual falls on theA.ame side of the mean on both variables. The Pearson correlation coefficje,))t is Simply the mean of these products. It will have a high positive val\ie:'W~~n corresponding standard scores are of equal sign and of approximately equal amount in the two variables. When subjects above the average in one variable are below the average in the other, the corresponding cross-products will be negative. If the sum of the cross-products is negative, the correlation will be nega-
Arithmetic
Reading
Pupil
X
Y
Bill Carol I Geoffrey
41
17
38
28
48 32 34 36 41 43 47 40 400 40
22 16 18 15 24 20 23 27 210 21
Ann
Bob Jane Ellen
:
Ruth Dick
Mary S M fT.
=
x
y
+1 -2 +8 -8 -6 -4 +1 +3 +7 0 0
-4 +7 +1 -5 -3 -6 +3 -1 +2 +6 0
IN . 10 --
= v'24.40= 4.94
r,,=~=
NUru.
fT,
y'
x:z
1 4 64 64 36 16
16 49 1 25 9
1 9
9 1 4· 36 186
36
49 0
2~4
- 4 -14 8 40 18 24 3
- ~ 14 0 86
-= ~186 10 = v'18.60 = 4.31
86 86 (10)(4.94)(4)R} = 212;91=.40 I
xI}
?
"':.:'Ii';~l . .'''_~~i~i
' .[
-
Reliability
'08
Prillcip1t's of PS!Jchological T('8ting
,
t the end as shown in the correlation form this division only once ad' ' the last column (xI)) have Th oss-pro uets m' d ula in Tab 1e, 7 e cr , d' g deviations in thc x an y · l' the cOITespon lll' d t 1 r) the sum of these cross-pro uc s en found by mu tIp ymg '( lumns,To compute the _~orrelatlOn(N ) , and by the product of the two divided bv the number. of cases ndard de~'iatiol1s (11':
109
whether the two variables are correlated in the population from which the sample was drawn. The minimum correlations significant at the .01 and ,05 levels for groups of different sizes can be found by consulting tables of the significance of correlations in any statistics textbook. For interpretive purposes in this book, however, only an understanding of the general concept is required. Parenthetically, it might be added that significance levels can be interpreted in a similar way when applied to other statistical measures. For example, to say that the difference between two means is significant at the .01 level indicates that we can conclude, with only one chance out of 100 of being wrong, that a difference in the obtained direction would be found if we tested the whole population from which our samples were drawn. For instance, if in the sample tested the bo),s had obtained a significantly higher mean than the girls on a mechanical comprehension test, we could conclude that the boys would also excel in the total population, THE RELIABILITY COEFFICIENT.Correlation coefficients have man)' uses in the analysis of psy.chological data, The measurement of test reliability represents one application of such coefficients. An example of a reliability coefficient, computed by the Pearson Product-Moment method, is to be found in Figure 10. In this case, the scores of 104 persons on two equivalent forms of a Word Fluency test' were correlated. In one form, the subjects were given five minutes to write as many words as:'they could that began with a given letter. The second form was identical, except that a different letter was employed. The two letters were chosen by the test authors as being approximately equal in difficulty for this purpose. The correlation between the number of words written in the two forms,\ of this test was found to be ,72. This correlation is high and significant at the ,01 level. With 104 cases, any correlation of .25 or higher is significant at this revel. Nevertheless, the obtained correlation is somewhat lower than is desirable for reliability coefficients, which usually fall in the .80's or .90's, An ~nation of the scatter diagram in Figure 10 shows a typical bivariate distribution of scores corresponding to a high positive correlation. It will be noted that the tallies cluster c~ose to the diagonal extending from the lower left- to the upper right-haridcorner; the trend is definitely in this direction, although there is a certain amount of scatter of individual entries. In the follOWing section, the uSe of the correlation coefficient in computing different measures of test reliability will be con' sidered.
lOne of the subtests of the SRA Tests of Primary Mental Abilities' for Ages 11 to 17. The data were obtained, in an investigation by Anastasi and Drake (1954).
ReliabilifY
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1954.)
;1;;:TYPES OF RELIABILITY
r,
ost obvious method for finding the reThe m. h'd ntical test on a second occaliabilityof te.st ~c~res is by. rcpeCatll1)gi:;h~S:ase is simply the correlation . " sian.The I'ehablhty coeffiCIent Tn on the two administra' d by the same persons ~betweenthe scores 0bt ame d to the random fluctua. Th . variance correspon s " lionsof the test. e enor . t the other These variations . f test seSSIOn 0 • tionsof performance rom one n d t ting conditions such as extreme may result in part from uncontr? e eds ther distractions or a broken . th dden nOlses an 0 '. h h they arise from changes in t e changes m wea er, su pencil point. To so~e ext:nt, lfowev~~~strated by illness, fatigue, emocondition of the subject h1l11Se.' as 1 f pleasant or unpleasant nature, . ecent experIences 0 a tionalstram, worry, r . ., h the extent to which scores on a test th higher the reliability, the and the like. Retest reliabIlIty sows. can hr I!eneralized over different occaSlDns; e ,
TEST-RETEST
RELIABILITY.
111
less susceptible the scores are to the random daily changes in the condition of the subject or of the testing environment. When retest reliability is reported in a test manual, the interval over which it was measured should always be specified. Since retest correlations decrease progressively as this interval lengthens, there is not one but an infinite number of retest reliability coefficients for any test. It is also desirable to give some indication of relevant intervening experiences of the subjects on whom reliability was measured, such as educational or job experiences, counseling, psychotherapy, and so forth. Apart from the desirability of reporting length of interval, what considerations should guide the choice of interval? Illustrations could readily be cited of tests showing high reliability over periods of a few days or weeks, but whose scores reveal an almost complete lack of correspondence when the interval is extended to as long as ten or fifteen years. Many preschool intelligence tests, for example, yield moderat~ly stable measures within the preschool period, but are virtually useless as predictors of late childhood or adult IQ's. In actual practice, however, a simple distinction can usually be made. Short-range, random fluctuations that occur during intervals ranging from a few hours to a few months are generally included under the error variance of the test score. :rhus, in checking this type of test reliability, an effort is made to keep the interval short. In testing young children, the period should be even shorter than for older persons, since at early ages progressive developmental changes are discernible over a period of a month or even less. For any type of person, the interval between retests should rarely exceed six months. Any additional changes in the relative test performance of individuals that occur over longer periods o£ time are apt to be cumulative and progressive rather than entirely random. Moreover, they are likely to characterize a broader area of behavior than that covered by the test performance itself. Thus, one's general level of scholastic aptitude, mechanical comprehension, or artistic judgment may have altered appreciably over a ten-year,period, owing to unusual intervening experiences. The individual's status may have either risen or dropped appreciably in relation to others of his own age, because of circumstances peculiar to his own home, school, or community environment, or for other reasons such as illness or emotional disturbance. The .extent to which such factors can affect an individual's psychological development provides an important problem for investigation. This question, however, should not be confused with that of the reliability of a particular test. When we measure the reliability of the StanfordBin~t, for example, we do not ordinarily correlate retest _~~res over a '-T.p be sure, penod of ten years, or even one year, but over a few ,,~et:1ks. long-range retests have been conducted wit~ such tests-; bpt the results are ~enerally discussed in terms of the predictability of adult intelligence
Prillciples of PsycllOlogical Testing omchildhood performance, rather than in terms of the reliability of a rticulartest. The concept of reliability is generally restricted to shortge, random changes that characterize the test performance itself .r;ilherthan the entire behavior domain that is being tested, It should be noted that different behavior functions may themselves .ry in the extcnt of daily fluctuation they exhibit. For example, steadiess of delicate finger movements is undoubtedly more susceptible to , ht changes in the person's condition than is verbal comprehension, If wish to obtain an over-all estimate of the individual's habitual finger diness, we would probably require repeated tests on several days, reas a single test session would suffice for verbal comprehension, ~gainwe must fall back on an analysis of the purposes of the test and 9iJ a thorough understanding of the behavior the test is designed to preBiet, :'l' Although.apparently simple and straightforward, the test-retest tech, '~iquepresents difficulties when applied to most psychological tests. lPracticewill probably produce varying amounts of improvement in the ~testscores of different individuals. Moreover, if the interval between reestsis fairly short, the examinees may recall many of their former reooses.In other words, the same pattern of right and wrong responses _likelyto recur through sheer memory. Thus, the scores on the two ad1Jlinistrations of the test are not independently obtained and the correIabetween them will be spuriously high, The natt\re of the test itself ay also change with repetition, This is especially true of problems inlyingreasoning or ingenuity. Once the subject has grasped the princiinvolvedin the problem, ur once he has worked out a solution, he can roduce the correct Iesponse in the future without going through the ervening steps. Only tests that are not appreciably affected by.'if!.'Jetin lend themselves to the retest technique, A number of sensory dis(~riminationand motor tests would fall into this category, For the large ,majorityof psychological tests, however, the retest technique is inapropriate.
RELIABILITY. One way of avoiding the difficulties enuntered 1n test-retest reliability is through the use of alternate forms the test. The same persons can thus be tested with one form on the stoccasjon and with another, comparable form on the second. The corlation between the scores obtained on the two forms represents the 'ability coefficient of the test. It will be noted that such a reliability efficientis a measure of both temporal stability and consistency of nse to different item samples (or test forms). This coefficient thus binestwo ty,pes of reliability. Since both types are important for most
. ALTERNATE-FORM
Reliability
113
testing purposes 110.... I measure for e\'al~at' 'ever, a temate-form reliability provides a useful mg many tests. The concept of item sam Iin ' alternate-form reliability bu~ al~ ~;hcontellt salllpl~llg: ?lIderlies not only . er types of reltabIhty to be discussed shortlv. It is the f re ore appropnate to ex . 't has probably h d th' amlOe 1 more close lv, Everyone a e expenence of taking . ..he felt he had a "I k b k" a course exammatlOn in \vhich very topics he happue~:d t~e~aveb;~:~:e many of the items covered the easion, he may have had th . ed mo~t carefully, On another oce opposite expenence, finding an unusually large number of l't . ems on areas he had f 'I d situation illustrates error va . I al e to reVICW, This familiar what extent do Scores on th.n~nc: ;esu ting from content sampling, To ticular selection of items? I:sa ~'ff epen? on ~actors speci~c to the parently, were to pre!)are another te It ~rent IO vestlgator,workmg independt' h s In accor dance with the 'fi IOns, ow much would an indi .d l' . same speci caLet us suppose that a 40't VI ua bS slcore differ on the two tests? -I em voca u ary t t h b a measure of general verbal c ,e.s - as een constructed as ~ist of 40 different words is ass~:b~:~e;~:~~~ :ow suppose that a second Items are constructed with I ame purpose, and that the cultv as the first test The d,effqua can~ to cover the same range of diffi. d: , ,I erences 111 the sco e bt' d b y the same m lVIduals on these two tests 'II t r s 0 ame ,IUS rate the type of ' conSIderation. Owing to fortuitous f . error vanance under ferent individuals the relat' , d'ffi aftors In the past experience of difwhat from pcrso~ to pe !VeT]·1 cu ty of the two lists will vary Somerson. IUS the Ii t I' t . h number of words unfamiliar to individ ;s IS mIg t contain a larp;el.ua A than does the second list. The second list on the oth h d er an mIght co t' d' 1arge number of' words unfamiIi t d' 'd n am a Isproportionately . d"d I ar 0 111 IVI ua lB If the t are apprOXimately equal in thei II . WO 111 IVI ua ~ "true scores") B' will neverth I r overa word knowledge (i.e., in thei~ excel B on th~ second The eIe~ excel A on the first list, while A will re therefore be reversed o'n th t a ].ve standing of these two persons will . e wo Ists o' t h selection of items, ' wmg 0 c anee differences in the I
•
' .. Like lest-retest rcliabilit, alt .£ accompanied by a stateme~' f t~rntc- ~rm rdl~bIhty should always be ministrations as well as ado . t~ engft of the mterval between test adescnp Ion 0 relevant' t . If t h·'e two forms are administered' . In ervenmg experiences. Ifn Immediate succession, the resulting correlation shows reliabilit . y across orms only not . error vanance in this cas 8' ' across occasIOns. The e represents uctuat'o' f one set of items to another b t H ,I ns In per ormance from In the d I ' u not uctuations over time eve Opment of alternate forms h Id· . cised to ensure that the are trul ' care s ou ..?f ('Ourse be exerof a test should be jnd~endc t{ parallel. F~ndamentaJ)y, parallel forms same specifications. The tests :h~ ~nstruct~ tests desi~ed to meet the U ('Ontam the same number of 1't elDS, .. .
Reliabilify
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10. A Reliability Coefficient of .72.
Data from An8~tasi & Drake,
1954.)
':TYPES OF RELIABILITY ,
ost obvious method for finding the reRELIABILITY. The m. h 'dentical test on a second occaTEST-RETEST .. liabilityof test scores is by. rcpeatlll)g.t :h~ ase is simply the correlation .: 'sion.The l'eliability coefficlenf (Tn III IS C, n the two administra. d b the same persons 0 \[1betwe~i'Ithe scores 0b tame Y. d to the random fluctua. Th . vanance correspoll S '; tions of the test. e enor . t the other These variations .. f e test seSSIOn 0 • " tions of performance rom on II d t t'ng conditions such as extreme , I' rt f ncontro e es 1 ' k may resu t 111 pa rom u . d ther distractions or a bro en I • h dden nOlses an 0 " h changes 111 we at er, su th y arise from changes m t e . . T extent however, e . pend pomt. 0 so~e .' f 'Uustrated by illness, fatigue, emocondition of the subject hmlsel : as 1 f pleasant or unpleasant nature, · recent expenences 0 a t . ., h the extent to which scores on a tes tionaI stram, worry, and the like. Retest rehablhty sows. the higher the reliability, the can he I':eneralized over different occaSIOns;
111
less susceptible the scores are to the random daily changes in the condition of the subject or of the testing environment. When retest reliability is reported in a test manual, the interval over which it was measured should always be specified. Since retest correlations decrease progressively as this interval lengthens, there is not one but an .infinite number of retest reliability coefficients for any test. It is also desirable to give some indication of relevant intervening experiences of the subjects on whom reliability was measured, such as educational or job experiences, counseling, psychotherapy, and so forth. Apart from the desirability of reporting length of interval, what considerations should guide the choice of interval? Illustrations could readily be cited of tests showing high reliability over periods of a few days or weeks, but whose scores reveal an almost complete lack of correspondence when the interval is extended to as long as ten or fifteen years. Many preschool intelligence tests, for example, yield moderarely stable measures within the preschool period, but are virtually useless as predictors of late childhood or adult IQ's. In actual practice, however, a simple distinction can usually be made. Short-range, random fluctuations that occur during intervals ranging from a few hours to a few months are generally included under the error variance of the test score. :rhus, in checking this type of test reliability, an effort is made to keep the interval short. In testing young children, the period should be even shorter than for older persons, since at early ages progressive developmental changes are discernible over a period of a month or even less. For any type of person, the interval between retests should rarely exceed six months. Any additional changes in the relative test performance of individuals that occur over longer periods of time are apt to be cumulative and progressive rather than entirely random. Moreover, they are likely to characterize a broader area of behavior than that covered by the test performance itself. Thus, one's general level of scholastic aptitude, mechanical comprehension, or artistic judgment may have altered appreciably over a ten-year, period, owing to unusual intervening experiences. The individual's status may have either risen or dropped appreciably in relation to others of his own age, because of circumstances peculiar to his own home, school, or community environment, or for other reasons such as illness or emotional disturbance. The .extent to which such factors can affect an individual's psychological development provides an important problem for investigation. This question, however, should not he confused with 'that of the reliability of a particular test, When we measure the reliability of the StanfordBinet, for example, we do not ordinarily correlate retest :~~res over a period of ten years, or even one year, but over a few weeks,'~'£p he SUfe~ long-range retests have been conducted wit~ such tests:; bpt the .fcsults are generally discussed in terms of the predictability of adult intelligence
Prillciples of Psychological Testing om childhood performance, rather than in terms of the reliability of a rticulartest. The concept of reliability is generally restricted to shortnge, random changes that characterize the test performance itself therthan the entire behavior domain that is being tested. It should be noted that different behavior functions may themselves , in the extent or daily fluctuation they exhibit. For example, steadiof delicate finger movements is undoubtedly more susceptible to ht changes in the person's condition than is verbal comprehension, If wish to obtain an over-all estimate of the individual's habitual finger diness, we would probably require repeated test~ on several days, 'hereas a single test session would suffice for verbal comprehension, gainwe must fall back on an analysis of the purposes of the test and i1 a thorough understanding of the behavior the test is designed to pret.
Althoughapparently simple and straightforward, the test-retest techique presents difficulties when applied to most psychological tests, .racticewill probably produce varying amounts of improvement in the .testscores of different individuals. Moreover, if the interval between res is fairly short, the examinees may recall many of their former I'e. Dnses.In other words, the same pattern of right and wrong responses .4 likelyto r~cur through sheer memory. Thus, the scores on the two adinistrationsof the test are not independently obtained and the correIan between them will be spuriously high, The natnre of the test itself :ayalso change with repetition, This is especially true of problems inDIvingreasoning or ingenuity. Once the subject has grasped the pdnci"Ieinvolvedin the problem, or once he has worked out a solution, he can produce the correct response in the future without going through the itervellingsteps, Only tests that are not appreciably affected by"lfi,etitiDnI~nd themselves to the retest technique. A number of sensory dis,criminationand motor tests would fall into this category. For the large ajority of psychological tests, however, the retest technique is inap' opriate,
ALTERNATE-FORM RELIABILITY. One way of avoiding the difficulties enimteredin test-retest reliability is through the use of alternate forms the test. The same persons can thus be tested with one form on the stDccasjonand with another, comparable form on the second. The coration between the scores obtained on the two forms represents the 'ability coefficient of the test. It will be noted that such a reliability cient is a measure of both temporal stability and consistency of nse to different item samples (or test forms). This coefficient thus binestwo types of reliability. Since both types are important for most
Reliability
~:~:~t~;~~':~~~~~:g'enYlear,
113
altternate-form reliability provides a useful ny ests. The concept of item sam tin ' altemate-fOlm reliability bu~ al~ ~;hcontellt sampl:llg: ~nderlies not only . er types of reltabllIty to be disclIssed short Iv. It is the f has p;obably h drethoreappr.opnate to examine it more closely, Everyone a e expenence of tak' g , he felt lIe had a "I k b k» 'In a course examination in which uc v rea because f h . very topics he happen~d to have studi many 0 t e Items covered the casion, he may have had th ' ed mo~t carefully, On another oclarge number of I't e opposIte expenence, finding an unusually ems on areas he had f 'I d . situation illustrates error' I al e to reVICW. This familiar what extent do Scores on ~~n~nc: ;esu ting from content sampling. To ticu]ar selection of items? Ifls eds'Hepen? on factors specific to the par. a I erent mvestigator k' . d ent Iy, were to preIJare another t t' d ' wor mg In ependt' h es m accor ance with th 'fi e same specI caIOns, ow much would an indi .dr, Let us suppose that a 40-'t VI ua bS slcore differ ort the hm tests? I em voca u ary test h b a measure of general verbal c h' . - as een constructed as ~ist of 40 different words is ass~:1~:d e:::~~~ ~ow suppose that a second Items are constructed with I ame purpose, and that the qua culty as the first test The d.eff can; to cover the same range of dim. d: , '. I erences 111 the sco e bt' d b r s a ame y the same III JVldua]s on these two tests ']1 t . I us rate the type of ' consIderation. Owing to fortuito f ' error vanance under ferent individuals the relat' d~~ ators In the past experience of difwhat from pcrso~ to pe Ive ·I cu ty of the two lists wiII vary SomerSOll. TIlUS the fi t I' t . h rs IS mlg t contain a larger number of words unfamiliar to individ ,ua] A than does the second list. The second list on the oth h d er an might conta'n d' 1arge number of' words unfamilia t' . d"d I I a Isproportionately lVI are apprOXimately egual in the; r 0 111n ua B. If the two individual~ ov ra "true scores"), B -will neverthele:s : word knowledge (i.e., in their excel B on the second Th ], e cel A on the first list, while A will re therefore be reversed o'n the t atll.ve standing of these two persons will . eWolstso' t h selection of items. ' wmg 0 c ance differences in the 'f '. , Like lest-retest rcliabilit· alt accompanied by a stateme~' f t~m:te- ~nn rell~blhty should always be ministrations as well as ado , t~ engft of the Interval between test adescnp Ion 0 relevant . t ' If t h·'e two forms are administered' . 111 ervenmg experiences. 'fn Immediate succession, the resulting correlation shows reliabilit . . y across orms only not error vanance in this cas fl' ' across occasIOns. The e represents uctuat'o' f R . I ns In per ormance from one set of items to another b t In the d I ' u not uctuations over time eve Opment of alternate forms h Id" . cised to ensure that the are tm] , care s ou ..of (,'ourse be exerof a test should be ind~endc t{ parallel. Fundamentally, parallel forms same specifications. The tests :h~ ~nstruct~d tests desi~ed to meet the U contam the same number of items , .
Principles of Psychological Testing
:,d the 'items should be expressed in the same form and should cover the metype of content. The range and level of difficulty of the items should o be equal. Instructions, time limits, illustrative examples, format, and I other aspects of the test must likewise be checked for comparability. It should be added that the availability of parallel test forms is desirIe for other reasons besides the determination of test reliability. Alterte forms are useful in' follow-up studies or in investigations of the ects of some intervening experimental factor on test performance. The useof several alternate forms also provides a means of reducing the possibilityof coaching or cheating. Although much more widely applicable than test-retest reliability, al"temate-form reliability also has certain limitations. In the first place, if the behavior functions under consideration are subject to a large practice elfeet, the!'use of alternate forms will reduce but not eliminate such an 'effect. To be sure, if all examinees were to show the same improvement with repetition, the correlation between their scores would remain un,"affected,since adding a constant amount to each score does not alter the <:orrelationcoefficient. It is much more likely, however, that individuals will differ in amount of improvement, owing to extent of previous practice with similar material, motivation in taking the test, and other factors. Under these conditions, the practice effect represents another source of variance that will tend to reduce the correlation between the two test forms, If the practice effect is small, reduction will be negligible. Another related question concerns the degree to which the nature of the test will change with repetition. In certain types of ingenuity problems, for example, any item involving the same principle can be readily solved by most subjects once they have worked out the solution to the first. In such a case, changing the specific content of the items in the second form would not suffice to eliminate this carry-over from the first form. Finallv, it should be added that alternate forms are unavailable for many tests, because of the practical difficulties of constructing comparable forms. For all these reasons, other techniques for estimating test reliability are often required.
Reliability
th
Once the two half-scores have b b' d be correlated by the usual m th een a tame for each person, they may shoufld be noted, however, that this correlation actuallv gives th e °l.d'b~lt. 'f hoe re la I It" a onlv a half test F 'I . - . . or examp e, I t e entire test consists of 100 ite - h ' tween two sets of scores each a .ms,. t e correlatIon IS computed betest-retest and alternate-fotm r:I;;~~~~,ls bas~d on only 50 items, In both f ' . -' on t e other hand, each score is based on the full nu b . m er 0 Items In the test Other thmgs being equ I th I . It is reasonable t . a I' e ~nger a test, the more reliable it will be? If' o expect t Iat, WIth a lar arrive at a more adequate and . ger samp e a behaVIOr, we can . ' consIstent measure The ff t th I h emng or shortening a test will hav . , .' e ec at engt f e allI Its ~oefficlent can be estimated by means of the Spearman-Bra wn ormu a, gIVen below: nr'lI
'II
=: ~--,,----_
, l+(n-l)r'u in which t is the estimated ffi' n is the number of times th ~o~. c~ent, ~11 the obtained coefficient, and number of test items is incr:a eS ~ eng~ ened or shortened. Thus, if the d from 60 to 30, n is %. Th sse rom 2.'Jto 100, n is 4; if it is decreased determining reliability bv ~heP:ari~~ntrown formula is Widely used in porting reliability in this 'fo p a f m.ethod, m~ny test manuals re, formula always involves do~~in"'~~: tpphed to spht-haIf reliability, the clitions, it can be simplified as f~Iows:ength of-the test. Under these con-
'1
SPLIT-HALF RELIABILITY, From a sin'gle,:administration of one form of a test it is possible to arrive at a measure 'of, reliability by various split-half procedures. In such a way, two scores are obtained for e~c1i person by dividing the test into comparable halves. It is apparent that split-half reliability provides a measure of consistency with regard to content sampling. Temporal stability of the scores does Ilot enter into such reliability, because only one test session is involved: This type of reliahility coefficient is sometimes called a coefficient of internal consistency, since only a single administration of a single form is required.
lIS
To find split-half reliabilit tl Ii. . order to obtain th y, Ie 1st problem IS how to split the test ill divided in man ~ most nearly comparable halves. Any test can be second half w~urd dl~e~ent wars. In most tests, the Rrst' half and the no difficulty level of 't e comparable, owing to differences in nature and I ems, as well as to the cu I t' If f Ul), })ractice fatig b d mu a Ive e ects 0 warming , ue, ore am and am' tI f sively from the beginning to th~ end ~f at Ie; ;ctors varying progresquate for most purposes is to fi d th e es.. procedure that is adeof the test. If the items we .n. e scores on the odd and even items of difficulty such a dl' . ~e on?llndally an.anged in an approximate order . I , VIsIon Yle s verv ne I· One precaution to b b d . .' ar)' eqUlva ent half-scores. e a serve 111 making such dd I' an a -even sp It pertains to groups of items d l' . h' ea mg WIt a smale problem h ferring to a particular mechanical di~ . ' sue. as questions rereading test. In this case a whole r glam. or to a gIven passage in a tact to one or the other h~lf \Vere ~ o~p of ~tems should be assigned inin different halves of the t~st th .e I:e~ls In such a group to be placed . '. e Slml anty of the half-scores would be spuriousl inflated' might aIf~ct items 'i~l~c;t~n~a~~,:~.leerror in understanding of the problem
Lenulhening a test h .I . " . ' owever, wll Increase 0 I "t, " . tent samplmg not its sl b'I't .,' n y. I S conSIstency m tenns of con, a II} over hme (see Cureton, 1965). ' 2
Principles of Psychological Testing
Tn
Reliability
2r'1I = 1 + r'lI
. s it-half reliability was developed by An alternate method for findmg p. f th differences between . 0 Ily the vanance a e I Ion (1939). It reqUires I If t ( , ) and the variance of tota f I ' the two ha -tes Sad ch person s scores on b 't t d in the following ormu a, res (a'r); these two values aTe su stJ u e. ,. hich yieids the reliability of the whole test duectl) . u'e!
111
= 1- -,u:;
,r , hi of this formula to the definition of . It is interesting to note the relations p 's scores on the two half'. , A d'ff ce between a person . 'd d 'errorvanance. ny I eren 'f these differences, dlvl e ' h r The vanance 0 , . 'tests represents c ance eTTO. , 'es the roportion of error variance 111 by the variance of total scores, gl\ 'b P t d from 1 00 it gives the h' 'ariance IS SU trac e , , I to the reliability coefficient. he scores. When t IS error \ h' h . proportion of "true" variance, w IC IS equa ,
. A fourth method for finding reliability, f . I form is based on the . 1 d" t 'ahon 0 a slllg e , , the test This interitem conalso utiliZing a slIlg e a mmlslII , f onses to a Items m . f ariance' (1) content samconsistencv 0 resp d by two sources a error v , h ,;:sistenclj is ~n uence . d s lit-half reliability); and (2) etero\1 piing (as III altemat~-form an. p m led. The more-homogeneous the geneitv of the behavlOr domalll sa.P ' For example if one test int enc\. ' • h' h tl . lteritem conSIS , b h'1 lo'ther cOllllJrises addition, su _ domain, the Ig er Ie 11 I . I' l' 'tcms w leal b hI " eludes only mu tip Ica IOn I ..'.. the former test will pro a y I· I' t' and dIVISIOnItems, ' traction, mu tip Ica lOn, h th latter In the latter, more h . . 't onsistenc\' t an e, ' show more mten em c "f better in subtraction t an III ' t t e subJ'ect ma\' per orm 1 ' heterogeneous es, on. "ons' another subject may score re a~, any of the other arithmetIc operatl ly in addition, subtrac'tems but more poor b h d' " , A ore extreme example would e tively well on t e IVI510n I tion and multiplication; and so on. mb I items in contrast to one ' b t . ti I IT of 40 voca u ary, . represented y a tcs consls I/::). I I t'ons 10 arithmetic reasomng, b 1 10 spaha re a I 0, ' containing 10 voca u ar~, ~ the latter test, there might be little or and 10 perceptual speed Item~'dI. 'd r performance on the different no relationship between an III IVI ua s KUDER·RICHARDSON RELIABILIT1:..
'. a
0'
0
0
.'
,
types of items. ill be less ambiguous when derived ., It is apparent that test scores w h t'. the highly heteroget ts Suppose t a III from relatively homogeneo~ es S' 'th and Jones both obtain a score of neous, 40-item test cited ave, rfml s of the two on this test were e 20, Can we conclude that the Ph ormance tly completed 10 vocabulary ? N t II Smith may aye correc .. equal. ot a a . 's and none of the arithmetic reasomng items, 10 perceptual speed ~tem 't t Jones may have received a score and spatial relations items, neon ras ,
U7
·of 20 by the successful completion of 5 pcrccptual speed, 5 spatial relations, 10 arithmetic reasoning, and no vocabulary items, Many other combinations could obViously producc the same total score of 20. This Score would have a very different meaning when obtained through such dissimilar combinations of items. In the relatively homogeneous vocabulary test, On the other hand, a Score of 20 would probably mean that the Subject llad succeeded with approximately the first 20 words, if the items were arranged in ascending order of difficulty, He might have failed two or three easier words and correctly responded to two or three more difficult itcms beyond the 20th, but such individual variations are slight in comparison with those found in a more heterogeneous test . A highly relevant question in this connection is whether the criterion that the test is trying to predict is itself relatively homogeneous or heterogeneous. Although homogeneous tests are to be preferred because their Scores permit fairly unambiguous interpretation, a single homogeneous test is obViously not an adequate predictor of a highly heterogeneous criterion. lvforeover, in the prediction of a heterogeneous criterion, the heterogeneity of test items would not necessarily represent error variance. Traditional intelligence tests provide a good example of heterogeneous tests designed'to predict heterogeneous criteria. In such a case, however, it may be desirable to construct several relatively homogeneous tests, each measuring a different phase of the heterogeneous criterion, Thus, unambiguous interpretation of test scores could be combined with adequate criterion coverage. The most common procedure for finding interitem consistency is that developed by Kuder and Richardson (1937). As in the split-half methods, interitem consistency is found from a single administration of a single test. Rather than requiring two half-scores, however, such a technique is based on an examination of performance on each item. Of the various formulas derived in the original article, the most Widely applicable, commonly known as "Kuder-Richal'dson formula 20," is the follo ing: w 3
In this formula, rll is the reliability coefficient of the whole test, n is the number of items in the test, and IJ't the standard deviation of total SCOl'es on the test. The only new term in this formula, 'S.pq, is found by tabulating the proportion of persons who pass (p) and the proportion who do not pass (q) each item. The product of p and q is computed for each item, and these products are then added for all items, to give ~pq. Since in the ptocess of ~est construction p is often routinely recorded in order 3
A Simple dcrivatiolJ of this formula can be found in Ebel (1965, ppo 32!hS27).
Pri'lcipks of Psychological
u8
Reliability
Testing
i6'find
the difficulty level of each item, this method of determining rci~bilityinvolves little additional cO,mputation. l' bT ,fIt can be shown mathematically that the Kuder-Ri~hardson r~ la Ilty , cient is actually the mean of aU split-half coeffiCients .resultll1~ from ent splittings of a test (Cronbach, 1951).4 The ordmary spht-half dent, on the other hand, is based on a planned split design~d to equivalent sets of items. Hence, unless the test items are hIghly mogeneous, the Kuder-Richardson coefficient will be .lo\~er than t~e lit-halfreliability. An extreme example will serve to hl.ghlight t?e dlf erence.Suppose we construct a 50-item test out of 25 diHerent kmd~ a emssuch that items 1 and 2 are vocabulary items, items 3 and 4 antheticreasoning, items 5 and 6 spatial orientation, a~d so on. The odd.and venscores on this test could theoretically agree qmte clos:ly, thus. YIeld'ng a high split-half reliability coefficient. The homogeneity of. thiS test, ince there would be little consistency of owever,wou Id be very low • S " ld erformance among the entire set of 50 items. In thIS example, we wou. '~xpectthe Kuder-Richardson reliability to be much lower th\lD th~ splIthalfreliability. It can be seen that the diHerence between Kuder-~Ichard,son and split-half reliability coefficients may serve as a rough ll1dex of
f
i,
. the heterogeneity of a test. The Kuder-Richardson formula is applicable to tests whose Items are scored as right or wrong, or according to some other all-or-none syste~. Sometests however may have multiple-scored items. On a personahty inventory,for exampie, the respondent may receive a di,~erent n,~~erical score on an item, depending on whether he checks . usually, some. " " I" "ne\1el'" For such tests a generahzed formula has times, rare y, or· ' . k been derived known as coefficient alpha (Cronbach, 1951; NOVIC & Lewis, 1967).' In this formula, the value ~pq is replaced by ~u'i, ~he sum of the variances of item scores. The procedure is to find the vana~ce of all individuals' scores for each item and then to ~dd these v~na~ces across all items. The complete formula for coeffiCIent alpha IS glVen below:
_ (~)U't - ~U'; TlI -
n- 1
119
one case, error variance covers temporal fluctuations; in another, it refers to differences between sets of parallel itcms; and in still another, it includes any interitem inconsistency. On the other hand, the factors excluded from measures of error variance are broadly of two types: (a) those factors whose variance should remain in the scores, since they are part of the true differences under consideration; and (h) those irrelevant factors that can be experimentally controlled. For example, it is not customary to report the error of measurement resulting when a test is administered under distracting conditions or with a longer or shorter time limit than that specified in the manual. Timing errors and serious distractions can be empirically eliminated from the testing situation. Hence, it is not necessary to report special reliability coefficients corresponding to "distraction variance" or "timing variance." Similarly, most tcsts provide such highly standardized procedures for administration and scoring that error variance attributable to these factors is negligible. This is particularly true of group tests deSigned for mass testing and computer scoring. 'With such insb'uments, we need only to make certain that the prescribed procedures are carefully followed and adequately checked. 'Vith~clinical instruments employed in intensive individual examinations, on the other hand, the!'e is evidence of considerable "examiner variance:' Through special experimental designs, it is possible to separate this variance from that attributable to temporal fluctuations in the subject's condition or to the use of alternate test forms. ~ne source of error variance that can be checked quite simply is scorer tests of creativity and projective vanance. Certain types of tests-notably tests of personality-leave a good deal to the judgment of the scorer. \Vith such tests, there is as much need for a measure of scorer reliability as there is for the more usual reliability coefficients. Scorer reliability can be found by having a sample of test papers independently scored by two examiners. The two scores thus obtained hv each examinee are then correlated in the usual way, and the resulti~g correlation coefficient is a measu,re of scorer reliability. This type of reliability. is commonly computed when subjectively scored instruments are e.mployed in research. "»est manuals should also report it when appropriate. '
u't
A clear description of the computational
layout for finding coefficient alpha can be found in Ebel (1965, pp. 326-330). SCORER RELIABILITY. It should now be apparent that the difIer:nt types of reliability vary in the factors they subsume under error vananee. In 4 This is strictly true only when the split-half coefficientsare found by the Rulon formula,not when they are found by correlation of halves and Spearman-Brown formula(Novick & LewiS, 1967).
OVERVIEW. The diHerent types of reliability coemsiel),ts discussed in this section are summarized in Tables 8 and 9. In Tablit18'the operations followed in obtaining each type of reliability are classffled,-,with regard to number of test forms and number of testing sessions required. Table 9 shows the sources of variance treated as error vitri~nce b},;,~achprocedure. Any reliability coefficient may be interpreted directly"in terms of the percentage of score variance attributable to different sources. Thus, a reliability coefficient of .85 signifies that 85 perceI1t 9f the variance in test
Reliability
121
Principles of Psyc11010gical Testing
lZ0
8 Techniquesfor Measuring Reliability, in Relation to Test Form andTesting Session
TABLE
Test Forms Required
Testing SessionS
Required Split-Half Kuder-Richardson
A1temate-Form (Immediate)
Scorer
Two
\
1'l..'C ••.:J";':'.:.•.;-...• :.~io!
Alternate- Form (Delayed)
Test-Retest ....:.Y:-:_~ :_~~,,::.;.c~.-:,~;:.:.;(;,tJ';;.!:. 4':~~ __ ••'~.~;-.:.;~
.•..c..::.t,at;.;..."Ulr'&.~~')l.t;·~ •..fW"6'.!':"i·:;",-
scores depends on true vati~nce in the trait measured and 15 percent epends on error variance (as:'opcrationally defined by the specific pr~edure followed). The statistically sophisticated reader may recall that It 's the square of a correlation coefficient that represents proportion of ommanvariance. Actually, the proportion of true variance in test scores 'sithe square of the correlation between scores on a single form of the est and true scores free from chance errors. This correlation, known as th6 index of re1iabdity,~ is equal to the square root of the reliability co-
efficient (\/;;-;-). When the index of reliability is squared, the result is the reliability coefficient (r1l), which can therefore be interpreted directly as the percentage of true variance. Experimental designs that yield more than one type of reliability coefficient for the same group permit the analysis of total score variance into different components. Let us consider the following hypothetical example. Forms A and B of a creativity test have been administered with a two-month interval to 100 sixth-grade children. The resulting alternateform reliability is .70. From the responses of either form, a split-half reliability coefficient can also be computed.6 This coefficient, stepped up by the Spearman-Brown formula, is .80. Finally, a second scorer has rescored a l'andom sample of 50 papers, from which a scorer reliability of .92 is obtained. The three reliability coefficients can now be analyzed to yield the error variances shown in Table 10 and Figure n. It will be noted that by subtracting the en'or variance attributable to content sampling alone (split-half reliability) from the error variance attributable to both content and time sampling (alternate-form reliability), we find that .10 of the variance can be attributed to time sampling alone. Adding the error vari~nces attributable to content sampling (.20), time sampling (_10), and mterscorer difference (.08) gives a total error variance of .38 and hence a true variance of .62. These proportions, expressed in the more familiar percentage terms, are shown graphically in Figure II.
TABLE
10
Anal)'sis of Sources of Error Variance in a H}'P0thetical Test :fABLE
9
,ourcesof Error Variance in Relation to Reliability Coefficients Type of Reliability Coefficient ,est-Retest lemale-Form(Immediate) emale-Form(Delayed) lit-Half
er-Richardsonand Coefficient Ipha rer
Time sampling Content sampling Time sampling and Content sampling Content sampling Content sampling and Content heterogeneity Interscorer differences
Derivations of the indexof reliability,based on two dilTerentsets of assumptions, \givenby Gulliksen (l950b, Chs. 2 and 3).
5
From delayed alternate-form reliability:
1 - .70
= .30
(time samplin'k plus content sampling)
From split-half, Spearman-Brown reliability:
1 - .SO
= .20·
(content sampling)
DiHerence TWDl
.10· (time sampling)
scorer reliability:
1- .92
= .OS· (interscorer difference )
=
Total Measured Error Varianetl· .20 + .10 + .08 True Variance = 1- .38 .62
=
= .38
. 6 For a better estimate of the coefficientqf internal consistency.split-half correlations could be computed for each fonn amI the two coeffiCientsaveraged by the appropriate statistical procedures. '-\;,. ;
'II,
',,I,II ;
i
i'
Error Variance:
38'J. A_- --x.--8-'X,-"'" 10
Stable over lime; consistent over !orms; free !rom interscorer difference
11. Percentage Distribution of Score Variance in a Hypothetical Test.
'LIABILITY OF SPEEDED TESTS "
oth in test construction and in the interpretation of test scores, an portant distinction is that between t~e ~ea.s~rement. of speed and of wer. A pure speed test is one in whIch md1~dual differences depend tirel\, on speed of performance. Such a test IS co~s~ructed fr~~ Items uniformly low difficulty, all of which are well wI~hm ~he. a?lhty level the persons for whom the test is designed. The hme 1Im1t.1~made so ort that no one can finish all the items. Under these conditIons, each erson's score rcflects only the speed with which he worked. A pur~ DICeI' test, on the other hand, has a time limit long el:ough ~o permIt veryone to attempt an items. The difficulty of the Items IS steeply , raded, and the test includes some items too difficult for anyone to solve, sothat no one can get a perfect score. " It will be noted that both speed and power tests are deSIgned to p~e-" vent the achievement of perfect scores. The reason for such.a precauh~, is that perfect scores are indeterminate, since it is impos~lble to .knm.Y how much higher the individual's score would have been If m?re.l~ems, 'ffi It items had been included, To enable each mdlVldual or more d I cu, ,,' .d d to show fully what he is able to a~c,qm1?H,~rthe test must proVI e a e. qllate ceiling, either in number o~ ~te"':iJr in. difficulty level. An..ex~ep~ lion to this rule is ,found in mastery ,Jng, as Illustrated by the cllt~no~ referenced tests discussed in ChaPtrc4. The purpose of such testm~ IS not to establish the limits of what th'e3hdividual can do, but to determme whether a preestablished performance level has or has not been rea.ehed. In actual practice, the distinction between speed and power :ests IS ~nc of degree most tests depending on both powe~ and speed 111 varymg proportiO~S. Information about these proportions is needed for each test . rder not onlv to understand what the test measures but also to ~o~se the prop~r procedures for evaluating its reliability. Single-trial reliability coefficients, such as t~ose found by odd-even or Ku.derRichardson techniques, are inapplicable to speeded tests. To the extent
that individual differences in test scores depend on speed of performance, reliability coefficients found by these methods will be spuriously high. An extreme example will help to clarify this point. Let us suppose that a 50-item test depends entirely on speed, so that individual differences in score are based wholly on number of items attempted, rather than on errors. Then, if individual A obtains a score of 44, he will obviously have 22 correct odd items and 22 correct even items. Similarly, individual B, with a score of 34, will have odd and even scores of 17 and 17, respectively. Consequently, except for accidental careless errors on a few items, the correlation between odd and even scores would be perfect, or + 1.00. Such a correlation, however, is entirely spurious and provides no information about the reliability of the test. An examination of the procedures followed in finding both split-half and Kuder-Richardson reliability \:vill show that both are based on the consistency in number of errors made by the examinee. If, now, individual differences in test scores depend, l~ot on errors, but on speed, the measure of reliability must obviously be based on consistency in speed of u:ork. 'Vhen test performance depends on a combination of speed and power, the single-trial reliability coefficient will fall below 1.00, but it will still be spuriously high. As long as individual differences in test scores are appreciably affected by speed, single-trial reliability coefficients cannot be properly interpreted. 'What alternative procedures are available to determine the reliability of Significantly spl1eded tests? If the test-retest techniqu~ is applicable, it would be appropriate. Similarly, equivalent-form reliability may be properly employed with speed tests. Split-half techniques may also be used, provided that the split is made in terms of time rather than in terms of items. In other words, the half-scores must be based on separately timed parts of the test. One way of effecting such a split is to administer two eqUivalent halves of the test with separate time limits. For example, the odd and even items may be separately printed on different pages, and each set of items given with one-half the time limit of the entire test. Such a procedure is tantamount to administering two equivalent forms of the test in immediate succession. Each form, however, is h¥f as long as the test proper, while the subjects' scores are normally based on the whole test. For this reason, either the Spearman-Brown or some other appropriate formula should be used to find the reliability of the whole test. If it is not feasible to administer the two half-tests separarely, an alternative procedure is to divide the total t,ime into quarters, and to find a score for each of the four quarters. This caneasil~':J;>~ 'done by having the examinees mark the item on which they ar~ w6rkiti~ whenever the examiner gives a prearranged signal. The number of items correctly completed within the first and fourth quarters can then be combined to
Principles of PsycllOlogical
Testing
'~w,' represent one half-score,
while those in the second and thir~ q~artcrs ," can be combined to yield the other half-score. Such a combmahon of . quarters tends to balance out the cumulative effects of practice, fatigue, and other factors. This method is especially satisfactory when the items are not steeply graded in difficulty level. When is a test appreciably speeded? Under what conditions must the . special precautions discussed in this section be observed? Obviously, the mere employment of a time limit does not signify a speed test. If all subjects finish within the giycn time limit, speed of work plays no part in determining the scores. Percentage of persons who fail to complete the test might be taken as a crude index of speed versus power. Even when no one finishes the test, however, the role of speed may be negligible. For example, if everyone (<()mpletes exactly 40 items of a 50-item .test, individual differences with regard to speed are entirely absent, although no one had time to attempt all the items. The essential question, of course, is: "To what extent are individual differences in test scores attributable to speed?" In more technical terms, we want to know what proportion of the total variance of test scores is speed variance. This proportion can be estimated roughly by finding the ... variance of number of items completed by different persons and dividing '\ it by the variance of total test scores (u·'/r:J't). In the example cited above, in which ev~ry individual finishes 40 items, the numerator of this fraction would be zero, since there are no individuaL differences in number of items completed (u'(' 0). The entire index would thus equal zero in a pure power test. On the other hand, if the total test variance (U2f) is attributable to individual differences in speed, the two variances will .. be equal and the ratio will be 1.00. Several more refined procedures have ;". been developed for determining this proportion, but their detailed consideration falls beyond the scope of this book., . '. An example of the effect of speed on single-trial reliability coefficients is provided by data collected in an investigi~on of the first edition of the SRA Tests of Primary Mental Abilitie.s.~.r Ages 11 to 17 (Anastasi & Drake, 1954). In this study, the reliab!lijY',uf each test was first determined by the usual odd-even procedm:e.;{~;fie~~coefficients, given in the first row of Table 11, are closely sinjil Jhose reported in the test manual. Reliability coefficients were the ..," ,nfited by correlating scores shown in the second on separately timed halves. These coef1i~~:are row of Table 11. Calculation of speed indexes showed that the Verbal Meaning test is primarily a power teSt;,l~i1e the Reasoning test is somewhat more dependent on speed. The Spa.~~,and Number tests proved to be highly speeded. It will be noted iri;1;~h'1' 11 that, when properly com-
=
7
See. e.g .• Cronbach & Warrington (1951 Y,Culliksen (1950a, 1950b), Cuttman Helmstadter & Ortmeyer (1953).
(1955),
TABLE
11
Reliability Coefficients of Four of the SRA Tesls of Primary MenIal Abilities for Ages 11 to 17 (1st Edition) (Data from Anastasi & Drake, 1954)
Reliability Coefficient Found by: Single-trial odd-even method Separately timed halves
Verbal Meaning Reasoning .94 .90
,96 .87
Space
Number
.90 .75
.83
.92
p~ted, the reliability of the Space test is .75, in contrast to a spuriously hIgh odd-even coefficient of .90. Similarly, the reliability of the Reasoning te,st drops f~on~..96 to .87, and that of the Kumber test drops from .92 to .8,3. The rehablhty of the relatively unspeeded Verbal Meaning test, all the other hand, shows a negligible difference whe'n computed by the two methods.
OF RELIABILITY DEPENDENCE ON THE SAMPLE TESTED
COEFFICIENTS
HET~ROG~XEITY. An important factor influencing the size of a reliability coeffiCient IS the nature of the group on which reliability is measured. In ~he. ~rst pla~e, any correlation coefficient is affected by the range of 1I1?~\')?ual dl~erenc:~ in the group. If every member of a group were ah~~ 111spcllmg ablhty, then the correlation of spelling with any other a~lll~y would be zero in that group. It would obviously be impossible;' WI~~1Ilsuch a group, to predict an individual's standing in any other ablhty from a knowledge of his spelling SCOFe. Anot~er, less extreme, example is provided by the correlation between tw~ aptItude tests, such as a verbal comprehenSion and an arithmetic reasonmg test. If these tests were administered to a highly homogeneous sampll:', such as a group of 300 college sophomores, the correlation beI tween the two would probably be close to zero().There is little relationS~i~, wi~hin such a .s~lected s~mple of college students, between any indn Idual s verbal abdlty and hiS numerical reasoning abilitv. On the other hand, wer~ the test~ to. be. give.n to a hetero~neous sample of 300 persons, rangmg f~om mstItut~ona1tzed mentally retar~ed persons to college graduates, a hIgh correlatlon would undoubted:}£,::be obtained betweep the two tests. The mentally retarded would o~ta1.~~hoore.r:scores than tile . hips would hold for college graduates on both tests, and similar no{ other subgroups within this highly heterogeneo'us ',pIe.'>
Principles of Psychological Testing
Reliability
mination of the hypothetical scatter diagram given in Figure 12 urther illustrate the dependence of correlatioll coefficients on the Hity, or extent of individual differences, within the group. This r diagram shows a high positive correlation in the entire, heteroges group, since the entries are closely clustered about the diagonal ding from lower left- to upper right-hand corners. If, now, we cononly the subgroup falling within the small rectangle in the upper -hand portion of the diagram, it is apparent that the correlation bethe two variables is close to zero. Individuals falling within this , icted range in both variables represent a highly homogeneous group, did the college sophomores mentipned above. 'ke all correlation coefficients, reliability coefficients depend on the 'iability of ,the sample within which they are found. Thus, if the reility coefficient reported in a test manual was determined in a group 'ing from fourth-grade children to high school students, it cannot be med that the reliability would be equally high within, let us say, an hth-grade sample. \Vhen a test is to be used to discriminate individual i I -'~-, I I
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127
differences within a more homogeneous sample than the standardization group, the reliabi~ity ~oefficient should be redetermined on such a sample. Formulas for estimating the reliability coefficient to be expected when the standard deviation of the group is increased or decreased are available in elementary statistics textbooks. It is preferable, however, to recompute the reliability coefficient empirically on a group comparable to that on which the test is to be used. For tests designed to cover a wide range ~f age or abil.ity, the test manual should report separate reliability coeffiCIents for relatively homogeneous subgroups within the standardization sample.
ABILITY LEVEL. Kot only does the reliability coefficient vary with the extent of individual differences in the sample, but it may also vary between groups differing in average ability level. These differences, moreover, cannot usually be predicted or estimated by any statistical formula, b~t c~n ~e' discovere~ .only by empirical tryout of the test on groups d.dfermg 111 age or abilIty levcl. Such differences in the reliability of a smgle test may arise from the faCt that a slightlv different combination of abilities is measured at different difficulty lev~ls of the test. it may result from the statistical properties of the scale itself, as in the StanfordBinet (Pinneau, 1961, Ch. 5). Thus, for different ages and for different IQ levels, the reliability coefficient of the Stanford-Binet varies from .83 to .98. In other tests, reliability may be relatively low for the younger and less able ¥roups, since their scores are unduly influenced by guessing. Under such CIrcumstances, the particular test should not be employed at these levels.
Or
It is apparen.t t~at every reliability coefficient should be accompanied by a fuD descnptIon of the type of group on which it was detelmined. Special attention should be given to the variability and the ability level of the sa~~le. The reported reliability coefficient is applicable only to ~amplef, s~nll]~r to that on which it was computed. A desirable and growlIlg practice In test construction is to fractionate the standardization sample into m~re homogeneous subgroups, with regard to age, sex, grade leve~, occupation, and the like, and to report separate reliability coeffic~ents for each s~bgroup. Under these conditions, the reliability cocHicIen¥ are more lIkely to be applicable to the samples ~~th which the test is to be used ill actual practice. ..
I
!
I
I
!
I
Score on Variable 1
.Frc. 12. The Effect of Restricted Range upon a Correlation Coefficient.
INTERPRETATION
OF INDIVIDUAL
The reliability of a test may be error of measllre~ent ((fmen.,), also
SCORES.
expressed in terms of the standard
Reliability
Principles of PsycllOlogical Testing
, called tIle standard error of a score. This measure is particularly wen of individual scores, For many testing pursuited to the interpretation poses, it is therefore more useful than the reliability coefficient., TI~e , standard error of measurement can be easily computed from the rehabll: ity coefficient of the test, by the following formula:
.in which al is the standard deviation of the test scores and '11 the reliability coefficient, hath computed on the same group. For example, if deviation IQ's on a particular intelligence test have a standard devia~iol1 of ~5 .and a reliability coefficient of .89, the a"" ••. of an IQ on thIS test IS;
=
=
=
;.15\/1- .89 15Y.ll 15(.33) 5. -v . To understand what the UI/H'.' tells us about a score, let us suppose that . ~"wehad a set of 100 IQ's obtai~ed with the above test by a single boy, t;tJim,Because of the types of chance errors discussed in this chapter, these :\ scores will vary, falling into a normal distribution around Jim's true ':score.The mean of this distribution of 100 scores can be taken as the true ,scoreand the standard deviation of the distribution can be taken as the , "11Im, • Like an\, standard deviation, this standard error can be interpreted in t~rms of the normal curve frequencies 'discussed in Chapter 4 (see Figure 3). It will be recalled that between the mean and ±lu there are ~pproximatf'ly 68 percent of the cases in, a normal curve. Th~s" we can .nclude .h-.;-the chances arc roughly 2:1 (or 68:32) that JUllS IQ on , is test :_..'" 'fluctuate between ± lUIII,n.'. or 5 points on either side of his Ie IQ. If his true IQ is no, we 'V<:mldexpect him to score between 105 ld U5 about two-thirds (68 percent)' of the time. If we want to be more certain of oiI~rprediction, we can choose higher '\lddsthan :2: 1. Reference to Figurei,1t~~Chapter 4 shows that ±3u covers 00.7 percent of the cases. It can be::~_sg~,~t.ainedfrom normal curve freuenc)' tables that a distance of 2.58?:7.?~.·~i!4erside of the mean includes 'actly 99 percent of the cases. II,tti{ee;:the chances are 99:1 that Jim's 13 points, on either side of will fall within 2.58u ras, or (2.58)(5) . true IQ. We can thus state at ttte 99 percent' confidence level (with Iy one chance of error out of l00J,:,that Jim's IQ on any single admination of the test will lie between"97 an9 123 (110 -13 and no + 13). ''Jimwere given 100 equivalent te~ts. ilis IQ would fall outside this band 'Valuesonly once.. 'In actual practice, of course, we do not have the true scores, but only e scores obtained in a single test administration. Under these circum~nces,we could try to follow ~t.above reasoning in the reverse direc. If an individual's obtal,p~l.score is unlikely to deviate by more 2.58O''''r ••. from his true"~ore, we could argue that his true score lie within 2.580'n1f.B, olflis obtained score. Although we cannot aslll
=
U9
sign a probability to this statement for any given obtained score, we call say that the statement would be correct for 99 percent of all the cases. On the basis of this reasoning, Gulliksen (1950b, pp. li-20) proposed that the standard error of measurement be used as illustrated abo've to estimate the reasonable limits of the true score for persons ""it-h any given obtained score. It is in terms of such "reasonable limits" that the en-or of measurement is customarily interpreted in psychological testing and it will be so interpreted in this book. The standard error of measurement and the reliabilitv coefficient are obviously alternative ways of exprt'ssing test reliability. Unlike the reliability coefficient, the error of measuren)('nt is independent of the variability of the group on which it is computed. Expressed in terms of individual scores, it remains unchanged when found in a homogeneous or a heterogeneous group. On the other hand, being reported in score units, the error of measurement will not be directly comparable from test to test. The usual problems of comparability of units would thus arise when errors of measurement are reported in terms of arithmetic problems, want to compare words in a vocabulary test, and the like. Hence, if the reliability of differetlt tests, the reliability coefficient is the better measure. To interpret individual scores, the standard error of measurement is more appropriatc.
,,"e
INTERPRETATI01IO OF SCORE DIFFERENCES. It is particularly important to consider test reliability and errors of measurement \\'hen evaluating the differellces between two scores. Thinking in terms of the range within which each score may fluctuate serves as a check against overemphasizing small diHerences between scores. Such caution is desirable both j when comparing test scores of different persons and when comparing the scores of the same individual in diHerent abilities. Similarly, changes in scores following instructiun or other experimental \'ariables need to be interpreted in the light of errors of measurement. A frequent question abollt test scores concerns the individuars relative standing in different areas. Is Jane more able along verbal than along numerical lines? Does Tom have more aptitude for mechanical than for verbal activities? If Jane scored higher on the verbal than on the numerical sub tests .on an aptitude battery and Tom scored higher on the mechanical than on the verbal, how sure can we be that they would still do so1on a retest with another form of the battery? In other words, could thc score differences have resulted merely from the chance: se)ection of specific items in the particular verbal, numerical, and mechahical tests employed? Because of the growing interest in the interpretation of score p'rofi.les, test publishers have been developing report forms that permit the evalua-
Reliability
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the difference between the Verbal Reasoning and Numerical Ability scores probably reflects a genuine difference in ability level; that bctween Mechanical Reasoning and Space Relations probably does not; the difference between Abstract Reasoning and Mechanical Reasoning is in the doubtful range. It is well to bear in mind that the standard error of the difference between two scores is larger than the error of measurement of either of the two scores. This follows from the fact that this difference is affected by the chance er1"Orspresent in both scores. The standard error of the diffe;ence between two scores can be found from the standard errors of measurement of the two scores by the follOWing formula:
-
-
-
40
..
131
". :
0
..
..
..
..
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..
in which Udi//. is the standard error of the difference between the two scores, and Umca8.) and Urneas .• are the standard errors of measurement of the separate scores. By substituting SDyll - TII for Umeus,) and SDyll - r2lI for Umeas .• , we may rewrite the formula directly in terms of reliability coefficients, as follows~
, 1
Flc. 13. Score Profile on the Differential Aptitude Tests, Illustrating Use of Percentile Bands. (Fig. 2, Fifth Edition Manual, p. 73. Reproduced b)' permission. Copyright ® 1973, 1974 by The Psychological Corporation, New York, N.Y. All rights reseT\'ed.)
tion of scores in terms of their errors of measurement. An example is, the Individual Report Form for use with the Differential Aptit,~~e Tests, reproduced in Figure 13. On this form, percentile scores ?~ each subtest of the battery are plotted as one-inch bars, '\\1th the ~1:l~jPed percentil~ ' at the center. Each percentile bar corresponds to a dist~nce of approxI~core.8 mately 1 Y2 to 2 standard error~ o~ :ithe~' ~,ide ~f 't~i!o~t~ine? Hence the assumption that the mdlVl~ua! s true ~~~allS Wlthm the bar is correct about 90 percent oftl,t,:.time. In iI'l~,~rp.tetingthe profiles, test users are advised not to attach Importance to olfferences between scores whose percentile bars overlap,- especially if they overlap by more 13, for example, than half their length. In the profil~%tl!ustrated~~f~gure ·1;-~:.
-,
,
8 Because the reliability coefficient (a¥d hence th~ er•• , ••. ) varies somewhat with subtest, grade, and sex. the actual ranges covered by the one-inch lines are not identical, but they are sufficiently close to permit uniform interpretations for practical purposes.
In this substitution, the same SD was used for tests 1 and 2, since their scores would have to be expressed in terms of the same scale before they could be compared. \Ve may illustrate the above procedllfe with the Verbal and Performance IQ's on the Wechsler Adult Intelligence Scale (WAIS). The splithalf reliabilities of these scores are .96 and .93, respectively. WAIS deviation IQ's have a mean of 100 and an SD of 15. Hence the standard error of the difference between these two scores can be found as follows: Udif/.
= 15y12 - .96 - .93
= 4.95
To determine how large a score difference could be obtained by at the .05 level, we multiply the standard error of the difference by 1.96. The result is 9.70, or approximately 10 points. Thus the ence between an individual's WAIS Verbal and Performance IQ be at least 10 points to be significant at the .05 level. 1 RELIABIUTY
OF CRITERION-REFERENCED
chance (4.95) differshould
TESTS
It will be recalled from Chapter 4 that criterion-referenced, tests usually (but not necessarily) evaluate performance in terms o(~ mastery rather than degree of achievement. A major statistical implication of
13Z
Pl'inciplt:s of Psychological Tcstillg Reliability
mastery testing is a reduction in yariability of scores among persons. Theoretically, if everyone continues training until the skill is mastered, variability is reduced to zero. Not only is low variability a result of the way such tests are used; it is also built into the tests through the construction and choice of items, as will be shown in Chapter 8. In an earlier section of this chapter, we saw that any correlation, including reliability coefficients, is affected by the variability of the group in which it is computed. As the vatiability of the sample decreases, so does the correlation coefficient. Obviously, then, it would be inappropriate to assess the reliahilitv of most criterion-referenced tests by the usual procedures.o Under thes; conditions, even a highly stable and internally consistent tcst could yield a reliability coefficient near zero. In the construction of criterion-referenced tests, two important questions are: (1) How many items must be used for reliable assessment of each of the specific instructional objectives covered by the test? (2) "What proportion of items must be correct for the reliable establishment of mastery? In much current testing, these two questions have been answered by judgmental decisions. Efforts are under way, however, to develop appropriate statistical techniques that will provide objective, empirical answers (see, e.g., Ferguson & i\ovick, 1973; Glaser & Nitka, 1971; Hambleton & l\ovick, 1973; Livingston, 19i2; Millman, 1974). A few examples will serve to illustrate the nature and scope of these efforts. The t,,'o question~ about number of items and cutoff score can be incorporated into a single hypothesis, amenable to ~testillg within the framework of decision theory and sequential analysis (Glaser & :\'itko, 197]; Lindgren & :'.1cElrath, 1969; Wald, 1947). Specifically, we wish to test the hypothesis that the examinee has achieved the required le"el of mastery in tllP content domain or instructional objective sampled by tne test items. Segucntial analysis consists in taking observations one at a timE' and deciding after cach observation whC'f.tper to: (1) accept the hypothesis; (2) rejcct the hypothes!s; or .(3~f~~ake add~tional o~serYatlOns. Thus the number of observations (m.;fhls case :t:lytnber of items) needed to reach a reliable conclusion is, itself deten~nined during the process of testing. Rather than being p.::fls~nted,,:ith a fixed, predetermined number of items the examine~~c;;dntimieS;ltaking tbe test until a mastery or nonmastery d~cision is r~·.·" ·'d. At that point, testing is discuntinue'd and the student is either dire '.,:fo~he next instructional level or returned to the nonmastered level '0 ; further study. \Vith the computer facilities described in Chaptn_~, such sequential decision pro9 For fuller discussionof special statistic;\"~rocedures required for the construction and evaluationof criterion-referencedtests,see Glaser and Nitko (1971), Hambleton and Novick (1973), Millman (1974), Popham and Husek (1969). A set of tables for determining the minimum number of ~lems required for establishing mastery at speCifiedlevels is provided by Millman (1972,1973).
133
ce~ures ar~ feasible and can reduce total testing time while yielding rehable ~stlma.tes of mastery (Glaser & Kitko, 1971). Some Investigators have been explorinO' the use of Ban'sian estimation techniques, whi.eh lend themselves well t~ the kind of decisions required by, ma~tery testmg. Because of the large number of specific instructional objectives to bc t~sted, criterion· referenced tests typically provide only a small number of Itcms for cach objective. To supplement this limited information, procedures have been developed for incorporatinO' collateral data from the student's previous performance history, as well ~s from the test results of other students (Ferguson & !'\oviek, 197:3; Hambleton & Novick, 1973). When flexible, individually tailored procedmes are impracticable, I~ore traditional techniques can be utilized to assess the reliability of a gl\'en .test. For example, mastery decisions reached at a prerequisite instructional level can be che{:ked against performance at the next instructional level. Is there a sizeable proportion of students who reached or exceeded the cutoff score on tIle masten' test at .the lower level and ~ailed t~ achi~\'e mastery at the next levei within a reasonable period of mstructlOnal tU1W?Does an analysis of their difficulties suggest that they had not truly mastered the prerequisite skiIIs:l If so, these findings would strongly suggest that the mastery test was unreliable. Either the addition of more items or the establishment of a higher cutoff score would seem to be indicated. Another procedure for determining the reliability of a master)' test is to administer two parallel forms to the same individuals and note the percentage of persons for ",hom the same decision (~mstery or nonmastery) is reached on both forms (Hambleton & No\'Ick, ] 973 ). In the development of several criterion-referenced tests, Educational Testing Service has followed an empirical procedure to set standards of mastery. This procedure involves administering the test in classes one grade below and one grade above the grade where the particular conce?t or skill i~ taught. The dichotomization can be fmther rcGned by usmg teacher Judgments to exclude any cases in the lower grade knoVl'll to have mastered the concept or skill and any cases in the higher grade who have demonstrably failed to master it. A cutting score, in terms of number or percentage of correct items, is then selected that best dis. criminates between the two groups. Allstatistical procedures for use with criterion-referenced tests are in an exploratory stage. Much remains to be done, in both theoretical develoIJ!nent and ~mpir.ical ~ryouts, before the most effective IJlethodology for different testmg situatlons can be formulated. 4
Validity: Basic Concepts
HAPTER
6
.alidity: .;Basic C011cepts , ,
T
·
HE VALIDlTY
of a test concerns u;lwf the test measures and how
wen it does so. In this connection, we should guard against ae-
cepting the test name as an index of .what. the ~est measures. Test names provide short, convenient labels for IdentificatIon purposes. Most test names are far too broad and vague to furnish meaningful clues to the behavior area covered, although increasing e£forts are being made to use more specific and operationally definable test names. ~he ~rait measured by a given test can be defined only through an e~amIna~l~n of. the objective sources of information and empirical operatIOns ut~li~ed In establishing its validity (Anastasi, 1950). Moreover, the vahdlty of ,a .tes; cannot be reported in general terms. No test can be said to ha.ve 'hl~h or "low" validitv in the abstract. Its validity must be determmed WIth reference to the' particular use for, which the test is being considered. Fundamentallv all procedures for determining test validity are concerned with the 'r~lationships between performance on the test and other independently observable facts about the behavio~ ehar~cte~stics under consideration. The specific methods ·employed for mvestIgatmg these relationships are numerous and have been descri~ed by various names. In the Standards for Educational and PsycJlOloglcal Tests,' (1974), these c~l1t~nt, procedures are classified under three prineip~~"categories: criterion-related, and construct validity. Each o~ tnese types of valIdatIon, procedures will be considered in one of the .fgll?c'~ir:!g.section~, and the relations amona them will be examined in,~ .concludmg section. Techniques for analyzing and intcrpreting vali1~tt "data with reference to practical decisions will be discussed in Chapter 7.
135
sample of the behavior domain to be measured. Such a validation -procedure is commonly used in evaluating achievement tests .. This type of test is designed to measure how well the individual has mastered a specific skill or course of study. It might thus appear that mere inspection of the content of the test should suffice to establish its "a1idih' for such a purpose. A test of multiplication, spelling, or bookkeeping '~'ould seem to be valid by definition if it consists of multiplication, spelling, or bookkeeping items, respectively. The solution, however, is not so simple as it appears to be.' Onc difficulty is that of adequately sampling the item universe. The behavior domain to be tested must be systematically analyzed to make certain that aJJ major aspects are covered by the test iteme;. and in the correct pro~r example, a test can easily become overloaded with those aspects of the field that lend thcmselves more readily to the pl'eparation of objective items. The domain under consideration should be fully described in advance, rather than being defined after the test has been prepared. A \VeIl-constructed achievement test should cover the objectives of instruction, not just its subject matter. Content must therefore be broadly defined to include major objectives, such as the application of principles and the interpretation of data,~ as well as factual knowledge. ~vloreover, content validity depends on the relevance of the individual's test responses to the behavior area under consideration, rather than on the apparent rcle\'ance of item content. Mere inspection of the test may fail to reveal the processes actually used by examinces in taking the test. It is. also important to guard against any tendency to overgeneralize regarding the domain sampled by the test. For instance, a multiple-choice spelling test may measure the ability to recognize correctly and incorrectly spelled worde;. But it cannot be assumed that such a test also measures ability to spell correctly from dictation, frequency of misspellings in written compositions, and other aspects of spelling ability (Ahlstrom, 1964; Knoell & Harris, 1952). Still another difficulty arises from the possible inclusion of irrelevant factors in the test scores. For example, a test designed to measure proficiency in such areas as mathematics or mechanics may be unduly influenced bv the ability to understand verbal directions or by speed o{performing si~ple, routi~e tasks.
Content validity is built into a test from the outtests, the prepfaration of items is preceded by a thorough and systematic examinati'Qn of relevant course syllabi and textbooks, as well as by consultation SPECIFIC
PROCEDURES.
set through the choice of appropriate' items. For educational
NATURE. Content validity involves essentially the systematic exami~ation of the test content to determine whether it covers a representative
I Further discussions of content validity from several angles ca,n be found in Ebel (1956), Huddleston (1956), and Lennon (1956). .
Principles of Psychological Testing
with subject-matter experts. On the basis of the information thus gath'-ered,test specifications are drawn up for the item writers. These specifications should show the content areas or topics to be covered, the instruc'onal objectives or processes to be tested, and the relative importance of 'ndividual topics and processes. On this basis, the number of items of ach kind to be prepared on each topic can be established. A convenient ay to set up such specifications is in terms of a two-way table, with ocesses across the top and topics in the left-hand column (see Table ,eh. 14). Not all cells in such a table, of course, need to have items, ,nee certain processes may be unsuitable or irrelevant for certain topics. t might be added that such a specification table will also prove helpful . the preparation of teacher-made examinations for classroom use in any ubject. ~Jn listing objectives to be co\'ered in an educational achievement test, e test constructor can be guided by the extensive survey of educational jectives given in the Taxonomy of ~ducational Objectives (Bloom a!., 1956; Krathwohl et al., 1964), Prepared by a group of specialists educational measurement, this handbook also provides examples of any types of items designed to test each objective. Two volumes are ilable, covering cognitive and affective domains, respectively. The jor categories given in the cognitive domain include knowledge (in sense of remembered facts, terms, methods, principles, etc.), compresion,application, analysis, synthesis, and evaluation. The classification affective objectives, concerned with the modification of attitudes, inrests, values, and appreciation, includes five major categories: recciv'g, responding, yaluing, organization, and characterization. IThediscussion of content validity in the manual of an achievement test uld include information on th~ content areas and the skills or obives covered bv the test, with some indication of the number of items ach category. 'In addition, the procedures followed in selecting cate, s and classifying items should be described. If subject-matter experts ipated in the test-construction process, their number and prolal qualifications should be stated. If they served as judges in classi- , items, the directions they were given should be reported, as well as extent of agreement among judges. Because curricula and course eilt change over time, it is paI:tJcularly desirable to give the dates n subject-matter experts were' consulted. Information should likebe provided about number and nature of 'course syllabi and texts surveyed, including publication dates. umber of empirical procedures may also be followed in order to ement the content validation of an achievement test. Both total s and performance on individual items can be checked for grade ess.In general, those items are retained that show the largest gains percentages of children passing them from the lower to the upper
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Principles of Psychological
Testing
es.Figure 14 shows a portion of a table from the manual of the ential Tests of Educational Progress-Series II (STEP). For every . in each test in this achievement battery, the information provided des its classification with regard to learning skill and type of mal,as well as the percentage of children in the normative sample who the right answer to the item in each of the grades for which that of the test is designed. The 30 items included in Figure 14 repret onepart of the Reading test for Level 3, which covers grades 7 to 9. ther supplementary procedures that may be employed, when appriate, include analyses of t~l)es of errors commonly made on a test observation of the work methods employed by examinees. The latter ld be done by testing students individually with instructions to "think ud" while ,solving each problem. The contribution of speed can be ckedby noting how many persons fail to finish the test or by one of e more refined methods discussed in Chapter 5. To detect the possible irrelevantinfluence of ability to read instructions on test performance, ,~res on the test can be ~rrelated \",ith scores on a reading comprensiontest. On the other hand, if the test is designed to measure readg comprehension, giving the questions v.oithout the reading passage on hich they are based will show how many could be answered simply fromthe examinees' prior information or other irrelevant cues.
APPLICATIONS. Especially when bolstered by such empirical checks as thoseilIusb'ated above, content vali,dity provides an adequate technique forevaluating achievement tests. It permits us to answer two questions ihat are basic to the validitv of an achievement test; (1) Does the test 'cover a representative sa~ple of the speCified skills and knowledge? (2) Is test performance reasonably free from the influence of irrelevant ; \Janables? ~. Content validity is particularly appropriate for the criterion-refer~n~d .. testsdescribed in Chapter 4. Because performance on these tests lS 111f .terpreted in tern1S of content meaning, it is obvious that content validity ~ is a prime requiremenf for their effective use. Content validation is also · applicable to certain occupational tests designed for employee selection and classification, to .be discussed in Chapter 15. This type of validation issuitable when the test is an actual job sample or otherwise calls for the sameskills and knowledge required on the job. In such cases, a thorough · job analysis should be carried out in order to demonstrate the close re· semblance between the job activities and the test. For aptitude and personality tests, on the other hand, content validity is usually inappropriate and may, in fact, be misleading. Although considerations of relevance and effectiveness of content must obviously enter
Validity: Basic Concepts
1.39
into the initial stages of constructing any test, eventual validation of aptitude or personality tests requires empirical verification by the procedures to be described in the following sections. These tests bear less intrinsic resemblance to the behavior domain they are trying to sample than do achievement tests. Consequently, the content of aptitude and personality tests can do little more than reveal the hypotheses that led the test constructor to choose a certain type of content for measuring a specified trait. Such hypotheses need to be empirically confirmed to estabiish the validity of the test. Unlike achievement tests, aptitude and personality tests are not based on a specified course of instruction or uniform set of prior experiences from which test content can be drawn. Hence, in the latter tests, individuals are likely to vary more in the work methods or psycholOgical processes employed in responding to the same test items. The identical test might thus measure different functions in different persons. Under these conditions, it would be virtually impossible to determine the psychological functions measured by the tcst from an inspection of its content. For example, college graduates might solve a problem in verbal or mathematical terms, while a,mechanic would arrive at the same solution in terms of spatial visualization. Or a test measuring arithmetic reasoning among high scho.ol freshmen might measure only individual differences in speed of computation when given to college" students. A specific illustration of the dangers of relying on content analysis of aptitude tests is provided by a study conducted with a digit-symbol substitution ~est"(Burik, 1950). This test, generally regarded as a typical "codelearmng test, was found to measure chiefly motor speed in a group of high school students.
FACE "ALIDITY. Content validitv should not be confused with face validity. The latter is not validity 'in the technical sense; it refers, not to what the test actually measures, but to what it appears superficially to measure. Face validity pertains to whether the test "looks valid" to the examinees who take it, the administrative personnel who decide on its use, and other technically untrained observers. Fundamentally, the question of face validity concerns rapport and public relations. Although common usage of the term validity in tlhs connection may make for confusion, face validity itself is a desirable feature of tests. For example, when tests originally designed for children and developed within a classroom setting were grst extended for adult use, they frequently met with ~esistance and criticism because of their lack of face validity. Certainly if test content appears irrelevant, inappropriate, silly, or childish, the result will be poor cooperation, regardless of the actual validity of the
140
Principles of Psychological Testing
~st.Especially in adult testing, it is not sufficie~t for a t~st to. be obctivelyvalid. It also needs face validity to function effectively In pracal situations. .Face validity can often be improved by merely reformulating test msin terms that appear relevant and plausible in the particular setting whichthe" will be used. For example, if a test of simple arithmetic soningis 'constructed for use with machinists, the items should be ded in tcrms of machine operations rather than in terms of "how y oranges can be purchased for 36 cents" or other traditional schoolk problems. Similarly, an arithmetic test for naval personnel can be ressedin naval terminology, without necessarily altering the functions asured.To be sure, face validity should never be regarded as a substie for objectively determined validity. It cannot be assumed that im\1ng the face validity of a test '\vill improve its objective validity. r can it be assumed that when a test is modified so as to increase its e validity,its objective validity remains unaltered. The validity of the in its final form will always need to be directly checked. o
riterion-relatedvalidity indicates the effectiveness of a test in predictan individual's beha\'ior in specified situations. For t~is purpose, peranceon the test is checked against a criterion, i.e., a direct and indent measure of that which the test is deSigned to predict. Thus, mechanical aptitude test, the criterion might bc subsequent job ormanceas a machinist; for a scholastic aptitude test, it might be ge grades; and for a neuroticism test, it might be associates' ratings ..her available information on the subjects' behavior in various life lions.
VALIDITY. The criterion measure against test scores are validated may be obtained at approximately the . time as the test scores or after a stated interval. The APA test ·urds (1974), differentiate between concurrent and predictive validthe basis of these time relations between criterion and test. The rediction"can be used in the broader sense, to refer to prediction he test to any criterion situation, or in the more limited sense of 'on over a time interval. It is in the latter sense that it is used in ression"'predictive validity:' The information provided by prevalidityis most relevant to tests used in the selection and dasn of personnel. Hiring job applicants, selecting students for onto college or professional schools, and assigning military per-
Validity: Basic Concepts
141
sonnel to occupational training programs represent examples of the sort of decisions requiring a knowledge of the predictive validity of tests. Other examples include the use of tests to screen out applicants likely to develop emotional disorders in stressful environments and the use of tests to identify psychiatric patients most likely to benefit from a particular therapy. In .a number of instances, concurrent validity is found merely as a su~stJt~te for predictive validity. It is frequently impracticable to extend vah~atlon ~rocedures over the time required for predictive validity or to o~tam a s~Itable preselection sample for testing purposes. As a comprom~se .solutIOn, therefore, tests are administered to a group on whom cntenon data are already available. Thus, the test scores of college stud~nts may b~ compared with their cumulative grade-point average at ~he tIme of testmg, or those of employees compared with their current Job success. For certain uses of psychological tests, on the other hand, concurrent validity ~sthe ~~st ~pprop!iate type and can be justified in its own right. The logICal dI~tinchon between predictive and concurrent validity is ?ased, not on hme, but on the objectives of testing. Concurrent validity ISrel.ev~nt to tests employed for diagnosis of existing status, rather than predIction of future outcomes. The difference can be illustrated bv asking: "Is Smith neurotic?" (concurrent validity) and "Is Smith lik"ely to become neurotic::>"(predictive validity) . . . Because ~he criterion for concurrent validity is always available at the hme of testmg, we might ask what function is served bv the test in such situa~ions. B~sicalIy, such tests provide a simpler, quicker, or less ex~ensive subs.htute for the criterion data. For example, if the criterion conSIStsof continuous observation of a patient during a two-week hospital- , ization period, a test that could sort out normals from neurotic and ' ?oubtful cases would appreciably reduce the number of persons requirmg such extensive observation.
'CURREI'.:T AND PREDICTIVE
• ~RITERION CO~TAMINATION. An essential precaution in finding the vahdlty of a test IS to make certain that the test scores do not themselves influence any individ~ars c~terion. status. For example, if a college ill
Validity: Basic Concepts rillciplesof Psychological Testing tion, since the criterion ratings become "contaminated" by the owledgeof the test scores. To prevent the operation of such an s absolutely essential that no person who participates in the asof criterion ratings have any knowledge of the examinees' test or this reason, test scores employed in "testing the test" must rictlyconfidential. It is sometimes difficult to convince teachers, s, military officers, and other line personnel that such a precauential. In their urgency to utilize all available information for decisions,such persons may fail to realize that the test scores e put aside until the criterion data mature and validity can be d, Any test may be validated against as many criteria e are specific uses for it. Any method for assessing behavior in tion could provide a criterion measure for some particular purhe criteria employed in £ndif\g the validities reported in test Is,however, fall into a few common categories. Among the criteria equendyemployed in validating intelligence test~ is some index of ic ac ' t. It is for this reason that such tests have often ore precisely described as measures of scholastic aptitude,. The cindicesused as criterion measures include school grades, achieveest scores, promotion and graduation records, special honors and as, and teachers' or instructors' ratings for "intelligence." Insofar as ratings given within an acade~ic setting are likely to be heavily ~dby the individual's scholastic performance, they may be properly ed with the criterion of academic achievement. e various indices of academic achievement have provided criterion at all educational levels, from the primary grades to college and uateschool. Although employed principally in the validation of genintelligence tests, they have also served as criteria for certain 'pIe-aptitude and personahty tests. In the validation of any of these s.oftests for use in the selection of college students, for example, a :~on criterion is freshman grade-point average. This measure is the .age grade in all courses taken during the freshman year, each grade g weighted by the number of course points for which it w.a~~ceived. variant of the criterion of academic achievement frequenl:ly emedwith out-of-school adults is the amount of education the individual pleted. It is expected that in general the more intelligent individuals inutl their education longer, while the less inte.lli ent drop out of 01earlier. The assumption underlying this crite . that the educaal ladder serves as a progressively selective nee, eliminating oseincapable of continuing beyond each step. Although it is undoubtly true that college graduates, for example, represent a more highly MON CRiTERIA.
143
selected group than elementary school graduates, the relation between amount of education and scholastic a titnde is far from erEect. EspecIa y at t e Ig er e ucationallevels, economic, social, motivational, and other nonintellectual factors may influence the continuation of the individual's education. Moreover, with such concurrent validation it is difficult to disentangle cause-and-effect relations. To what extent ~re the obtain~d differences in intelligence test scores simply the result of the yarymg amount of education? And to what extent could the test have predicted individual differences in subsequent educational progress? These questions can be answered only when the test is administered before the criterion data have matured, as in predictive validation. I.n t~e development of special aptitude tests, a frequent type of criteno~ is bas~d on performance in specialized training. For example, mechamcal aptitude tests may be validated against final achievement in sho~ courses. Various business school courses, such as stenographY, t~l~g, or bookkeeping, provide criteria for aptitude tests in these area's. SlIl~Ilarly,p~rformance in music or art schools has been employed in validatmg musIc. or art. aptitude tests. Several professional aptitude tests have been validated In terms of achievement in schools of law medicine dentistry, engineering, and oth;r areas. In the case of custom-:nade tests' deSigned for use within a specific testing program, training reco;ds are ~ f:equent ~ource of ~riterion data. An outstanding illustration is the validahO~ ~f Au Force pIlot selection tests against performance in basic flight tr~m~g. Performance in training programs is also commonly used as a ~ntenon ~or test validation in other military occupational specialties and m some mdustrial validation studies. ~mong the specific indices of training performance employed for critenon purposes may be mentioned achievement tests administered on .completion of training, formally assigned grades, instructors' ratings, and succ~ssful co~pletjon of. training versus elimination from the program. l\ful~lple .aptItude battenes have often been checked against grades in spec,IRehIg? school or college courses, in order to determine their validity as dIfferential predictors. For example, scores on a verbal comprehension test may be compared with grades in English courses spatial visualization scores with geometry grades, and so forth. ' In connection with the use of training records in general as criterion measures, a useful distinction is that between intermediate and ultimate criteria: In the development of an Air Force pi!Pt-selection test or a medical aptItude test, for example, the ultimate criteria would be combat perfo~mance a~d eventual achievement as a practicing physician, respectIvely. ObVIOuslyit would require a long time for such criterion data to mature. It is doubtful, moreover, whether il~ly ultimate criterion is ever obtained in actual practice. Finally, even were such an ultimate criterion available, it would probably be subject to many unconttolled
4
Principles of Psychological Testing
. tors that would render it relatively useless. For example, it would be cult to evaluate the relative degree of success of physicians practicing erent specialties and in different parts of the country. F'or these reas, such intermediate criteria as performance records at some stage of iningare frequently employed.as criterion measures. or many purposes, the most satisfactory type of criterion measure is t based on follow-up records of actual ;ob performance. This criterion been used to some extent in the validation of general intelligence as as personality tests, and to a larger extent in the validation of special tude tests. It is a common criterion in the validation of custom-made . for specific jobs. The "jobs" in question may vary widely in both I and kind, including work in business, industry, the professions, and armed services. Most measures of job performance, although probnot representing ultimate criteria, at least provide good interiate criteria for many testing purposes. In this respect they are to be erred to training records. On the other hand, the measurement of perform;mce does not permit as much uniformity of conditions as is , ible during training. Moreover, since it usually involves a l?nger low-up,the criterion of job puformance is likely to entail a loss m the mber of available subjects. Because of the variation in the nature of inally .similar jobs in different organizations, test manuals reporting 'ditydata against job criteria should describe not only tbe specific terion measures employed but also the job duti~s performed by the rkers. Validation by the method of contrasted groups generally involves a compositecriterion that reflects the cumulative and uncontrolled selective j~fluencesof everyday life. This critcrion is ultimately based on survi"al ,withina particular group versus elimination therefrom. For example,. ip e validation of an intelligence test, the scores obtained by institution~l, ed mentally retarded children may be compared with those obtained y schoolchildren of the same age. In this case, the multiplicity of factors etermining commitment to an institution for the mentally retarded conitutes the criterion. Similarly, the validity of a musical aptitude or a echanical aptitude test may be checked by comparing the scores obtained by students enrolled in a music school or an engineering school, respectively,with the scores of unselected high school or college student~. , To be sure, contrasted groups can be selected on the basis of any cnterion, such as school grades, ratings, or job performa!1ce, by simply choosingthe extremes of the distribution of criterion me~sures. The contrasted groups included in the present category, ho}'-'wer, are disti?ct groupsthat have gradually become differentiated through the operation ofthe multiple demands of daily living. The criterion under cons~deralionis thus more complex and less clearly definable than those preVIously discussed.
Validity: Basic Concepts
145
. The method o~ contrasted groups is used quite commonly in the validahon of persollahty tests. Thus, in validating a test of social traits, the test perform~nce of salesmen or executives, on the one hand, may be compar~d WIth that of clerks or engineers, on the other. The assmnption' underlymg such a procedure is that, with reference to man v social traits individua.ls who hav~ entered and remained in such occupatiq9~:~s selling or executive work Will as a group excel persons in such fiela~['ils clerical work or engine.ering. Similarly, college students who hav~>:engaged in man~ .extracl~rncular activities may be compared with those who have partlcIp~ted 111 nOlle during a comparable period of college attendance. Oc~up~tlOnaI groups have frequently becn used in the development and vahdahon ?f interest tests, such as the Strong Vocational Interest Blank, as well as ~n the preparation of attitude scales. Other groups sometimes employed. m the validation of attitude scales include political, religious, ~eograp~lCal, or ot~er spccial groups generally knO\vn to represent distmetly dIfferent pomts of "iew on certain issues. In the developmc.nt of certain personality t~sts, psychiatric diagnosis is used both as a basIS for the selection of items and as evidence of test v~lidity, Ps.y~hiatric diagnosis may serve as a satisfactory criterion proVIded that It IS based on prolonged observation and detailed case history rather than on a cursory psychiatric interview or examination. In th; latter. case, there is no reason to expect the psychiatric diagnosis to be supenor to the test score itself as an indication of the individual's emotion~l ~ondition. Such a psychiatric diagnosis could not be regarded as ~ c:ltenon measure, but rather as an indicator or predictor whose own validIty would have to be determined. Mention has already been made, in connection with other criterion cate,?o~ies, of certain types of ratings by school teachers, instructoml in speclahzed. cou~s.es, an~ jo~ supervisors. To these can be added ratings by offic~rs 10 mIhtary sltuahons, ratings of students by school counselors, and ratmgs by co-workers, classmates, fellow club-members and other grou?~ of associ~tes. The ratings discussed earlier represent~d merely a SUhsldI~ry tec?mque for obtaining information regarding such criteria as academiC achIevement, performance in specialized training, or job succe~s. :Ve are now considering the use of ratings as the very core of the cntenon mea~ur~. Under these circuwstances, the ratings themselves define the CrItenon. Moreover, such.:ratings are not restricted to the evaluation of speci~c achievement, but involve a personal judgment by an observer regardmg any of the variety;of traits that psychological tests attempt to measure. Thus, the subjects in the vali~\ltion sample might be ~ate? on such c?aracteristics as dominance, mech~ll.icaI ingenuity, origmali~, leadership, or honesty.':":" Ratings have bee~ employed in the valid~tion of,lltmost every type of test. They are partICularly useful in providing criteria for personality
Validity: Basic Concepts ril1ciplesof Psychological Testing ation,since the criterion ratings become "contaminated" by the owledgeof the test scores. To prevent the operation of such an .'s absolutely essential that no person who participates in the ast of criterion ratings have any knowledge of the examinees' test or this reason, test scores employed in "testing the test" must rictlyconfidential. It is sometimes difficult to convince teachers, s, military officers, and other line personnel that such a precauential. In their urgency to utilize all available information for decisions,such persons may fail to realize that the test scores e put aside until the criterion data mature and validity can be
d. Any test may be validated against as many criteria e are specific uses for it. Any method for assessing behavior in ation could provide a criterion measure for some particular purhe criteria employed in finding the validities reported in test Is, however, fall into a few common categories. Among the criteria equentlyemployed in validating intelligence test~ is some index of ic ac . t. It is for this reason that such tests have often ore precisely described as measures of scholastic aptitude .. The cindicesused as criterion measures include school grades, achieveest scores, promotion and graduation records, special honors and as, and teachers' or instructors' ratings for "intelligence." Insofar as ratings given within an acade~ic setting are likely to be heavily ,edby the individual's scholastic performance, they may be properly . ed with the criterion of academic achievement. e various indices of academic achievement have provided criterion at all educational levels, from the primary grades to college and .uateschool. Although employed principally in the validation of gen.intelligence tests, they have also served as criteria for certain tiplc-aptitude and personality tests. In the validation of any of these of tests for use in the selection of college students, for example, a on criterion is freshman grade-point average. This measure is the , ge grade in all courses taken during the freshman year, each grade g weighted by the number of course points for which it waJJ~ceived. variant of the criterion of academic achievement frequently emyedwith out-of-school adults is the amount of education the individual pleted. It is expected that in general the more intelligent individuals tinue their education longer, while the less int~lli ent drop out of 001 earlier. The assumption underlying this erite . that the educaal ladder serves as a progressively selective . nee, eliminating se incapable of continuing beyond each step. Although it is undoubtly true that college graduates, for example, represent a more highly MON CRiTERIA.
143
selected group than elementary school graduates, the relation between amount of education and scholastic a titude is far from erfect. EspecIa y at t e Ig er e ucationallevels, economic, social, motivational, and other nonintellectual factors may influence the continuation of the individual's education. Moreover, with such concurrent validation it is difficult to disentangle cause-and-effect relations. To what extent ~re the obtain~d differences in intelligence test scores simply the result of the yarymg amount of education? And to what extent could the test have predicted individual differences in subsequent educational progress? These questions can be answered only when the test is administered before the criterion data have matured, as in predictive validation. I.n t~e development of special aptitude tests, a frequent type of criteno~ is bas~d on performance in specialized training. For example, mechamcal aphtude tests may be validated against final achievement in sho~ courses. Various business school courses, such as stenography, t~l~g, or bookkeeping, provide criteria for aptitude tests in these areas. SlIl~Ilarly,p~rformance in music or art schools has been employed in validatmg musIC,or art. aptitude tests. Several professional aptitude tests have been validated m terms otachievement in schools of law, medicine, dentistry, engineering, and other areas. In the case of custom-made tests designed for use within a specific testing program, training reco;ds are ~ f:equent ~ource of ~riterion data. An outstanding illustration is the validahO~ ?f Alr Force pllot selection tests against performance in basic flight tr~m~g. Performance in training programs is also commonly used as a ~ntenon for test validation in other military occupational specialties and m some industrial validation studies. ~mong the specific indices of training performance employed for critenon purposes may be mentioned achievement tests administered on completion of train,ing, formally assigned grades, instructors' ratings, and succ~ssful co~plehon of. training versus elimination from the program . l\ful~lple .aphtude battenes have often been checked against grades in spec.,fi~hlg~ school or college courses, in order to determine their validity as dIfferential predictors. For example, scores on a verbal comprehension test may be compared with grades in English courses spatial visualization scores with geometry grades, and so forth. ' In connection with the use of training records in general as criterion measures, a useful distinction is that between intermediate and ultimate criteria: In the development of an Air Force pilpt-selection test or a medical aptitude test, for example, the ultimate criteria would be combat perfo~mance a~d eventual achievement as a practidng physician, respectively. ObVIOuslyit would require a long time for such criterion data to mature: It is. doubtful, moreover, whether a".truly ultimate criterion is ever obtamed m actual practice. Finally, even were such an ultimate criterion available, it would probably be subje,ct to many uncontrolled
44
Principws of Psychological Testing
tors that would render it relatively useless. For example, it would be cultto evaluate the relative degree of success of physicians practicing rent specialties and in different parts of the country. For these reasueh intermediate criteria as performance records at some stage of iningare frequently employed as criterion measures. or many purposes, the most satisfactory type of criterion measure is t based on follow-up records of actual ;ob performance. This criterion .been used to some extent in the validation of general intelligence as as personality tests, and to a larger extent in the validation of special tude tests. It is a common criterion in the validation of custom-made for specine jobs. The "jobs" in question may vary widely in both and kind, including work in business, industry, the professions, and armed services. Most measures of job performance, although probnot representing ultimate criteria, at least provide good interiate criteria for many testing purposes. In this respect they are to be erred to training records. On the other hand, the measurement of perform;mce does not permit as much uniformity of conditions as is ible during training. Moreover, since it usually involves a longer low-up,the criterion of job ptrformanee is likely to entail a loss in the mber of available subjects. Because of the variation in the nature of minallv.similar jobs in different organizations, test manuals reporting ~ditydata against job criteria should describe not only the specific 'terion measures employed but also the job duti~s performed by the rkers. Validation by the method of contrasted groups generally involve~ a ill osite criterion that reflects the cumulative and uncontrolled selectIve fluencesof everyday life. This critcrion is ultimately based on sur\'iY~1 'thin a particular group versus elimination therefr?m. For.ex~mp.le,.~n, e validation of an intelligence test, the scores obtamed by mSbtutlOnalmentally retarded children may be compared with those obtained schoolchildren of the same age. In this case, the multiplicity of factors etermining commitment to an institution for the mentally ret~rded constitutes the criterion. Similarly, the validity of a musical aptitude or a echanical aptitude test may he checked by comparing the scores obained by students enrolled in a music school or an engineering school, espectively, with the scores of un selected high school or college student~. To be sure, contrasted groups can be selected on the basis of any cnterion, such as school grades, ratings, or job performa!!ce, by simply choosingthe extremes of the distribution of criterion metsures. TIle contrasted groups included in the present category, h~~wer, are disti~ct groupsthat have gradually become differentiated through the ope~ation of the multiple demands of daily living. The criterion under cons~derationis thus more complex and less clearly definable than those preViously discussed.
Validity: Ba51c Concepts
145
. The method o~ contrasted groups is used quite commonly in the validation of personahty tests. Thus, in validating a test of social traits, the test perform~nce of salesmen or executives, on the one hand, maybe compar~d WIth that of clerks or engineers, on the other. The assumption' underlymg such a procedure is that, with reference to many socialtraits individua.ls who hav~ entered and remained in such occupatiQp~r~s selling or executive work Will as a group excel persons in such fie1~&~iisclerical work or engineering. Similarly, college students who hav~.'~ngaged in man! .extracl~rricular activities may be compared V\'ith those who have partlcIp~ted 111 nOlle during a comparable period of college attendance. Oc~up~tlOl1al.groups have frequently been used in the development and vahdabon ?f mterest tests, such as the Strong Vocational Interest Blank, as well as ~n the preparation of attitude scales. Other groups sometimes employed. III the validation of attitude scales include political, religious, ~eograp~lCal, or other special groups generally known to represent distmetly different points of \oiew on certain issues. In the developme.nt of certain personality t~sts, psychiatric diagnosis is used both as a basIS for the selection of items and as evidence of test v~lidity. Ps.y~hiatric diagnosis may serve as a satisfactory criterion proVIded that It is based on prolonged observation and detailed case history rather than on a cursory psychiatric interview or examination. In th~ latter. case, there is no reason to expect the psychiatric diagnosis to be supenor to the test score itself as an indication of the individual's emotion~l ~ondition. Such a psychiatric diagnosis could not he regarded as ~ c:ltenon measure, but rather as an indicator or predictor whose own validity would have to be determined. Mention has already been made, in connection with other criterion catel?o~ies, of certain types of ratings by school teachers, instructor,s in speCialized. cou~s.es. an~ jO~ supervisors. To these can be added ratings by officers m mIlitary Situations, ratings of students bv school counselors and ratings by co-workers, classmates, fellow club-~embers, and othe; grou?~ of associ~tes. The ratings discussed earlier represented merely a suhsldl~ry tec?mque for obtaining information regarding such criteria as academIC achievement, performance in specialized training, or job succe:s. :Ve are now considering the use of ratings as the viery core of the cntenon mea:ur~. Under these circutJIstances, the ratings themselves define the crltenon. Moreover, suchuatings are not restricted to the evaluation of speci~c achievement, ~ut involve a personal judgment by an observer regardmg any of the vanety,of traits that psychological tests attempt to measure. Th~s, .the subjects in the vali~\ltion sample might be ~ate~ on such charactensbcs as dominance, mechll.:nical ingenuity, origmality, leadership, or honesty. .,;,. Ratings have bee~ employed in t?e validl!tion of;,almost every type of test. They are partIcularly useful In providing criteria for personality
146
Principles of PSljchological Testing
Validity: Basic COllcepts
'J
;,tests,since objective criteria are much more difficult to find in this area. }lfhisis especially true of distinctly social traits, in which ratings based on ;personal contact may constitute the most logically defensible criterion. iiAlthoughratings may be subject to many judgmental errors, when ob. )ained under carefully controlled conditions they represent a valuable 's9urce of criterion data. Techniques for improving the accuracy of i:iatingsand for reducing common types of errors will be considered in ,{,Chapter20. ,11 Finally, correlations between a new test and previously available tests i~arefrequently cited as evidence of validity. When the new test is an ab,breviated or Simplified form of a currently available test, the latter can ,;Properly be regarded as a criterion measure. Thus, a paper-and-pencil ',test might be validated against a more elaborate and time-consuming per
1
SPECIFICITY OF CRITERIA.Criterion-related validity is most appropriate 'for local validation studies, in which the effectiveness of a test for a ,; specificprogram is to be assessed. This is the approach followed, for , example, when a given company wishes to evaluate a test for selecting , applicants for one of its jobs or when a given college wishes to determine i how well an academic aptitude test can predict the course performance ~"ofits students. Criterion-related validity can be best characterized as the ~practical validity of a test in a specified situation. This type of validation ',represents applied research, as distinguished from basic research, and as : such it provides results that are less generalizable than the results of I other procedures. That criterion-related validity may be quite specific has been demon, strated repeatedly. Figure 15 gives examples of the wide variation in the correlations of a single type of test with criteria of job proBciency. The , .~'firstgraph shows the distribution of 72 correlations found between in~:telligence test scores and measures of the job proficiency of general c. clerks; the second graph summarizes in similar fashion 191 correlations . :' between finger dexterity tests and the job proficiency of benchworkers. ,:; Although in both instances the correlations tend to chIster in a particular ',~range of validity, the variation among individual studies is considerable. ~,.The validity coefficient may be high and positive in one study and negli'; gible or even substantially negative in another. £.1"
147
Similar .vari~tion with r~gard to the prediction of course grades is illustrated m Flgure 16. ThIS Bgure shows the distribution of correlations obtained between grades in mathematics and scores on each of the subtests Of,the Differential Aptitude Tests. Thus, for the Numerical Ability test (NA), the largest number of validity coefficients among boys fell between .50 and .59; but the correlations obtained in different mathem~tics ~ourses and in different schools ranged from .22 to .75. Equally Wide dlff~rences we~e found with the other subtests and, it might be added, WIth grades 10 other subjects not included in Figure 16.
20
c:~
.,
72 coefficients for general c1erh on intelligence tests, proficiency criteria
10
'u
~
••0
U
~ 0 ~ -1.00
+1.00
'0
... 20 > 0
191coefficients for bench workers on finger dexterity tests, proficiency criteria
"0
Ol
.,~
C
••
0..
10
o -1.00
-0.50
.00
+0.50
+1.00
FIG. 15. Examples of Variation in Validity Coefficients of Given Tests for Particular Jobs.
(Adapted from Ghiselli, 1966, p. 29.)
Some. of .the variation in validity coefficients against job criteria reported l.n FIgure 15 r~ults from differences among the specific tests em. , .. rity. In plo ed 10 different studies to measure' the resu s 0 0 19ures and 16, moreover/some variation is attributable to diHerences in homogeneity and lev~l~£ the groups tested . The range of validity coefficients found, however, is far wider than could be explained in these terms. J)ifferences in the' crjtena themselves ~un~oubtedb' a m.!!iorr~ason for th.~~~ariatiQnQ~~~rvgafilong vali
:~2,
148
Principles of Psychological
Testing
. de artments in the same company. 'dely among compames or amo~. tP differ in content, teaching milarlv, courses in the same su Jec may t' student achieveethod'instructor characteristics, bases for evalua mg . to be the ' c· ntly w llat appears ellt, and l~umerous other ways. o~sd~e:ent ' combmation of traits in e critefJon ma resent ver t'. the same situation. i rrent situations. .. criteria riteria may also vary over Ime In. e validitv coefficient of a test against Job .tra~m(th' lli omits v~lidity against job performance cntena Ise, 'evidence that the traits required for successful terfo~~:nor
For example, often differs 1966) There ce of ~ iven job e;peri-
b or even a. si~g~detaslk(;~r~' ~vi~n th:9;~~o~~iS~!::c& Fruchter, 1960; ce of the mdivi ua eiS m .' . ' . 1960) There is also ~:~~::le~d~:1~~I'Sh~~~6;h~~~~I~ri:ri~~:~ge ove~. timt.e fo1rgOotha~r . f . b shIfts In orgamza IOna al d't'ons ('.lac- , asons such as changmg nature (} )0 s, ' . k d ther tempor con 1 1 IV. dividual advancement In ra~ ' an kn° f course that educational 1966) It IS we ll own, 0 , . 1967 P . .nne)', ' . d; nen,. t t change over t'Ime. In other words , the ... IIi ence and aptitude tests meula an course con en. teria most commonly used m vaiidatmg mte g d' 'namely, job performance and edut:ational achievement-are ynamlc
Validity: Basic Concepts
rather than static. It follows that criterion-related to temporal changes.
149
validity is itself subject
< SYl':mETIC VALIDITY. Criteria not only differ across situations and over time, but they are also likely to be complex (see, e.g., Richards, ~llor, Price, & J aeo bsen, 1965). Success on a job, in school, or in other actiryties of daily life depends not on one trait but on many traits. Hence, 'practical criteria are likely to be multifaceted. Several ,different indicators or measures of job proficiency or academic achievement could thus be used in validating a test. Since these measures may tap different traits or combinations of traits, it is not surprising to find that they yield different validity coefficients fpr any given test. '\'hen different criterion measures are obtained for the same individuals. their interoorre!atioDs are \" often quite low. For instance, accident records or absenteeism may show virtually no relation to productivity or error ,data for the same job (Seashore, Indik, & Georgopoulos, 1960). These differences, of course, are reflected in the validity coefficients of any given test against different criterion measures. Thus, a test may fail to correlate significantly with supervisors' ratings of job proflciency and yet show appreciable validity in predicting who will resign and who will be promoted at a later date (Albright, Smith, & Glennon, 1959),
Because of criterion complexity, validating a test against a composite criterion of job proficiency, academic achievement, or other similar accomplishments '~a be of uestionable value and is certainl of limited generality. If different subcriteria are relatively independent, a more effectIve procedure is to validate each test against that aspect of the criteiiO'i1Jf IS best designed to measure. An analysis of these more speCific reIahonships lends meaning t6 the test Scores in terms of the multiple dimensions of criterion behavior (Dunnette, 1963; Ebel, 1961; S. R. Wallace, 1965). For example, one test might prove to be a valid predictor of a clerk's perceptual speed and accuracy in handling detail work, another of his ability to spell correctly, and still another of his ability to resist distraction.
16. GraphIC• Summary 0 f· "\' al'd'ty I I Coefficients of the . Differential Th bad Aptitude ac. (Forms Santi T) for Course Grades in Mathematics! em ~rst ~ the anyingnumb~r.sin each column indicate the number 0 coe clen S In givenat the left. " R roduced by permiSSIon. CopyrIght © 1975, Y k N Y All rights reserved.) Fifth Edition Manual, p. 82: eP by The Psychological Corporatlon, N ew or, .•
If, now, we return to the practicClI question of evaluating a test or combination of tests for effectiveness in predicting a complex criterion such as success on a given job, we are faced with the necessity of conducting a separate validation stud in each loc tion and re eatin it at frequent mten~ S. This is admittedly a desi procedure and one that is often recommended in test manuals. In ma~r situations, however, it is not feasible to follow this procedure be~jise of well-nigh insurmountable practical obstacles. Even if adequatel~ p'ained' personnel are available to carry out the necessary research, mosf Critf:'rion-related validity studies conducted in industry afe likely to prove unsatisfactory for
tso
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Principles of Psychological Testing
at leastthree reasons, First, it is difficult to obtain dependable and sufScientlycomprehensive criterion data. Second, the number of employees engagedin the same or closely similar jobs '~ithin a co~pany i,s often 60 small for significant statistical results. Thlfd, correlations will very ~robablybe lowered by restriction of range through preselection, si~ce polythose persons actuany hired can be followed up on .the Job. : For all the reasons discussed above, personnel psychologJ.sts have - shownincreasing interest in a technique 1.."110\\'11 as synthetic validity. \Firstintroduced by Lawshe (1952), the concept of synthetic validity has !beendefined by Balma (1959, p. 395) as "the inferring of validity in a specificsituation from a systematic analysis of job elements, a determina_Honof test validity for these elements, and a combination of elemental fvalidities into a ~'hole." Several procedures have been developed for ",.gathering the1needed empirical data and for ~mbining these d~ta. to , obtainan estimate of synthetic validity for a particular complex cntenon (see,e.g., Guion, 1965; Lawshe & Balma, 1966, Ch. 14; McCormick, 1959; l'rimoff, 1959, 1975). Essentially, the process involves three steps: (1) _. detailed job analysis to identify the job elements and their relative _weights; (2) analysis and empirical study of each test to determine ~he .i extent to which it measures proficiency in performing each of these Job elements; and (3) finding the validity of each test for the given job synthetically from the weights of these elements in the job and in the test. In a long-term research program conducted with U.S. Civil Service job applicants, Primoff (1975) has developed the J-coefficient (for "jobcoefficient") as an index of synthetic validity. Among the special features of this procedure are the listing of job elements expressed in terms of worker behavior and the rating of the relative importance of these elements in each job by supervisors and jo1},}p$]Jmbents. Correlations between test scores and sell-ratings on jOp;Jj~m~~s are found in total applicantsamples (not subject to thep~1f'~-~~lW? of employed workers). Various chec1..ing procedures are fon9~~ed to ensure stability of correl~tions and weights derived from self-~~~gs. as wen as adequacy of C[lterion coverage. For these purpose.s;~a~a_ are ?btained from d~Herent samples of applicant populations. 1\~~£nal estimate of correlation between test and job performance is,!9Pnd from the correlation of each job element with the pifticular job';~~ the weight of the same element in the given test.' There i" evidence that the J-coefficient has proved
~f·' , The statistical procedures aTe essentiaIly an adaptation of multiple regression equations, to be discussed in Chapter- 7. For each job element, its correlation with the job is multiplied by its weight in the test, and these produtcs are added across all appropriate job elements.
helpful in improvin~ th~ employment opportunities of minority applicants and persons WIth lIttle formal education, because of its concentration on job-relevant skills (Primoff, 1975). , A different application of synthetic validity, especially suitable for use m a sn~all company with few employ~es in each type of job, is described by Gmon (1965). The study was carried out in a company having 48 employee~, each of whom was doing a job that was appreCiably different from the Jobs of the other employees. Detailed job analyses nevertheless revealed seve.n job elements commo!}Jto many jobs. Each employee was rated on the Job elements appropriate to his job; and these ratings were then checked against the employees' scores on each test in a trial battery. On the basis of these analyses, a separate battery could be "svnthesized" for each job by co~bining the two best tests for each of the j~b elements demanded by that Job. When the batteries thus assembled were applied t~ a subsequently hired group of 13 employees, the results showed conSIderable promi~e. Because of the small number of cases, these results are only suggestive. The study was conducted primarily to demonstrate a model for the utilization of synthetic validity. The two examples of synthetic validity were cited only to illustrate the scope of possible applications of these techniques. For a description of the actual procedures followed, the reader is referred to the ariginal sources .. In ~ummary, the Concept of synthetic validity can be imple~ented III diHerent ways to fit the practical exigencies of different situatIOns.. It oH~rs .a promising approach to the problem of complex and changmg. cntena; and it permits the assembling of test batteries to fit ~he reqUIrements of specific jobs and the detennination of test validity 1D many contexts where adequate criterion-related validation studies are impracticable.
!he construct validity o~ a test is the extent to which the test may be saId to me~ure. a theoretical construct or trait. Examples of such constructs ~re mtelhge~~, mechanical comprehension, verbal fluency, speed of ,;alking, neurotiCIsm, and anxiety. Focusing on a broader, more endunng, .and more abstract kind of behavioral description t'han the previ. ously dlscusse~ types ,of validity, construct validation requires the gradual a~um~latIon of mfonnation from a variety of sources. Any data thrOWIng hght on the nature of the trait under consideration and the ~~~tions .aHecting i~ developm.e~t and manifestations' are grist for this ,al~dl~ mill: IllustratIOns of speCific technique~ $uitabl~, for construct ':&-" vahdatlon Will be considered below.
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acco~~ing to. a hierarchical pattern of learned skills, they, too, can utilize empmcal eVidence of hierarchical invariance in their validation. DEVELOPMENTAL CHANGES. A major criterion employed in the validation ',',ofa number of intelligence tests is age d.ifferentiation. Su.ch tests a.~the ,Stanford.Binet and most preschool tests arc checked agamst chronolog':ical age to determine whether the scores show a pr~gressive i~crease , .with advancing age. Since abilities are expected to mcre~se \~lth age , ,during childhood, it is argued that the test scores should likewise show , such an increase, if the test is valid. The very concept of an age scale ,:'0£ intelligence, as initiated by Binet, is based on the assumption that "in~telligence"increases with age, at least until maturit,Y- . . The criterion of age differentiation, of course, IS mapp1icable to any ,functions that do not exhibit clear-cut and consistent age changes. In the area of personality measurement, for example, it ~as found li~ited u~e. Moreover, it should be noted that, even when apphcable, age differentiation is a necessary but not a sufficient condition for validity. Thus, if the . test scores fail t~ improve with age, such a finding probably indicates " that the test is not a valid measure of the abilities it was designed to ."sample. On the other hand, to prove that a test measures something that illcr,eases with age does not define the area covered by the test very precisely. A measure of height or weight would al~o show regul~r ag~ inc1'ements,although it would obviously not be deSignated as an mtelli-
";:
'\ gencetest. . .' A final point should be emphasized reg~rding the. mterpretahon .of ~e age criterion. A psychological test validated a?amst such a cnteno~ measures behavior characteristics that increase w1th age under the condl' tions existing in the type of environment in which the test was standardized. Because different cultures may stimulate and foster the development of dissimilar behavior characteristics, it cannot be assumed that the criterion of age differentiation is a universal one .. Lik~ all ~th~r , criteria, it is circumscribed by the particular cultural settmg m whlCh It is derived. Developmental analyses are also basic to the construct validation of the JPiagetian ordinal scales cited in Chapter 4. A fundamental assump, tion of such scales is 1thesequential patterning of development, such that the attainment of earlier stages in concept development is prerequisite to the acquisition of later conceptual skills. T'here is thus. an ~ntrinsic h~erarchy in the content of these scales. The construct vahdahon of ~rdi~al scales should therefore include empirical data on the sequential 10variance of the successive steps. This involves checking the performance of children at different levels in the development of any tested concept, such as conservation or object permanen,ce. Do children who demonstrate mastery of the concept at a given level :also exhibit mastery at the ~ower levels? Insofar as criterion-rt:ferenced tests are also frequently deSIgned
CO~~Anoss WlTIl OTHER TESTS. Correlations between a new test and slIDllar earlier tests are sometimes cited as evidence that the new test me~sures apprOximately the same general area of behavior as other tests des~gnated by"the ~ame name, such as "intelligence tests" or "'mechanical aphtude tests: Unlike the correlations found in criterion-related validity, these correlahons sh~uld be ~oderately high, but not too high. If the new test correlates too lughly With an already available test, withuut such added advantages as brevity or ease of administration, then the new test represents needless duplication. Correlations with other tests are employed in still another way to d~m~nstrate that the new test is relatively free from the influence of certa~n m~le:ant factors. For ex~~ple, a special aptitude test or a personalItr teat "hould hav.e a neglIgtble correlation with tests of general inte1hgence ~r scholastic aptitude. Similarly, reading comprehension should not appreCiably affect performance on such tests. Thus, correlations with t~sts of general intelligence, reading, or verbal comprehension are someh~es reporte~ as indirect or negative evidence of validity. In these cases, hlgh correlations, would make the test suspect. Low correlations, however, would n~t 10 t~emselves insure validity. It will be noted that this use o~ correlations With other tests is similar to one of the supplementary techmques described under content validity. '
FA~OR ANALYSrs.Of particular relevance to construct validitv is fador an~lySlS: a s~atistical procedure for the identification of psy~hological ~ralts. E,s~entia.lly, factor analysis is a refined technique for analyzing the I~terrelationships of behavior data. For example, if 20 tests have been glven ~o 300 persons, the first step is to compute the correlations of each t~st Wlth e:ery other., An inspection of the resulting table of 190 eoi-relati,O~ may Itself reveal. certain clusters among the tests, suggesting the 10catI?n of common traIts. Thus" it_ tests as vocabulary, analogies oppOSites, and sent~nce ~mpletioJl •• high correlations with each ~ther and low correlations With all ot~ ~ts, we could tentatively infer the pre~en.(:e of a verbal :omprehe~ioj "tor. Because',~uch an inspectional ana ~m of .a ~rrelaho~ table is ~t and uncetjtirln, however, more precIse statistical teclm1ques have blWft developed to locat th """'e e common . cd f ac to account for the'ttbtai, . t ors reqmr ff "rre,a·ned co i ti'ons. Th ese tee h m~ues a .actor a~alysis will be e~amiil~d further in Chapter 13, together WIth multnple aptItude tests developed~~y means of I~r analysis.
Validity: BasicCaacepts
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Principles of PSljchological Testing ~orrelation of .subtest scores with total score. Many intelligence tests, for lD:tance,. con~lst of separately administered subtests (such as vocabulary, anthmehc, picture completion, etc.) whose scores are combined in finding the total test score. In the construction of such tests, the scores on each subtest are often correlated with total score and any subtest whose correlation with total score is too low is eliminated. The correlations of the rem~ining sUbte~ts with total score are then reported as evidence of the Internal consistency of the entire instrument. . It is app.arent that internal consistency correlations, whether based on Items or subtests,. are essentially measures of homogeneity. Because it helps to charactenze the behavior domain or trait sampled by the test, the degree of homogeneity of a test has some relevance to its construct validity .. Ne.vert~eless, ~he contribution of internal consistency data to test vahdatlOn IS very limited. In the absence of data external to the test itself, little can be learned about what a test measmes.
n the process of factor analysis, the number of variables or .cate~ories erms of which each individual's performance can be descnbed lS reed from the number of original tests to a relatively small number of rs, or common traits. In the example cited above, five or six factors t suffice to account for the intercorrelations among the 20 tests. Each 'dual might thus be described in terms of his scores in the five or six ors, rather than in tcrms of the original 20 scores. A major purpose of (>ranalysis is to simplify the description of behavior by reducing the er of categories from an initial multi licit of test vari bles to a few 1
ac ;Aft~rthe factors have been idcntified, they can be utilized in describing e factorial composition of a test. Each test can thus be cl1afacterized in rmsof the l1)a)or factors determining its scores, together with the weight r loading of each factor and the correlation of the test with each facto~. uch a correlation is known as the factorial validity of the test. Thus, lf he verbal comprehension factor has a weight of .66 in a vocabulary test, he factorial validity of this vocabulary test as a measure of the trait of erbal comprehension is .66. It should be noted that factorial validity is entially the correlation of the test with whatever is common to a group of tests or other indices of behavior. The set of variables analyzed can, ofcourse, include both test and nontest data. Ratings and other criterion 'measurescan thus be utilized, along with other tests, to explore the factorial validity of a particular test and to define the common traits it measures. INTERNAL CONSISTENCY. In the published descriptions of certain tests, especially in the area of personality, the statement is made that the test has been validated by the method of internal consistency. The essential characteristic of this method is that the criterion is none other than the -total score on the test itself. Sometimes an adaptation of the contrasted . grOUpmethod is used, extr'"eme groups being selected on the basis of the total test score. The performance of the upper criterion group on each test item is then compared with that of the lower criterion group. Items that fail to show a significantly greater proportion of "passes" in the upper than in the lower criterion group are considered invalid, and are either ~liminated or revised. Correlation~l pr.qcedures may also be employed for this purpose. For example, the biserial'correlation between ."pass-f~il" .on each item and total test score can be computed. Only those Items )'leldmg significant item-testcorr~fliJi.Pns would be retained. A test whose items were selected by this meth,qd can be said to show internal consistency, since each item differentiates in the same direction as the entire test. Another application of the criterion of internal consistency involves the
i
EFFECT OF EXPERIYENTAL VARIABLES ON TEST SCORES' A further source of data forconstmct validation is provided by ex-periments on the effect of selecte(;I~ariables on test scores. In checking the validitv of a ~riterionreferellce'O test for use in an individualized instruction~l program, for example, one approach is through a comparison QE pretest and posttest scor~s.. The rationale of such a test calls for low scores on the pretest, admlms~ered b~fore ~he relevant instruction, and high scores on the posttest. ThiS relationshIp can also be checked for individual items in the te~t (Po.pharo, 1971). Ideally, the largest proportion of examinees should fall an Item ?n the pretest and pass it on the posttest. Items that are commonly falled on both tests are too difficult, and those passed on both tests ~oo easy, for t~e purposes of such a test. If a sizeable proportion of exa~mees pass an ltem on thc pretest and fail it on the posttest, there is obvlOusly something wrong with the item, or the instruction, or both. A. test designed to measure anxiety-proneness can be administered to sub!ects who are subsequently put through a situation designed to arouse amQe.~, such as .t~~ng an examination under distracting and stressful conditions. The lDltlal anxiety test scores can then be correlated with phySiolog!cal. and other indices of an~iety expression du~pg and after the exammatIon. A different hypothesis regarding an anxietY· test could ?e evalua~ed by admini~tering the test before and after an anxiety-arousmg expen:~ce an~ seemg whether test scores rise Significantly on the retest. PosItive flndmgs from such an experiment would indicate that the test scores. reBect current anxiety level. In a similar w,lI.y;' exper4;h.lents can be. designed to test any other hypothesis regarding th.~;;tfait ~~SUred by a gIVen test.' .'
TABLE
In a thoughtful analysis nstruet validation, D. T. Campbell (1960) points out that in order emollstrate construct validity we must show not only that a test cores highly with other variables with whi~h .it should ~heoret.ically elate, but also that it does not correlate sIgmficantly wIth van abIes which it should differ. In an earlier article, Campbell and Fiske ) described the former process as convergent validation and the er as discriminant validation. Correlation of a mechanical aptitude with subsequent grades in a shop course would be an example of vergent validation. For the same test, discriminant validity would be rated by a low and insignificant correlation with scores. on a .reading prehension test, since reading ability is an irrelevant varIable m a test gnedto measure mechanical aptitude. ., . t will be recalled that the requirement of low correlatlOn WIth trrelet variables was discussed in connection with supplementary and pretionary procedures followed in content validation. Discrin;inant va~ionis also especially relevant to the validation of personality tests, In ich irrelevant variables may affect scores in a variety of ways. ampbell and Fiske (1959) proposed a systematic experimental deSign the dual approach of convergent and discriminant validation, which ey called the multitrait-multimet1lOd J7latrix. Essentially, this procedure quiresthe assessment of two or more traits by tw.o Qr ~ore metho~s. A pathetical example provided by Campbell and FIske WIll serve to IUUSate the procedure. Table 12 shows all possible correlations among the ores obtained when three traits are each measured by three methods. , e three traits could represent three personality characteristics, such as A) dominance, (B) sociability, and (C) achievement motivation. The hreemethods could be (1) a self-report inventory, (2) a projective tech'iquc,and (3) associates' ratings. Thus, Al would indicate dom~na~ce oreson the self-report inventory, A2 dominance scores on the projective est,C3 associates' ratings on achievement motivation, and so forth. The hypothetical correlations giv~n in Ta~le 12 include reli.ability cofficients (in parentheses, along principal dIagonal) and validity coefcients (in boldface, along three shorter diagonals). In these validity same trait by different methods coefficients,the scores obtained fc",~~~p arecorrelated; each measure "is.thu~ 'being checked against other, independent measures of the same'::'trait, ~s'.in the familiar validati~n procedure. The table also includes correlations between different traIts measured by the same riJ":.thod'(in solid triilngles) ~nd corrclati.ons between different traitsllleasured by different methods (Ill broken trIangles). For satisfactory construct validity, the validity coefficients should obviously be higher than the correlations between different traits measured by different methods; they should also be higher than the correlations beNVERGENT AND DISCRIMINANT
VALIDATiON.
12
A Hypothetical
Multitrait-M:ultimethod
Matrix
(From Campbell & Fiske, 1959, p. 82.)
Traits
A, Method 1
B,
C,
A, Method 2
B. C. ,...56::-:- ...~22---:11:
67-'---42-------:
.33 I: :.23'".58"',)2: :.43 '".~6',,:.34: II..... ',',
I
.•.
"...
I
1'"
',.
I : ......•...... , ....•....•..
....,~
t
••••••
I
l ~~1 :..~~:~~~45L~~ .:~~~::::~58~ .58 •...• ·::;"'-~"':'_~~~'~:;~'::>'.-~;~I;;,';"_:~~~~
(.85)
..•_.:;.::~:=.t;,..~~~':Q.~IM&~)
Note: Le~tersA. B, C refer to traits, subSCripts1,2,3 to methods. Validity coefficients (rnon~tralt-heteromethod) are the three diagonal sets of boldface numbers; reliability c~efficlents (~ono~ralt-rnonomethod) are the numbers in parentheses along principal diagonal. Sohd tnangles enclose heterotrait-monomethod correlations; broken triangles enclose heterotrait-hcteromethod correlations. 'l
tween different traits measured by the same method. For example, the COITf:lationbetween dominance scores from a self-report inventory and dOITt~ijancescores from a projective test should be higher than the correlatIon between dominance and sociability scores from a self-report in. ventor~. If ~he l~tter correlation, representing common method variance, :-rere hIgh, It mIght inllicate, for example, that a person's scores on this Inventory are unduly affected by some irrelevant common factor such as ability to understand the questions or desire to make oneself appear in a favorable light on all traits. Fiske (1973) has added still another set of correlations that should be checke~, esp~cially in the construct validation of personality tests. These ~rrelab~ns Involve the same trait measured by the"same method, but With a dlffer~nt test. For examplc, two il)vestigators may each pliepare a self-report Inventory designed to assesseIl,durance. Yet the end~rance scores obtained with the two inventories may show quite diffe~~nt. patterns of correlations with measures of other personality traits. Under these
Principles
Validity: Basic Conc('pts
of Psychological Testing
.ditions,it cannot be concluded tllat both inventories measure the same ·sonalityconstruct of endurance. ., . t might be noted that within the framework of the mnlhtrmt-mulhhod matrix, reliability represents agreement between two measures of same trait obtained through maximally similar methods, such as alle! forms of the same test; validity represents agreement between measures of the same trait obtained by maximally different methods, chas test scores and supervisor's ratings. Since similarity and difference methods arem~tters of degree, theoretically reliability and validity can regarded as falling along a single continuum: O~~inarily, ho\~'e~er, the hniques actually employed to measure rehabllIty and validIty corond to easily identifiable regions of this continuum.
We have considered several ways of asking, "How valid is this test?" Topoint up the distinctive features of the different types of validity, let us apply each in turn to a test consisting of 50 assorted arithmetic problems.Four ways in which this test might be employed, together with the type of validation procedure appropriate to each, a:e illustra:ed ~n Table 13. This example highlights the fact that the chOIce of valIdahon pro; cedure depends on the use to be made of the test scores. The same test, when employed for different purposes, should be validated in different ways.If an achievement test is useet to predict subsequent performance
TABLE
13
Validationof a Single Arithmetic Test for Different Purposes Illustrative Question . Achievement test in elementary school aritlunetic Aptitude test to predict performance in high school mathematics Technique for diagnosing learning disabilities Measure of logical reasoning
Type of Validity
How much has Dick learned in the past? How well will Jim learn in the future?
Criterion-related: predictive
Does Bill's performance show specific disabilities? How can we describe Henry's psychological functioning?
Criterion-related: concurrent
159
at a higher educational level, as when selectinO' school students for b hiO'h t:< college admission, it needs to be evaluated against the criterion of subsequent college performance rather than in terms of its content validity. The examples given in Table 13. focus on the differences among the various types of validation procedures. Further consideration of these procedures, however, shows that content, criterion-related, and construct validity do not correspond to distinct or lOgically coordinflte categories. On the contrary, construct validity is a comprehensive concept, which includes the other types. All the specific techniques for establishing content and criterion-related validity, discussed in earlier sections of this chapter, could have heen listed again under construct validity. Comparing the test performance of contrasted groups, such as neurotics and normals, is one way of checking the construct validity of a test designed to measure emotional adjustment, anxiety, or other postulated traits. Comparing the test scores of institutionalized mental retardates with those of normal schoolchildren is one way to investigate the construct validity of an intelligence test. The correlations of a mechanical aptitude test with performance in shop courses and in a wide variety of jobs contribute to our understanding of the construct measured by the test. Validity against various practical criteria is commonly reported in test manuals to aid the potential user in understandin~ what a test measures. Although he may not be directly concerned with the prediction of any of the specific criteria employed, by examining such criteria the test user is able to build up a concept of the behavior domain sampled by the test. Content validity likewise enters into both the construction and the subsequent evaluation of all tests. In assembling items for any new test, the test constructor is guided by hypotheses regarding the relations between the type of content he chooses and the behavior he wishes to measure. All the techniques of criterion-related validation, as well as the other techniques discussed under construct validation, represent ways of testing such hypotheses. As for the test user, he too relies in part on content validity in evaluating any test. For example, he may check the vocabulary in an emotional adjustment inventory to determine whether some of the words are too difficult for the persons he plans to test; he may conclude that. the scores on a particular test depend too much on speed for his purposes; or he may notice that an intelligence test developed twenty years ago contains many obsolescent items unsuitable for use today. All these observations about content are relevant to the construct validity of a test. In fact, there is no information provided by any validation procedure that is not relevant to construct validity. The term construct validity was officially introduced into the psychome~rist's lexicon in 1954 in the Technical RecommenN4a{ions for Psyc11010glcal Tests and Diagnostic Techniques, which constituted the first edition of the current APA test Standards (1974). Although the validation
160
Pritlci,Jles of PSlJchological Testing
procedures subsumed under construct validity were not new at the time, the discussions of construct validation that followed served to make the . implications of these procedures more explicit and to provide a systematic ,; rationale for their use. Construct validation has focused attention on the role of psychological theory in test construction and on the need to formulate hypotheses that can be proved or disproved in the validation process. It is particularly appropriate in the evaluation of tests for use in research. In practical contexts, construct validation is suitable for investigating ; the validity of the criterion measures used in traditional criterion-related " test validation (see, e.g., James, 1973). Through an analysis of the correlations of different criterion measures with each other and with other , relevant variables, and through factorial analyses of such data, one can learn more about the meaning of a particular criterion. In some instances, the r~sults of such a study may lead to modification or replacement of the criterion chosen to validatc a test. Under any circumstances, the results will enrich the interpretation of the test validation study. Another practical application of construct validation is in the evaluation of tests in situations that do not permit acceptable criterion-related validation studies. as in the local validation of some personnel tests for industrial use. The difficulties encountered in these situations were discussed earlier in thi.s chapter, in connection with synthetic validity. Constr~ct validation offers another alternative approach that could be followed in evaluating the appropriateness of published-tests for a particular job. Like synthetic validation, this approach requires a systematic job analysis, followed by a description of worker qualifications expressed in ;.:''terms of relevant behavioral constructs. If, now, the test has bcen subjected to sufficient research prior to publication, the data cited in the manual should permit a specification of the principal constructs measured by the test. This information could be used directly in assessing the relevance of the test to the required job functions, if the correspondence of constructs is clear enough; or it could serve as a basis for computing a J-coefficient or some other quantitative index of synthetic validity. . Construct validation has also stimulated the search for novel ways of gathering validity data. Although the principal techniques employed in investigating construct validity have long been familiar, the field of operation has been' expanded to admit a \\rider variety of procedures. This very multiplicity of data-gathering techniques, however, presents certain hazards. It is possible for a test constructor to try a large number of different validation procedures, a few of which will yield positive results by chance. If these confirmatory results were then to be reported without mention of all the validity probes that yielded negative results, a very misleading impression about the validity of a test could be created. Another possible danger in the application of construct validation is that I
I
Validity: Basic Concepts 161 it may open the way for s b" . validity. Since . ~ J~chve, unvenfled assertions about test cept, it has bE':~~~~~~ v;~~~~;s ~uc~ asbroad and loosely dcflned canconstructors Seem to ~r . . rs 00. ome textbook writers and test psychological trait na~lescelVe It as content validity expressed in terms of subjective accounts of ~h~:~~e, t~e~ present as construct validity purely A further source of ossibl ey e ~ve (o~ hope) the test measures. construct validation "is ; I e Co~fuslOn anses from a statement that d a measure of some at .~vo ve w e~ever ~ test is to be interpreted as quahty whIch is not 'operationally deoned'." (Cronbach & ~:e~tel~r 282). Appearing in the first detailed published analysis of the co' ~nstruct "alidity, this statement was often incorrectl acce ted :c~p the absence of ~ata ~hat t~ Justifrng a claim for construct validity in such an interpretati;n is i1lus:a~~t ors of .the sta~e~ent did. not intend article, that "unless the n t k d b ytheIr own inSIstence, III the same e war ma k es contact with b . construct validation cannot b I' d" 0 servations . . . e c alme (p. 291) In th . .. . h t ey cnhclze tests for wh' h" fi . e same connectIon, been oHered as if it wcre l~al'; t.ne~pun network of rationalizations has l construct, trait or behavio d a I~n (p, 291). Actually, the theoretical ' r omam measured bv rti I b e a d equateI), defined only' th I' h f - a pa cu ar test can validating that test Such I~ Iie. ~g t 0 data gathered in the process of abIes with which th~ test c~ ~ ~lhO~ would take into account the varifound to affect its Scores an~et~ ed SIgnificantly, as well as the conditions scores. These procedures are e ; ~~~ps that diff~r significantly in such butions made bv the co t n fIre :- m aCcord w1th the positive contrl. ncep 0 construct valid'ty I ' 1. t IS only through the empirical investigation of the r I' h' external data that we can d' ehahons IpS of test SCores to other ISCOverw at a test measures.
5;,?f'
HArTER
7
alidity: Measuremel~t and lrlterpretation 6 was concerned with different concepts of validity and their appropriateness for various testing. f~nctions; t~is. chapter deals with quantitative expressions of vahdlty and theIr mterpretation. The test user is concerned with validity at either or both of two stages. First, when considering the suitability of a test for his purposes, he examin~ailable validit)'data reported in the test manual or ot~er p~ed so.Jltces..Through such in~ormation, he arrives at a tentative concept of what psychological fu~ctlOns the test actually measures, and he judges the relevance of such function~ to his p.rop~sed use of t~e test. In effect, when a test user relies on published validation data, he IS dea.ling with construct validity, regardless of the specific pro?ed~res used m gathering the data. As we have seen in Chapter 6, the cntena employed in published studies cannot be assumed to be iden?cal. with th~se the test user wants· to predict. Jobs bearing the same title m two dIfferent companies are rarely identical. Two courses in freshman English taught i in different colleges may be quite dissim~1;l.r· Because of the specificity of each criterion, te~t users are .us~ally advised to check the validity of anv chosen, 'test agamst local cnterla whenever possible. Although publishe'd dat~ay str~ngl~ sugg~st that a given test should have high validity in a particular sltuatio~, dlTee: corrobo~ation is always desirable. The dete:t'inination of validJ!Y agamst specific local criteria represents the second stage in the test ~r's evaluation of valKTfty.The teChnIques ttr'1le dIscussed 1~ this chapter are esp~cially relevant to the analysis of validity data obtamed by ~e test u.ser hlms~1f. Most of them are also useful, however, in understanding and mterpretmg the validity data reported in test manuals.
C
HAPTER
.
J6z
MEASUREMEXT OF RELATIONSHIP. A validity coefficient is a correlation between test score and criterion measure. Because it provides a single numerical index of test validity, it is commonly used in test manuals to report the validity of a test against each criterion for which data are available. The data used in computing any validity coefficient can also be expressed in the form of an expectancy table or expectancy chart, illustrated in Chapter 4. In fact, such tables and charts provide a convenient way to show what a validity coefficient means for the person tested. It will be recalled that expectancy charts give the probability that an individual who obtains a certain score on the test will attain a specified level of criterion performance. For example, with Table 6 (Ch. 4, p. 101), if we know a student's score on the DAT Verbal Reasoning test, "",e can look up the chances that he will earn a particular grade in a hIgh school course. The same data yield a validity coefficient of .66 When both test and criterion variables are continuous, as in this example, the familiar Pearson Product-Moment Correlation Coefficient is applicable. Other types of correlation coefficients can be computed when the data are expressed in different forms, as when a two-fold pass-fail criterion is employed (e.g., Fig. 7, Ch. 4). The specific procedures for computing these different kinds of correlations can be found in any standard statistics text.
COI\"DITIONS AFFECTING VALIDITY COEFFlCIEXTS. As in the case of reliability, it is essential to specify the nature of the group on which a validity coefficient is found. The same test may measure different functions when given to individuals who differ in age, sex, educational level, occupation, or any other relevant characteristic. Persons with different experiential backgrounds, for example, may utilize different work methods to solve the same test problem. Consequently, a test could have high validity in predicting a particular criterion in one population, and little or no validity in another. Or it might be a valid measure of different functions in the two populations. Thus, unless the validation s~ple is repri'!seiififiVe of the population on which the test is to be used, validity should be redetermined on a more appropriate sample. The question of sample heterogeneity is relevant to the measurement of validity, as it is to the measurement of reliability,'.,since both characteristics ale commonly reported in terms of correlation eoefficiElnts. It will be recalled that, other things being equal, the wider the range of scores, the higher will be the correlation. This fact should be kept in
Principles
of
Psychological
mind when interpreting
Testing
the validity coefficients given in test manuals. ,;. Il.special difHcttlt}, encountered in many validation samples arises from preselection. For example, a new test that is being validated for job selee.tionmay be admini$tered to a group of newly hired employees on whom ;criterJIonmeaSures of job performance will eventua11y be available. It is ~likely;however, that such employees represent a superior selection of all "!hosewho applied for the job. Hence, the range of such a group in both .'tests¢ores and criterion measures will be curtailed at the lower end of the :·bdistribution.the effe~t of such preselection will therefore be to lower the 'validity coefficient. In the subsequent use of the test, when it is admindster¢d to all applicants for selection purposes, the validity can be expected to be somewhllt higher. " Validity coefficients may also change over time because of changing .'selection standards. An example is provided by a comparison of validity ,coefficients compll.ted over a 3D-year interval with Yale students (Burn"ham, 1965). Correlations were found between a predictive index based , on College Entrance Examination Board tests and high school records, f onthe one hand, and average freshman grades, on the other. This correlation dropped from .11 to .52 over the 30 years. An examination of the r' bivariate distributions dearly reveals the reason for this drop. Because of ~higher admissibn standards, the later class was more homogeneous than .:the earlier class in both predictor and criterion performance. Consequently, the correlation was lower in the later group, although the act curacy with whkh individuals' grades were predicted showed little ch~nge. In other words, the observed drop in correlation did not indicate . that the predictors were less va-lid than they had been 30 years earlier. Had the difference$ in group homogeneity been ignored, it might have " been 'Wrongly concluded that this was the case. '0' For the propet interpretation of a validity coefficient, attention should alm be given to the form of the relationship between test and criterion. , The computation of a Pearson correlation coefficient a;;sumes that the relationship is linear and uniform throughout the range. There is evidence I situations, however, these' conditions may not be met I that in certain , (Fisher, 1959; Kahneman & Ghiselli, 1962). Thus, a particular job may " require a minimum level of reading comprehension, to enable employees to read instructiorl manuals, labels, and the like. Once this minimum is e:,tceeded, however, further increments in reading ability may be unrelated to degree of job success. This would be an example of a nonlinear relation between test and job performance. An examination of the bivariate distributjon or scat.\:er diagram obtained by plotting reading comprehension scores a!Ylinst criterion measures would show a rise in job perI fprmance up to the minimal required reading ability and a leveling off beyond that point. Hence, the entries would cluster around a curve rather
Validity: Mcasuremcnt
and Interprctation
~65
In other situations th 1" f b individual entries m;y d: .lfIte~ ~st 6t may be a straight line, but the at the lower end of the s:~ e Sart er around this line at the upper than aptitude test is a necClisa; ~ut u~:se that 'performa~c::e on a scholastic achievement in a course Th t' h a tufficlent condItion for successful poorly in the cOU"se' bl!lt'a' a IS t, h~ how-scoring students will perform • ,. mong the Ig -scor' t d . fonn well in the course . d th mg s u ents, some WIll per:erf~rm poorly because of low motivation. In this situat~:n ~h ers performance among the ·h.'h ere. WI e WIder variability of criterion dents, This condition in ~g ~sco~g t~an. am?ng the low-scoring stuscedasticih.' Th p. bwanate dIstrIbution is known as hctero'J' e earson correlatio h variability throughout tb ~ assum:s ?moscedasticity or eqll.al present example, the bivae..r:n~ o'b th~ bIVanate distribution. In the at the upper end and n na e shtn utIon would be fan-shaped-wide ' , arrow at t e lower end A . ' . b Ivanate distribution itsdf ill 11 . . II exammation of the nature of the relations·hip b 'tV usua y give a, good indication of the e ween test and 't' E and expectancy charts also I cn erIOn. xpectancy tables the test at different levels. correct y reveal the relative effectiveness of
",:::1
MAGNITUDE
OF
A V.Aj.LIDITY·COEFFr
•
coefficient be? No gener I CIE~T. How hIgh should a validity . . a answer to thIS gr' . mterpretation of a validit ffi . ues lOll IS pOSSIble, since the of concomitant circumsta; coe clent ~ust take into account a number be high enough to be sta~~~·' o~tamed correlation, of course, should such as the 01 or 05 level' d~8.Ica !Jds~gnificant at some acceptable level . . . s ISCusse in Cha t 5 I h ' drawing any conclusions about th • lid' per . not er words, before sonably certain that the obt' d el~d~ Ity of a test, we should be rea~ . ame va I Ity coeffi' t ld . Clen cou not ,have arisen throug~ chance fluctuatip.tls of sam Ii Havmg establjshed a signiflcant p ng fro.m a true correlation of zero. criterion, however, we need to e correlat1~n between test Scores and f v~luate the SIZeo~ the correlation in ~he light of the uses to be m d vidual's exact criterion s~ e 0 ~le test. If we WIsh to predict an indias:: grade-point average a student will receive in college the of the standard erro; of estimare coe .clen.t may be interpreted in terms measurement discussed in : whl7h IS analogous to the ,error of that the errOr of measure.:~;~c~~n WIth reliability. It wl"ll be recalled pected in an individual's n Icates the margin,. of error to be ex~irni1ar1y, the eITor of esti=~: :~ a res~t of th~ unreliability of the t~t. 't o~s t e margm of ~r,rotto be expe~tec:l m the individual's predicted validity of the test. cn erIon score, as a ~lwf the imper{~(;t
n;~
~:fi~~t
The error of estimate is found b th f 11 . Y e 0 owmg fOfn,ula:
";"'"
6
Prillciples of Psychological Testing
: whichr2 >'V is the square of the validity coefficient and Uv is th~ ~tandard eviatiol1 of the criterion scores. It will be noted that if the vahdlty were erfect(r >'V ;::: 1.00), the error of estimate would be zero. On the other and, with a test having zero validity, the error of estimate is as large as e standard deviation of the criterion distribution (ucBr.;::: ulIVI -0 = v), Under these conditions, the prediction is no better. than. a ~ues~; and he range of prediction error is as wide as the enbre distnbutIOn of criterionscores. Between these two extremes are to be found the errors ofestimate corresponding to tests of varying validity. Reference to the formula for cr •• t. will show that the term VI - r'''11 , servesto indicate the size of the error relative to the error that wou~ , result from a mere guess, i.e., with zero validity. In other words, lf v'l- r'xv ig equal to 1.00, the error of estimate is ~s .lar~e as it would be if we were to guess the subject's score. The predlc~ve lmprove~~nt attributable to the use of the test would thus be rol. If the validlty coefficientio; .80, then VI - "XI/ is equal to .60, and -the error is 60 percent aslarge as it would be by chance. To put it diffe:ently, the use of s~ch a test enables us to predict the individual's critenon performance wlth a marginof error that is 40 percent smaller than it would be if we were to guess. . . . . It would thus appear that even with a validlty of .80, whl~h 1S unusu~lIy high, the error of predicted scores is.conside~abl~..u th,e pnmary ~~ctl~n of psychological tests were to predlct each mdIvl~ual ~ exact l?OSlhO~in the criterion distribution, the outlook would be qUite dlscouraglOg. \\ hen examined in the light of the error of estimate, mos~ t~sts do not appear very efficient. In most testing situations, ho~ev~r,. lt IS not necessary to predict the specific criterion performance of mdlvl~ual .c~ses, but rather to determine which individuals will exceed a certam mlmmum standard of performance, or cutoff point, in the cri:erion. What are the ch.an:es that Mary Greene will graduate from medIcal school, tI:at Tom Hlggms ",'in pass a course in calculus, or that Beverly ~ruce WIll succeed as an astronaut? Which applicants are likely to be satlsfactory clc::rks,salesmen, or machine operators? Such information is ~seful not only fo~ ~roup i selection but also for individual career planmng. For example, lt 15 advantageous for a student to know that he has a gOO? chanc~ of pas~ing all courses in law school, even if we are unable to estimate WIth certamty whether his grade average will be 74 or ~I: . ., A test may appreciably improve predIctive effiCIency If It sho~s a~1J significant correlation with the criterion, however 10w..Un.der.certa~n Cltcumstanees even validities as low as .20 or .30 may Justify lncluslon of the test in ~ selection program. For many testing purposes, evaluation .of tests in terms of the error of estimate is unrealistically stringent. Conslderation must be given to other ways of evaluating the contribution of a
Validity: AI easuremellt and Interpretation
167
test, which take into account the types of decisions to be made from the scores. Some of these procedurcs will be illustrated in the following section.
BASIC APPROACH. Let us suppose that 100 applicants have been given fln aptitude test and followed up until each could be evaluated for success on a certain job. Figure 17 shows the bh'ariate distribution of test scores and measures of job success for the 100 subjects. The correlation between these two variables is slightly below .70. The minimum acceptable job performance, or criterion cutoff point, is indicated in the diagram by a heavy horizontal line. The 40 cases falling below this line would represent job failures; the 60 above the line, job successes. If all 100 appli~ants are hired, thereforc, 60 percent will succeed on the job. Similarly, if a smaller number were hired at random, without reference to test scores, the proportion of successes would probably be close to 60 percent. Suppose, however, that the test scores are used to select the 45 most promising applicants out of the 100 (selection ratio;::: .45). In such a case, the 45 individuals falling to the right of the heavy vertical line would be chosen. Within this group of 45, it can be seen that there- arc 7 job failures, or false acceptances, falling below the heavy horizontal line, and 38 job successes. Hence, the percentage of job successes is now.84 rather than 60 (i.e., 38/45 .84). This increase is attributable to the use of the test as a screening instrument. It will be noted that errors in predic:te:d criterion score that do not affect the decision can be ignored. Opl)' those prediction errors that cross the cutoff line and hence place the individual in the wrong category will reduce the selective effectiveness of the test . . For a complete evaluation of the effectiveness of the test as a screening mstrument, another category of cases in Figure 17 must also be examined. This is the category of false re;ections, comprising the 22 persons who score below the cutoff point on the test but above the criterion cutoff. From these data we would estimate that 22 percent' of the total applicant sample are potential job successes who will be lost if the test is used as a screening device with the present cutoff point. These false rejects in a personnel selection situation correspond to the false positives in clinical evaluations. The latter term has been adopted frO,J:lk medical practice, in whi~ .a t~st for a pathological condition is reported ~positive if the condltion 1S present and negative if the patient is Dormal. A false positive thus refers to ~ case in ~hich the test erroneously 4l~~atf,(~-1:hepresence ?f ~ ?athologJ~1 condition, as when brain damage~,-~ mdicated in an mdlVldual who lS actually normal. This terminology is likely to be COD-
=
Validity: Measurement and Interpretation
, I
openin s, and the ur ('nc or seed with which t , filled.
'~
I
I
I
Job
Successes
Criterion
Cutoff
Job failures
Low Low
Test Score ~'FIC.
17. Increase in the Proportion of "Successes" Resulting from the Use of
, a Selection Test.
fusingunless we remember that in clinical practice a positiv~ result po a In pers~n~el . selectiona positive result conventionally refers to a favorabJ~ prediCtIon : regardingjob performance, academic achievement, and the lI~e. . In settin on a test, attention should be ven to the percentage of false rejects (or false positives as we as to the .erc:nt-i ) a cesses an ai ures wit in t~_se eete grou.!} In certam SItu;; ations,the cutoff point should be set sufficiently higt, to e~clu?e all but ',' a few possible failures. This would be the case when t~~',;obIS of such !: a nature that a poorly qualified worker could cause senous loss or dami age. An example would be a commercial airline. pilot. Under o.ther :' circumstances, it may be more important to admit. as many qualIfied ~ personsas possible, at the risk of including more fallures .. In the latter ',> case the number of false rejects can be reduced by the choice of a lower ,~,cutoffscore. Other factors that normally determine the position of ~he ."i, cutoffscore include the available personnel snpP4:, the number of job r.'
, test denotes pathology and unfavorable diagnosis, whereas
'i.
.
"
169
In many personnel decisions, the selection ratio is determined by the practical demands of the situation. Because of supply and demand in filling job openings, for example, it may be necessary to hire the top 40 percent of applicants in one case and the top 75 percent in another. When the selection ratio is not externall,T imposed, the cutting smre 011 a test can be set at that point giving the maximum differentiation be. tw~ Clilelioll grouEs. TIus can be done roughly by comparing the distrl ution of test scores in the two criterion groups. More precise mathematical procedures for setting optimal cutting scores have also been worked out (Darlington & Stauffer, 1966; Guttman & Raju, 1965; Rorer, Hoffman, La Forge, & Hsieh, 1966). These procedures make it possible to take into account other relevant parameters, such as the relative seriousness of false rejections and false acceptances. In the terminology of decision theofy, the example given in Figure 17 illustrates a simple strategy, or plan for deciding which applicants to accept and which to reject. I~ mor.e.~eral terms, a strategy is a technique for utilizing information in order to reach a decision about individuals. In tTllscase, the strategy was to accept the 45 persons with the highest te; scores. The increase in percentage of successful employees from 60 to 84 could be used as a basis for estimating the net benefit resulting from the use of the test. Statistical decision theory was developed by Wald (1950) with special reference to the decisions required in the inspection and quality control of industrial products. Many of its implications for the construction and interpretation of psychological tests have been systematically worked out by Cronbach and GIeser (1965). Essentially, decision theory is an attempt to put the decision-making process into mathematical form, so thdt available information may be used to arrive at the most effective decision ~nder .s~ecified circumstances. The mathematical procedures employed lD. d~c1Slon.th~ory a~e often quite complex, and few are in a form permItting theIr Immediate application to practical testing problems. Some of the basic concepts of decision theory, however, are proving helpful in the reformulation and clarification of certain questions about tests. A few of these ideas were introduced into testing before the formal development of statistical decision theory and were later recognized as Dtting into that framework.
PREDICTION OF OUTCOMES. A precursor of decision theory ini.psychologi. ca.1testing is ~o b~ found in the Taylor-Russell table~( 193,~),which permIt a detennmation of -the net gain in selection acc~racy atbibutable to the use of the test. ~ information required inc1\ip s'the validity co-
l
Validity: Measurement and Interpretation o
Principles of Psychological
Testing
cient of the test, the proportion of applicants who m~~t be acclep~e~ lection ratio), and the proportion of successfu~ app lc~n~ :: ~~r:e thout the use of the test (base rate). A change many 0 t I" ctors can alter the predictive efficiency of the test. For urposes of illustration, one of the Taylor-Russell tables has been e rod~eed in Table 14. This table is designed for us~ when the base .aie or ercenta e of successful applicants selected pnor to the use of he test 1s 60. Ot~er tables are prOVided by Taylor and Russe~l for ~t~~r base ra~es Across the top of the table are given different va ues ~ .e selection ;atio, and along the side are the tes~ validities. The entnes 111 the' body of the table indicate the proportion of successful· persons
TABLE
14
i
f G'
(
Proportionof "Successes" Expected through the Use 0 Test Validityand Given Selection Ratio, for Base Rate .60. (From Taylor and Russell, 1959, p. 576) ~':~~,",7"'J2'-':UliH~~'.:>,JI;~~,.:~!M.r
0
lven
=-"
.
••_.:::·..:;.':5.~~~
Selection Ratio .30
.40
.50
.60 .70 .80 .90
.95
.60 .60 .60 ·60 .60 .61 .61 .61 .60 .60 .63 .62 .61 .61 .60 .64 .63 .62 .61 .61 .65 .64 .63 .62 .61
.66 .65 .63 .62 .61 .68 .66 .64 .62. .6J .69 .70
.75 .80
.85 .90
.95 1.00
.99 1.00
1.00 1.00 1.00 1.00
.99 1.00 1.00 1.00
.96 .98 .99 1.00 1.00
.93 .95 .97 .99
.90 .92
.95 .97
.86 .88 .91 .94
1.00
1.00
1.00
1.00
.99 1.00
1.00
.99
.97
.67 .68
.65 .66
.63 .62 .63.62
.72 .69 .66 .64
.62
.73 .70 .67 .64 .75 .71 .68 .64 .76 .73 .69 .65 .78 .74 .70 .65 .80 .75 .71 .66
.62
.62 .63 .63
.63
.81 .77 .71 .66 .63 .83 .78 .72 .66 .63 .86 .80 .73 .66 .63 .88 .82 .74 .67 .63 .92 .84 .75 .67 .63 1.00 .86 .75 .67 .63
171
selected after the use of the test. Thus, the difference between .60 and anyone table entry shows the increase in proportion of successful selections attributable to the test. Obviously if the selection ratio w.ere 100 percent, that is, if all applicants had to be accepted, no test, howen'r valid, could improve the selection process. Reference to Table 14 sho\\'s that, when as many as 95 percent of applicants must be admitted, even a test with perfect validity ( r = 1.00) would raise the proportion of successful persons by only 3 percent (.60 to .63). On the other hand, when only 5 percent of applicants need to be chosen, a test with a validity coefficient of only .30 can raise the percentage of successful applicants selected from 60 to 82. The rise from 60 to 82 represents the incremental vaUdity of the test (Sechrest, 1963), or the increase in predictive validity attributable to the test. It indicates the contribution the test makes to the selection of individuals who will meet the minimum standards in criterion performance. In applying the Taylor-Russell tables, of course, test validity should be computed on the same sort of group used to estimate percentage of prior successes. In other words, the contribution of the test is not evaluated against chance success unless 'applicants were preViously selected by chance-a most unlikely circumstance. If applicants had been sele<;:teq on the basis of previous job history, letters of recommendation, and interviews, the contribution of the test should be evaluated ODe. the- ,basis at what the test adds to these previous selection procedures. .. The incremental validity resul~~~ from the use of a test depends not only on the selection ratio but l\~'()ll the base rate. In the previously illustrated job selection situation, the base rale refers to the proportion of successful employees prior to the introduction of the test for selection purposes. Table 14 shows the anticipated outcomes when the base rate is .60. For other base rates, we need to consult the other appropriate tables in the cited reference (Taylor & Russell, 1939). Let us consider an example in which test validity is .40 and the selection ratio is 70 percent. Under these conditions, what would be the contribution or incremental validity of the test if we begin with a base rate of 50 percent? And what would be the contribution if we begin with more extreme base rates of 10 and 90 percent? Reference to the appropriate Taylor-Russell tables for these base rates shows that the percentage of successful employees would rise from 50 to 75 in the Hrst case; from 10 to 21 in the second; and from 9 to 99 in the third. Thus, the improvement in percentage of successful employees attributable tQ .the use of the test is 25 when the base rate was 50, but only 11 and 9 when the b,ase rates were more . extreme. The implications of extreme base rates are of specia~,,interest in clinical psychology, where the base rate refe~ to' the frequency of the patholOgical condition to be diagnosed in the, p.qpulation tested (Buchwald,
Princillies of PSljcllological Testing ,t1965; Cureton, 1957a; Meehl & Rosen, 1955; J. S. Wiggins, 1973). For :)example, if 5 percent of the intake population of a clinic has organic :brain damage, then 5 percent is the base rate of brain damage in this ,~population. Although the introduction of any valid test win improve :~.predictive or diagnostic accuracy, the improvement is greatest when the . base rates are closest to 50 percent. '''ith the extreme base rates found ;i'wfth rare pathological conditions, however, the improvement may be .:, negligible. Under these conditions, the use of a test may prove to be unjustified when the cost of its administration and scoring is taken into '; account. In a clinical situation, this cost would include the time of professional personnel that IDlght otherwise be spent on the treatment of • additional cases (Buchwald. 1965). The number of false positives, or normal individuals incorrectly classified as pathological, would of course increase this overall cost in a clinical situation. "'Then the seriousness of a rare condition makes its diagnosis urgent, .. tests of moderate validity may be employed in an early stage of sequential decisions. For example, all cases might first be screened with an easily administered test of moderate validity. If the cutoff score is set high enough (high scores being favorable), there will be few false negatives but many false positives, or normals diagnosed as pathological. The latter can then be detected through a more intensive individual examination given to all cases diagnosed as positive by the test. This solution would be appropriate, for instance, when available facilities !Jlake the intensive individual examination of all cases impracticable.
RELATION OF VALIDITY TO MEAN OUTPUT LEVEL. In many practical situations, what is wanted is an estimate of the effect of the selection test, not on percentage of persons exceeding the minimum performance, but on overall output of the selected persons. How does the actual level of job proficiency or criterion achievement of the workers hired on the basis of the test compare with that of the total applicant sample that would have been hired without the test? Following the work of Taylor and Russell, several investigators addressed themselves to this question (Brogden, 1946; Brown & Ghiselli, 1953; Jarrett, 1948; Richardson, 1944). Brogden (1946) first demonstrated that the expected increase in output is directly proportional to the validity of the test. Thus, the improvement resulting from the use of a test of validity .50 is 50 percent as great as the improvement expected from a test of perfect validity. The relation between test validity and expected rise in criterion achievement can be readily seen in Table 15. Expressing criterion scores
0 0 ,..(
It:l
~ 0
~
It:l
ce: 0
~ It:l
1:-: 0 I,,;
It:l
~
..,
c ·8 II)
esIII 0 C,)
.e-
:2 ~
0
C'1 \I')
~
0
~
1
A table including more values for both selection ratios and validity coefficients was prepared by Naylor and Shine (1965). 1
o
~
~ c.2 Qj:8~ tn IX:
Validity: Measurement and Interpretation Principles of Psychological Testing standard scores with a mean of zero and an SD of 1.00, this table gives e expected mean criterion score of workers selected with a test of given idity and with a given selection ratio. In this context, the base output an, corresponding to the performance of applicants selected without se-ofthe test, is given in the column for zero validity. Using a test with ero validity is equivalent to using no test at all. To illustrate the use of he table, let us assume that the highest scoring 20 percent of the appli.cantsare hired, (selection ratio == .20) by means of a test whose validity coefficientis.50. Reference to Table 15 shows that the mean criterion .performance of this group is .70 SD above the expected base mean of an Illitested sample. \Vith the same 20 percent selection ratio and a perfect test (validity coefficient 1.00), the mean criterion score of the accepted applicants }vould be 1.40, just twice what it would be with the test of validity .50. Similar direct linear relations will be found if other mean criterion performances are compared within any roW of Table 15. For instance, with a selection ratio of 60 percent, a validity of .25 yields a mean criterion score of .16, while a validity of .50 yields a mean of .32. Again, doubling the validity doubles the output rise. The evaluation of test validity in terms of either mean predicted output or proportion of persons exceeding a minimum criterion cutoff is obviously much more favorable than an evaluation based on the previously discussed error of estimate. The reason for the difference is that prediction errors that do not affect decisions are irrelevant to the selection situation. For example, if Smith and Jones are both superior workers and are both hired on the basis of the test, it does not matter if the test shows Smith to be better than Jones while in job performance Jones
=
175
vidual's preferences and I h out, however, that decisi:: Ut~:~ste~: It a~ been repeatedly pointed values into the d .. ry Id not mtroduce the problem of eClSlon process, but merely made it explicit Value-:"· . ~ tems h ave a 1ways enter d . t d .. clearly re~gnized or sy:te:a~ica~~s~:~dl~~~ they were not heretofore
lY'
In choosmg a decision strate th 1 . utilities across all outcome R e goa IS to maximize expected of a Simple de . . s. . e er.enee to the schematic representation cedure Th' d~Islon strategy m FIgure 18 \vill help to clarify the pro17 in :.vhic~ la~ralm sho~s the decision strategy illustrated in Figure a smg e test IS administered to a group of applicants and the' d " eClSIon to . t an app Iicant is made on the basis of a cutoff score on accept the t or t ~Jec valid and fals es. here are four possible outcomes, including ability of he acceptances and valid and false rejections. The probeac outcome can be f d fr h each of the four sectio . oun om t e number of persons in in that example th ns ofbFIgu:e. 17. Since there were 100 applicants , ese num ers dIVIded b 100' h the four outcomes listed in Fi . 18 gIVe t e probabilities of utilities of the diff gure. e other data needed are the erent outcomes expre d of th ' sse on a common scale. The expected overall utili ing the probability h e,strategy could then be found by multiplythese products forOt~:c faoutco~e by the utility of the outcom~, adding u~ ou comes, and subtracting a value correspondin to h
rh
t
10:
r
val:d~;~:t;~r:e~:~:r t~h~s last ~erm ~i?h~ights th~ fact that a test of easily administered by reIat' e r~tamed If It IS short, mexpensive, group administration An 1· IdV:~dun1tramed personnel, and suitable for . n IVI ua test req . . t' d or expensive equipment would llee d a h'Igh er Uln~g. vahdltya torame justifyexaminer its use.
excels Smith. Decision
It is characteristic of decision theory that tests are evaluated in terms of their effectiveness in a specific situation. Such evaluation takes into account not only the validity of the test in predicting a particular criterion but also a number of other parameters, including base ra:e and s~~ Another important' parameter is the relative utility of expected outcomes, the judged favorableness or unfl\.vorablcness of each outcome. The lack of adequate systems for assigning values to outcomes in terms of a uniform utility scale is one of the chief obstacles to the application of decision theory. In industrial decisions, a dollar-and-cents value can frequently be asSigned to different outcomes. Even in such cases, however, certain outcomes pertaining to good will, public relations, and employee morale are difficult to assess in monetary terms. Educational decisions must take into account institutional goals, social values, and other relatively intangible factors. Individual decisions, as in counseling, must consider the indi-
Outcome
Probability
Valid Acceptance
.38
False Acceptance
.07
V~lid Rejection
.33
False';Rejection
.22
TIlE ROLE OF VALUES IN DECISION TIIEORY.
Administer test and C1pply
cutoff score
FIG.
18. A$imple
Decision Strategy.
2 For ,w fl'ctitious example illustraf all .' Wiggins"0973), pp. 257-274. mg steps II! these computations, see
y, a
It should also be noted that many personnel decisions are in effect sequential, although they may not be so perceived. Incompetent employees hired because of prediction errors can usually be discharged after a probationary period; failing students can be dropped from college at several stages. In such situations, it is only adverse selection decisions that are terminal. To be sure, incorrect selection decisionS- that are later rectified may be costly in terms of several value systems. }Jut " ", they are often less costly than terminal wrong decisions. A second condition that may alter the effectiveness of a psychological test is, the availability of alternative treatments and the possibility of adaptmg treatments to individual characteristics, An example would be the utilization of different training procedures for workers at different aptitude levels, or thc introduction of CQ.l!lpensatory educational programs for students with certain educational disabilities. Under these conditions, the decision strategy followed in individual eases should take into account available data on the interaction of initial test score and differential treatment. When adaptive treatments ar~ utilized, the success rate js likely to be substantially improved. Be£ause, the assignment of in
SEQUEXTIAL STRATEGIES AND ADAPTIVE TREATMENTS. In some situations, ~;the effectiveness of a test may be increased through the use ~f more complex decision strategies which take still more param,etoe~s.lllto .ac. count. Two examples will serve to illustrate these poss~blhtles, ,~ust, , ,t t may be used to make sequential rather than termmal deCISIOns, '. es sod' F' 17 d 18 aU ;,With the simple decision strategy Illustrate III 19ures an , :"decisions to accept or reject ar: treated as terminal. Figure 19, on the " other hand, shows a two-stage sequential decision, T~st A could be a ,';shortand easilv administered screening test. On the baSIS of. per~orma~ce , on this test, in'dividuals would be sorted into three categ?nes.: mcludl~~ those clearly accepted or rejected, as well s. 3n in~ermedlat~ uncertam group to be examined further with more intenSIve tec~mque~, repre.. sented by Test B. On the basis of t~e second-sta?e testmg, tIllS group ,; wouldbe sorted into accepted and rejected categorIes. ';,
Such sequential testing can also be cmployed within a si~gle test~ng , f t to t'm (DeWItt & \Velss ,> session,to ma'Ximize the effectlve usc 0 es mg Ie.' ..~. 1974; Linn, Rock, & Cleary, 1969; Weiss- -& 13etz, 1973): Altho~gh. applicable to paper-and-pencil printed grou~ ~ts, seq~entIal testmg IS particularly well suited for computer testing, ~ssenhally the sequen~e ~f items ~r item groups 'within the test is determine? b~ the examl,nee s ownperfom1anceo For example, everyone might begm w1th a set of Ite~s of intermediate difficulty. Those who score poorly are routed t? easIer items' those who score well, to more difficult items. Such branchmg may oeeu; repeatedly at several stages, The princip~l eff.e~t is that each examinee attempts only those items suited to h~s abJ1l~y level, rather than trying all items, Sequential testing ~~del.s WIll be dlscusse~ further in Chapter 11, in connection with the utlhzahon of computers 10 group testing. hI' I d' d Another strategy, suitable for the diagnosis of psye 0 ogICa 1~or ers, is to use only two categories, but to test further. a~ cases clas~ified as .. positives (i.e., possibly pathol~gi~al) ~y the.prel~mmary sc~eem~g test. .', This is the strategy cited earlIer ll1 this. s.e~tion, ~n connection Wlth the use of tests to diag,nose pathological condItIons With very low base rates.
,.~ \
I
DIFFERENTIALLY PIlEDlCTABLE SUBSETS OF PERSONS. The validity of a test for a given criterion may vary among subgroups differing in personal characteristics. The classic psychometric model assumes that prediction errors are characteristic of the test rather than of the person and that these errors are randomly distributed among persons. With the flexibility of ap~roach ushe,re~ in by decision theory, there has been increasing exploration of prediction models involving interacti~ hetween persons and
For a ,fuller discussion of the implications of decision theory for test use, see S. Wlggms (1973), Ch. 6, and at a more technical level; Cronbach and GIeser
3
J.
(1965),
.
178 ~
Validity:
Principles of Psychological Testing
.' ts. Such interaction implies that the same test may be a better pretor for cert~i~Ciasses or subsets of persons than it is for others. For xamplc,a given test may be a better predic~or of criterio~ performance or men than for women, or a better predlctor for applicants from a ower than for applicants from a higher socioeconomic level. In. these xamples,sex and socioeconomic level are known as moderator vanables, sincethey moderate the validity of the test (Saunders, 1956). I When computed in a total group, the vali~ity coe!R<,ient of a test may 'be too low to be of much practical value In prcdlction. But when reo < computed in subsets of individuals differing in some i~e~tifia?le charac, teristic, validity may be high in one subset and negl1g~~le In anot~er. ; The test could thus be used effectively in making declSJons regardmg persolls in the first group but not in the second. Per~aps anothe~ test or " some other assessment device could be found that IS an effective pre. dictor in the second group. A moderator variable is some characteristic of persons that makes It i posS'ibfeto-pre'ct e pre ictability 0 I erent 10 ividuals with a given ins rument. t may e a emograp lC vana e, such as sex, age, e u.al level, or socioeconomic background; or it may be a score on another test. Interests and motUlation often function as moderator variables. Thus, if an applicant has little interest in a job, he will probably perform poorly regardless of his scores on relevant aptitude tests. Among such persons, the correlation between aptitude test scores and job performance would be low. For individuals who are interested and highly motivated, on the other hand, the correlation between aptitude test score and job success may be quite high. !
VARIABLES. Evidence for the opEMPmlCALEXAMPLESOF MODERATOR eration of moderator variables comes from a variety of sources. In a survey of several hundred correlation coefficients between ap~tude test scores and academic grades, H. G. Seashore (1962) found htgher correlations for women than for men in the large majority of instances. Tht; same trend was founa in high sChool and college, although the trend was more pronounced at the coll~ge level. ~he ?~ta do not in.dicate. the reason for this sex difference in the predictabIhty of academlc achievement, but it may be interesting to speculate about it in the light of other known sex differences. If women students in general tend to be more conforming and more inclined to accept the values and standards of the school situation, theiJ;class achievement will probably devend largely on their abilities. If, on the other hand, men students tend to concentrate their efforts on those activities (in or out of school) that arouse their individual interests, these interest differences wO..!,Jldintroduce additional and would make it more difficult to val'ianee-in their......courseachiev~t
Mr:a~'U"C11lentand Interpretation
179
predict achievement from test scores. Whatever the reason for the difference, sex does a ear to function as a moderator variable in the predictability of academic gra es from aphtu e test scores. A number of investigations have been specially designed to assess the role of moderator variables in the prediction of academic achievement. Several studies (Frederiksen & Cilbert, 1960; Frederiksen & Melville, 1954; Stricker, 1966) tested the hypothesis that the more compulsive students, identified through two tests of compulsivity, Y{,ouldput a great deal of effort into their course work, regardless of their interest in the courses, but that the effort of the less compulsive students would depend on their interest. Since effort will be reflected in grades, the correlation between the appropriate interest test scores and grades should be higher among noncompulsive than among compulsive students. This hypothesis was confirmed in several groups of male engineering students, but not among liberal arts students of either sex. Moreover, lack of agreement among different indicators of compulsivity casts doubt on the generality of the construct that was being measured. In another study (Grooms & Endler, 1960), the college grades of the .63) with aptitude and more anxious students correlated higher (r achievement test scores than did the grades of the less anxious litudents .19). A different approach is illustrated by Berdie (1961), who in(r vestigated the relation between intraindividual variability on a test and the predictive '-'ilidity of the same test. It was hypothesized that a given test will be a- better predictor for those individuals who perform more consistently in different parts of the test-and whose total scores are thus more reliable. Although the hypothesis was partially confirmed, the relation proved to be more complex than anticipated (Berdie, 1969). In a different context, there is evidence that self-report personality inventories may have higher validity for some types of neurotics than for others (Fulkerson, 1959). The characteristic behavior of the two types tends to make one type careful and accurate in reporting symptoms, the o~her ~areless and evasive. The individual who is characteristically preClSe and careful about details, who tends to worry about his problems, and who uses intellectualization as a primary defense is likely to provide a more accurate picture of his emotional difficulties on a self-report inventory than is the impulsive, careless individual who tends to avoid expressing unpleasant thoughts and emotions and who llses denial as a primary defense. Ghi~elli (1956, 1960a, 1960b, 1963, 1968; Chise~!C Sander~, 1967) has extenslvely explored the role of moderator variaBles iIl. UidiIstrial situations. In a study of taxi drivers (Ghiselli, 1956), the @rrelati~n between an aptitude test and a job-performance criterion in the t6tl;J applicant sa'ijl~ was only .220. The group was then sorted into tpirds qp the basis ~ ~~ ..~ on an occupational interest test. When the validity of the
=
=
180
Principles of Psychological Testing
aptitude test was recomputed within the third whose occupational interest level was most appropriate for the job, it rose to .664. A technique employed by Chiselli in much of his research consists in finding for each individual the absolute difference (D) between his :. actual and his predicted criterion scores. The smaller the value of D, the , morepredictable is the individual's criterion score. A predictability scale ~; is then developed by comparing the item responses of two contrasted :- subgroups selected on the basis of their D scores. The predictability -: scaleis subsequently applied to a new sample, to identify highly preo dictableand poorly predictable subgroups, and the validity of the original . testis compared in these two subgroups. This approach has shown considerablepromise as a means of identifying persons for whom a test will " be a good or a poor predictor. An extension of the same procedure has .'been developed to determine in advance which of two tests will be a '\ better predictor for each individual (Chiselli, 1960a). Other investigators (Dunnette, 1972; Hobert & Dmmette, 1967) have "'. argued that Chiselli's D index, based on the absolute amount of pre.~dictionerror without regard to direction of error, may obscure important individualdifferences. Alternative procedures, involving separate analyses of overpredicted and underpredicted cases, have accordingly been pro'posed. . ;\ Atthis time the identification and use of moderator variables are still ,'i,n' an explor;tory ·phase. Considerable caution is_required to avoid methodologicalpitfalls (see, e,g., Abrahams & Alf, 1972a, 1972b; Dunnette,1972;Ghiselh, 1972; Velicer, 1972a, 1972b). The results are usually ~9uitespecific to the situations in which they were obtained. And it is iinportant to check the extent to which the use of moderators actually 'proves the prediction that could be achieved through other more 'rect means (Pinder, 1973).
':;xForthe prediction of practical criteria, not one but several tests are eperallyrequired. Most: criteria are complex, the criterion measure de. ing on a number of different traits. A single test designed to measure a criteriQn would thus have to be highly heterogeneous. It has aly been pointed out, however, that~ re~!i.~~ homogeneous _~~st, is more satisfactory b~~.e_iL)'ieIasJess--.--. suringlargely' a singlet~ . ---US-Scores ('Ch-:;)). Hence, it is usually preferable to use a ination of several relatively homogeneous t~sts, each covering a ent aspect of the criterion, rather than a single test consisting of a podge of many diffe:rent kinds of items. en a number of speciaUy selected tests are employed together to
,_~
Validity: Measurement and Interpretation
181
a s~n.gle.criterion, they are known as a test batten(. 1Jpe chief arlsmg 10 the use of such batteries concerns the way 'in which scores ,on the di~ert:n~ tests are to be combined in arrivi,!!g at a decision regardmg each IndiVIdual. The. statistical procedures followed for this purpose ~re of tw.g major typ:s, namely, multiple regression equation and multiple cutoff scores. --------'--:...::-.~-=..::!.:.::.:.:.:=___,
/?I?'e:-T~!'~redict
Of:tlp.fJ701(.fl.problem
..
~Vhe~~ts ~re adIriinistered in the intensive study of individual cases,?1t~/et-,VV1C 111 ~li~lCaldiagnosis, counseling, or the evaluation of high-level execu//' I ' "."",,ves, It Isa£.QmIDOlLpr.actice.fOLtb~aminer to utilize test scores with~1 out further st~tistical...analpis.-W preparing a case report and in making! recom~endatI~ns, the examiner relies on judgment, past experience, and \ theoret~cal ratIOnale to interpret score patterns and integrate findings \ from dl~erent tests. Such clinical use of test scores will be discussed \ further 1ll Chapter 16. \ ::
The multiple regression equation YIelds a predicted cntenon Score for each individual on the basis of his score . b t . '1'1.. £ II ._-' .', '. a te ~L1e 10 owing regression equation illu~trates the applIcation of this technique to predicting a student's achIevement in high school mathematics courses from his scores on verbal (V), numerical (N), and reasoning (R) tests: • MULTIPLE
~RESS~ON.
EQUATION.
. Math~matics Achievement =: .21 V
+ .21 N + .82 R +
6
~::~~~
: +
(.21) ( 4) +( .32)( 8)
J
Ii,)' L :1"11
'I
1
I: :1
';:
1 ; I ".
1 + 1.35 = 6.01
Bill's ~redictcd stanine is approximately 6. It ~l be recalled (Ch. 4) that a stanme of 5 represents average pedormance. Bill would thus be expected to ~o somewhat better than average in mathe~tics courses. His very supenor performance in the reasoning test (R =8') and his above~verage score on the verbal test (V = 6) compensate for his poor score 10 spee~ and a~uracy of computation (N 4). _ SpecIRc techmques for the computation of regression equations can be
=
'--"1
..-;f ir ':' v(.{li,(,Gi/ltt/Vl. U _-1.::- .... ------...
; :If
The estimated ma'h Lema ti'cs ach'levement of this student is found as follows: Math. Achiev. == (.21)(6)
I
'V~,
,1
1.35,
In t~IS ~quabon, the student's stanine Score on each of the three tests is multiplied by the corresponding weight given in the equation. The sum of t~c..sepr~~uct~, plus a constant (1.35), gives the student's predicted s~!!~ne pOSItIon lD mathematics courses. :.'Suppose that Bill Jones receives the following stanine scores: Verbal
\
'\
'lii,'1 'i
'
1
i,II
fill
I illl'
1 i: \ (i 11 111:1
'I,i! J
'J, ,"
