Chapter 7 –Sampling –Sampling
V.E.S College of Arts, Science & Commerce
Chapter 7 Sampling
SAMPLING
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Chapter 7 –Sampling –Sampling
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Census versus Sample •
Cens Census us in simp simple le term terms s mean means s to meas measur ure e each each elem elemen entt in the the grou group p or population of interest.
•
A part of a population, or a subset from a set of units, which is provided by some some proc proces ess s or othe other, r, usua usually lly by delib deliber erat ate e sele select ctio ion n with with the the obje object ct of investigating the properties of the parent population or set.
•
Surveys of industrial consumers or of distributors of consumer products are frequently in the form of a census.
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However there are certain reasons, which make census impractical or even impossible. The reasons are as follows: 1.
Cost: Cost: Cost is an obvious constraint on the determination of whether a census should should be taken. taken. If informa informatio tion n is desire desired d on grocer grocery y purch purchase ase and use behaviour (frequencies and amounts of purchase of each product category, average amount kept at home and the like) and the population of interest is all households in a country, the cost will preclude a census being taken. Thus a sample is the only logical way of obtaining new data from a population of this size.
2.
Time: The kind of cost we have just considered considered is an outlay cost. The time involved in obtaining information from either a census or a sample involves the possibility of also incurring an opportunity cost. That is, the decision until information is obtained may result in a smaller gain or a larger loss than would have been the case from making the same decision earlier. The opportunity to make more (or save more, as the case may be) is, therefore, foregone.
3.
Accuracy : A study using a census, cens us, by definition, definit ion, contains cont ains no sampling samplin g error. A study using a sample may involve sampling error in addition to other types of error. Other things being equal, a census will provide more accurate data than a sample. However it has been argued that a more accurate estimate of the population of a country could be made from a sample than from a census. Taking a census of a population on a “mail out – mail back” basis requires that the name names s and and addr addres esse ses s of almo almost st all all hous househ ehol olds ds be obta obtain ined ed,, cens census us Page 2
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questionnaires mailed, and interviews conducted of those
not responding.
The questionnaires are sent to a population of which only about half have completed high school. The potential for errors in a returned questionnaire is therefore high. 4.
Destru Destructi ctive ve nature nature of the measu measurem rement ent:: Measur Measureme ements nts are someti sometime mes s destructive in nature. When they are, it is apparent that taking a census would usua usually lly defe defeat at the the purp purpos ose e of a meas measur urem emen ent. t. If one one were were prod produc ucin ing g firecrackers, electrical fuses, or gas seed, performing a functional use test on all products for quality control purposes would not be considered from an economic standpoint. A sample is then the only practical choice. On the other hand, if the light bulbs, bicycles, or electrical appliances are to be tested, a 100% sample (census) may be entirely reasonable.
Advantages of Sampling 1. Sampling Sampling is cheaper cheaper than a census census survey. survey. It is obviously obviously more econom economical, ical, for instance, to cover a sample of households than all households in a territory although the cost per unit of study may be higher in a sample survey than in a census. 2. Since Since magnitu magnitude de of operat operation ions s involved involved in a sample sample survey survey is small small,, both both the execution of the fieldwork and the analysis of the results can be carried out speedily. 3. Samp Samplin ling g resu results lts in grea greate terr econ econom omy y of effo effort rt as rela relati tive vely ly smal smalll staf staffs fs is required to carry out the survey and to tabulate and process the survey data. 4. A sample sample survey survey enables enables the resear researche cherr to colle collect ct more more detail detailed ed informatio information n than would otherwise be possible in a census survey. Also, information of a more specialised type can be collected, which would not be possible in a census survey on account of availability of a small number of specialists. 5. Since the scale scale of operation operations s involved involved in a sample survey survey is small, small, the quality quality of interv interview iewing ing,, superv supervisio ision n and other other relate related d activit activities ies can be better better than than the quality in a census survey.
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Limitations of Sampling 1. When When the the info inform rmat atio ion n is need needed ed on ever every y unit unit in the the popu popula lati tion on suc such as individuals, dwelling units or business establishments, a sample survey cannot be of much help for it fails to provide information on individual count. 2. Sampling Sampling gives gives rise to certain certain errors. errors. If these errors errors are too large, large, the results results of the sample survey will be of extremely limited use. 3. While in a census census survey survey it may may be easy to check check the omissio omissions ns of certain certain units in view of complete coverage, this is not so in the case of sample survey.
The Sampling Process Step 1. Defi Define ne the the pop popul ulat atio ion n
Description The The pop popul ulat atio ion n is defi define ned d in term terms s of of a) elem elemen ent, t, b) b)
2. Spec Specif ify y samp sampli ling ng fram frame e
units, c) extent and d) time. The The mean means s of repr repres esen enti ting ng the the elem elemen ents ts of the the population – for example telephone book, map, or
3. Spe Specify ify samp amplin ling unit nit
city directory – are described. The unit unit for sam sampling ling – for for exam examp ple, le, city ity bloc block, k, company, or household – is selected. The sampling unit nit
may
conta ontain in one one
or
sever everal al popul opulat atio ion n
elements. 4. Spec Specify ify samp samplin ling g meth method od The The meth method od by whic which h samp samplin ling g unit units s are are to be 5. Dete Determ rmin ine e samp sample le size size
selected is described. The The numb number er of elem elemen ents ts of the the popu popula lati tion on to be
6. Spe Specify ify samp amplin ling plan lan
sampled is chosen. The operat eratio ion nal proc proce edure dures s for for selec electi tion on of the the
7. Select the sample
sampling units are selected. The of office ice an and fifieldwork necessary for th the se selection of the sample are carried out.
Step 1: Define the population It is the aggregate of all elements defined prior to selection of sample. A population must be defined in terms of •
elements, Page 4
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•
sampling units,
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extent and
•
time.
V.E.S College of Arts, Science & Commerce
Eliminating any one of these specifications leaves an incomplete definition of the population that is to be sampled.
Step 2: Specify the Sampling frame If a probability sample is to be taken, a sampling frame is required. A sampling frame is a means of representing the elements of the population. A sampling frame may be a tele teleph phon one e book book,, city city dire direct ctor ory, y, an empl employ oyee ee rost roster er,, a list listin ing g of all all stud studen ents ts attending a university, or a list of possible phone numbers. Maps also serve frequently as sampling frames. A sample of areas within a city may be taken and another sample of household then be taken within each area. City blocks blocks are somet sometime imes s sample sampled d and all househ household olds s on each each sample sample block block are included. A sampling of street intersections may be taken and interviewers given instructions as to how to take “Random walks”. From the intersection and select the households to be interviewed. A perfe perfect ct samp samplin ling g fram frame e is one one in whic which h every every eleme element nt of the popul populati ation on is represented once but only once. One does not need a sampling frame to take a nonprobability sample.
Step 3: Specify the sampling Unit The sampling unit is the basic unit containing the elements of the population to be sampled. It may be the element itself or a unit in which the element is contained. For example, if one wanted a sample of males over 13 years of age, it might be possible to sample them directly. In this case, the sampling unit would be identical with the element. However, it might be easier to select households as the sampling unit and interview all males over 13 years of age in each household. Here the sampling unit and the population element are not the same.
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Step 4: Specify the Sampling Methods It indicates how the sample units are selected. One of the most important decisions in this this regard regard is to determ determine ine which which of the two –proba –probabil bility ity and non-pr non-proba obabil bility ity sample –is to be chosen. Probability samples are also known as random samples and non-probability samples as non-random samples. There are various types of sample designs, which can be covered under two broad grou groups ps – rand random om or prob probab abil ility ity samp sample les s and and nonnon-ra rand ndom om,, or nonnon-pr prob obab abil ilit ity y samples.
Step 5: Determination of the Sample size Traditional sampling theory generally ignores the concept of the cost versus the value of the information to be provided by various sized samples. The problem of determination of sample size is dealt later on in depth.
Step 6: Specify the Sampling Plan The sampling plan involves the specification of how each of the decisions made thus far is to be implemented. It may have been decided that the household will be the element and the block the sampling unit. How is a household defined operationally? How How is the the inter intervi view ewer er to be inst instru ruct cted ed to dist distin ingu guis ish h betw betwee een n fami famili lies es and and households in instances where two families and some distant relatives of one of them are sharing the same apartment? How is the interviewer to be instructed to take a systematic sample of households on the block? What should the interviewer do when a housing unit selected is vacant? What is the callback procedure for households at which no one is at home? What age respondent speaking for the household is acceptable?
Step 7: Select the Sample The final step in the sampling process is the actual selection of the sample elements. This requires a substantial amount of office and fieldwork particularly if personal interview are involved.
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Characteristics of a good Sample Design A good sample design requires the judicious balancing of four broad criteria –goal orientation, measurability, practicality and economy. 1. Goal orientati orientation: on: This suggest suggests s that a sample sample design design “should “should be oriented oriented to the resear research ch object objective ives, s, tailore tailored d to the survey survey design, design, and fitted fitted to the survey survey conditions”. If this is done, it should influence the choice of the population, the measurement as also the procedure of choosing a sample. 2. Meas Measur urab abil ilit ity: y: A sam sample ple desi design gn shou should ld enab enable le the the comp comput utat atio ion n of vali valid d estimates of its sampling variability. Normally, this variability is expressed in the form of standard errors in surveys. However, this is possible only in the case of probability sampling. In non-probability samples, such a quota sample, it is not possible to know the degree of precision of the survey results. 3. Practicalit Practicality: y: This implies implies that that the sample sample design design can be be followed followed properly properly in the survey, as envisaged earlier. It is necessary that complete, correct, practical, and clear instructions should be given to the interviewer so that no mistakes are made in the selection of sampling units and the final selection in the field is not different from the original sample design. Practicality also refers to simplicity of the design, i.e. it should be capable of being understood and followed in actual operation of the field work. 4. Economy: Economy: Finally, Finally, economy economy implies implies that that the objectives objectives of the survey survey should should be achieved with minimum cost and effort. Survey objectives are generally spelt out in terms of precision, i.e. the inverse of the variance of survey estimates. For a given degree of precision, the sample design should give the minimum cost. Altern Alternati ativel vely, y, for a given given per unit unit cost, cost, the sample sample design design should should achiev achieve e maximum precision (minimum variance).
It may be pointed out that these four criteria come into conflict with each other in most of the cases, and the researcher should carefully balance the conflicting criteria so that he is able to select a really good sample design.
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Sampling Techniques Sampling techniques may be broadly classified as non-probability and probability sampling techniques.
Non-probability sampling techniques: 1. It relies relies on the perso personal nal judgme judgment nt of the resear researche cherr rather rather than t he chance chance to select sample elements. 2. The researche researcherr can arbitrarily arbitrarily or conscio consciously usly decide decide which which element element to include include in the sample. 3. NonNon-pr prob obab abili ility ty may may yield yield good good esti estima mate tes s of the the popu popula lati tion on char charac acte teris ristic tic.. However they do not allow for objective evaluation of the precision of the sample results. 4. Since there there is no way of determinin determining g the probability probability of selecting selecting any any particular particular element for inclusion in the sample, the estimates obtained are not statistically projectable to the population.
Probability sampling techniques: 1. Sampling Sampling units are selected selected by chance. chance. 2. It is possible possible to pre-specif pre-specify y every potentia potentiall sample of of a given size size that could could be drawn from the population, as well as the probability of selecting each sample. 3. Every potentia potentiall sample sample need not have have the same probab probability ility of selection selection,, but it is possible to specify the probability of selecting any particular sample of a given size. 4. This This requires requires not only a precise precise definitio definition n of the target target popula populatio tion, n, but also a genera generall specif specifica icatio tion n of the sampli sampling ng frame frame.. Becaus Because e sample sample eleme elements nts are selected by chance. 5. It is poss possib ible le to dete determ rmin ine e the the prec precis isio ion n of the the sam sample ple esti estima mate ted d of the the char charac acte teri rist stic ics s of inte intere rest st.. Conf Confid iden ence ce inte interv rvals als,, whic which h cont contai ain n the the true true population value with a given level of certainty, can be calculated. This permits the researcher to make inferences of projections about the target population
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from from whic which h the the samp sample le was was draw drawn. n. Prob Probab abili ility ty samp sampli ling ng tech techni niqu ques es are are classified based on : −
Element versus cluster sampling
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Equal unit probability versus unequal probabilities
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Unstratified versus stratified selection
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Random versus systematic selection
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Single-stage versus multistage techniques Diagrammatic representation of the sampling techniques. Sampling techniques
Non
probability sampling
Convenience Sampling
Judgmental Sampling
Simple Random Sampling
Systematic Sampling
Prob Probab abil ilit ity y sam samplin pling g techniques
Quota Sampling
Stratified Sampling
Non-probability techniques:
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Cluster Sampling
Multistage Sampling
Chapter 7 –Sampling –Sampling
V.E.S College of Arts, Science & Commerce
Convenience Sampling Definition A non-probability sampling technique that attempts to obtain a sample of convenient elements. The selection of sampling units is left primarily to the interviewer . Explanation 1. It is a form form of Non-P Non-Prob robabi abilit lity y sampli sampling. ng. 2. It is mainly mainly used used for Dipstick Dipstick studies studies.. This type of samplin sampling g is norma normally lly used used to get basic information to take elementary decisions. 3. Conven Convenien ience ce samples samples are often used in explo explorat ratory ory situati situations ons when there there is a need to get only an approximation of the actual value quickly and inexpensively. 4. Comm Common only ly used used Conv Conven enie ienc nce e samp samples les are are asso associ ciat ates es and and “the “the man man on the the street”. Such samples are often used in the pre-test phase of the study, such as pre-testing of a questionnaire. Examples: •
Use of students, church groups, and members of social organizations,
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Mall-intercept interviews without qualifying the respondents, r espondents,
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Department stores using charge account lists
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Tear out questionnaire included in a magazines, and
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People on the street interviews
Advantages •
Convenience sampling is the least expensive and least time consuming of all sampling techniques.
•
The sampling units are accessible, easy to measure and co-operative.
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This technique is used in exploratory research for generating ideas, insight or hypothesis.
Disadvantages •
Conv Conven enie ienc nce e samp sample les s cont contai ain n unkn unknow own n amou amount nts s of both both varia variabl bles es and and systematic selection errors.
•
These errors can be very large when compared to the variable error in a simple random sampling of the same size. Page 10
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Convenience samples are not representatives of any definable population. So they are not recommended for descriptive or casual research.
Judgmental sampling Definition A form of convenience sampling in which the population elements are purposively selected based on the judgment of the researcher. Explanation A judgment sample is one in which there is an attempt to draw a representative sample of the population using judgmental selection procedures. Judgment samples are common in industrial market research. Example A sample of addresses taken by the municipal agency to which questionnaires on bicycle riding habits were sent. A judgment sample was taken after researchers looked at traffic maps of the city, considered the tax assessment on houses and apartment buildings (per unit), and kept location of schools and parks in mind. Advantages •
Judgmental sampling is low cost, convenient and quick.
•
Judgmental sampling is subjective and its value depends entirely on the researchers judgment, expertise and creativity.
•
It is useful if broad population inferences are not required.
Disadvantage •
It does not allow direct generalization to a specific population, usually because the population is not defined explicitly.
Quota Sampling
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Definition A non probability sampling techniques that is a two stage restricted judgmental sampling. The first stage consists of developing control categories or quotas of population elements. In the second stag, sample elements are selected based on convenience or judgment. Explanation •
It is a form of Non-Probability sampling.
•
In Quota Sampling, the samples are selected in such a way that the interest parameters represented in the sample are in the same proportion as they are in the universe/ population.
•
Quota Sampling is widely used in consumer panels.
•
The following aspects must be kept in mind while choosing the control variables: −
The variables must be available and should be recent.
−
They should be easy for the interviewer to classify.
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They should be closely related to the variable being measured in the study.
−
The number of variable must be kept to a reasonable number so as to avoid confusion while analyzing the data
The cost of sample per unit is directly proportional to the number of control variables. In order to have a check mechanism about the quality of samples taken so as to reduce the selection errors, Quota Samples are “validated ” after ” after they are taken.
The process of validation involves a comparison of the sample and the population with respect to characteristics not used as control variables. For e.g. in a quota sample taken from a consumer panel for which income, education, and age group are used as control variables. If the comparison of this panel and the population might be made with respect to such characteristics as average number of children, occupation of the chief wage earner and home ownership. Then if the panel differed significantly from the population with respect to any of these characteristics, it would be an indication of the potential bias in the selection procedures. It should be noted that the similarity does not necessarily mean the absence of bias.
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Example If one wants to select a Quota sample of persons for a test of flavored tea and wants to control (control variables are the parameters based on which he would like to class classify ify the univer universe) se) it by ethnic ethnic backgr backgroun ound, d, income income bracke bracket, t, age group group and geogra geographi phical cal area. area. Then Then the sample sample taken taken would would have have the same same propor proportio tion n of people in each ethnic background, income bracket, age group and geographical area as the population. Disadvantages •
Scope for high variances
•
Scope for sizable selection errors.
•
Selection errors arise from the way interviewers select the persons/ variables to fill the quota. Incorrect information of the proportions of the population in each of the control variables, biases in the relationship of the control variables to the variables being measured, and from other sources.
Probability Techniques: Proba Probabil bility ity sampli sampling ng techni technique ques s vary vary in terms terms of sampli sampling ng effici efficienc ency. y. Sampli Sampling ng efficiency is a concept that reflects a trade-offs between sampling cost and precision. Precision refers to the level of uncertainty about the characteristic being measured. The greater the precision, the greater the cost and most studies require trade-off.
Simple Random Sampling Definition A probability sampling technique in which each element in the population has a known known and equal equal probab probabilit ility y of selec selectio tion n is known known as simple simple random random sampli sampling ng (SRS). Every element is selected independently of every other element and the sample is drawn by a random procedure from a sampling frame. Explanation In rand random om samp samplin ling, g, each each elem elemen entt in the the popu popula lati tion on has has a know known n and and equa equall probability of selection. Furthermore, each possible sample of a given size (n) has a known and equal probability of being the sample actually selected. This implies that Page 13
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every other element is selected independently of every other element. The sample is drawn by a random procedure from a sampling frame. This method is equivalent to a lottery system in which names are placed in a container, the container is shaken, and the names of the winners are then drawn out in an unbiased manner.
To draw a simple random sample, the researcher first compiles a sampling frame in which which each each elemen elementt is assign assigned ed a unique unique identi identific ficati ation on numbe number. r. Then Then random random numbers are generated to determine which element to include in the sample. The random numbers may be generated with a computer routine or a table. Advantages •
It is easy to understand
•
The sample result may be projected to the target population.
Disadvantages •
It is often difficult to construct a sampling frame that will permit a simple random sample to be drawn.
•
SRS can result in samples that are very large or spread over large geographic areas, thus increasing the time and cost of data collection.
•
SRS often results in lower precision with larger standard errors than other probability sampling techniques.
•
SRS may or may not result in a representative sample. Although samples drawn will represent the population well on average, a given simple random sample may grossly misrepresent the target population. This more likely if the size of the sample is small.
Systematic sampling Definition A probability sampling technique in which the sample is chosen by selecting a random starting point and then picking every ith element in succession from the sampling frame.
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Explanation In systematic sampling, the sample is chosen by selecting a random starting point and then picking every i th element in succession from the sampling frame. The sampling interval, i , is determined by dividing the population size N by the sample size n and rounding to the nearest integer. Example Suppos Suppose e there there are 100,000 100,000 eleme elements nts in the popula populatio tion n and a sample sample of 1000 1000 desired. In this case the sampling interval, i , is 100. A random number between 1 to 100 is selected. If say number 23 is selected, the sample will then consists of elements 23, 123, 223, 323, 423, 523, and so on. Systematic sampling is similar to SRS in that each population element has a known and equal probability of selection. However, it is different from SRS in that only the permissible samples of size n that can be drawn have a known and equal probability of selection. The remaining samples of size n have a zero probability of being selected. For systematic sampling, the researcher assumes that the population elements are orde ordere red d in some some resp respec ect. t. In some some case cases s the the orde orderi ring ng (alp (alpha habe beti tic c list listin ing g in a telephone book) is unrelated to the characteristic of interest. In other instances, the orderi ordering ng is direct directly ly relate related d to the charac character terist istic ic under under invest investiga igatio tion. n. (Credi (Creditt card card customers may be listed in order of outstanding balances. If the population elements are arranged in a manner unrelated to the characteristic of interest, systematic sampling will yield result quite similar to SRS. On the other hand, when the ordering of the element is related to the characteristic of interest, systematic sampling increases the representatives of the sample. Advantages •
System Systemati atic c sampli sampling ng is less less costly costly and easier easier that that SRS, SRS, becaus because e random random selection is done only once.
•
The random numbers numbers do not have to be matched with individual individual element as in SRS. Since some lists contains millions of elements, considerable time can be saved. This in turn turn again reduces reduces the cost. cost.
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If the information related to the characteristic of interest is available for the population, systematic sampling can be used to obtain a more representative and reliable sample than SRS.
•
Systematic sampling can even be used without knowledge of the composition (elements) of the sampling frame.
Stratified Random Sampling Definition A probab probabili ility ty sampli sampling ng techn techniqu ique e that that uses uses a two-st two-step ep proces process s to partiti partition on the population into subpopulations, or strata is known as stratified random sampling. Elements are selected from each stratum by a random procedure. Explanation Strati Stratifie fied d Rando Random m Sampli Sampling ng emerge emerges s from from the word word Stratum. Stratum. A Stratum in a population is a segment of that population having one or more characteristics. E.g. people in the age strata of 35-40, people in the income strata to Rs. 20000 p.m. etc Stratified Sampling involves treating each stratum as a separate subpopulation for sampling purposes, and from each stratum sampling units would be drawn randomly. The reasons for conducting Stratified Random Sampling are: •
To reduce sampling error by ensuring representation from the population.
•
The required sample size for the same level of sampling error will usually be smaller.
As comp compar ared ed to othe otherr meth method ods s of samp samplin ling, g, in Stra Strati tifie fied d Rand Random om Samp Sampli ling ng representativeness to a certain degree is forced. for ced. The greater degree to which there is similarity within stratum, smaller is the sample size required to provide information about that stratum. Thus the more homogeneous each stratum is with respect to the variable of interest the smaller is the sample required. Example If the head of the household age strata (18-34, 35-49, 50+) are of interest in a study on household spending habits on household furnishings, then each of these groups
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would be taken separately for sampling purposes. That is, the total population could be divided into age groups and a separate sample is drawn from each group.
Cluster Sampling Definition The target population is divided into mutually exclusive and collectively exhaustive subpopulation called clusters. Then a random sample of clusters is selected based on probab probabilit ility y sampl sampling ing techni technique ques s such such as simple simple random random sampli sampling. ng. For each each selected clusters, either all the elements are included in the sample or a sample of elements is drawn probabilistically. Explanation •
If all the elements in each selected cluster are included in the sample, the procedure is called one stage cluster sampling.
•
If a sample of elements is drawn probabilistically from each selected cluster, the procedure is called two-stage cluster sampling.
•
The key distinction between cluster sampling and stratified sampling is that in cluster sampling only a sample of subpopulations (clusters) is chosen, whereas in stratified sampling all the subpopulations are selected.
•
The objective of the cluster sampling is to increase the sampling efficiency by decreasing costs.
Example If the study requires studying the households in the city then in cluster sampling the whole city is divided into Blocks and to take each household on each block selected. Thus to get a representative whole of the universe. Advantages •
Low population heterogeneity / high population homogeneity
•
Low expected cost of errors.
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The main advantage of cluster sampling is the low cost per sampling unit as compared to other sampling methods.
Disadvantage •
High potential of sampling error as compared to other methods. Page 17
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For eg: The lower cost per unit and higher sampling error potential of a cluster sample is illustrated by considering a sample of 100 households to be selected for personal interviews from a particular city. In this method the city would be divided in blocks and 10 households from 10 selected blocks would be selected and and inte interv rvie iewe wed. d. Thus Thus the the cost cost of pers person onal al inte interv rvie iew w per per unit unit will will be low low because of the close proximity of the units in the cluster. This sample may not be the exact representation of the entire city. Thus there is a possibility of sampling error.
Single Stage V/s Multistage Sampling Explanation The number of stages involved in the sampling method is partially a function of the number number of sampli sampling ng frame frame availa available ble.. If a perfec perfectt frame frame were were always always availa available ble comp comple lete te with with all all the the asso associ ciat ated ed info inform rmat atio ion n one one migh mightt want want for for purp purpos oses es of clustering and / or stratifying, there would be far fewer multiple samples taken than there are now. In practice, it is not uncommon to have a first stage area sample of, say, census tracts, followed by a second stage sample of blocks, and completed with a systematic sample of households within each block. These stages would not be necessary if a complete listing of households were available. Example AC Nielsen’s Multistage Sampling Procedure to select i ts PeopleMeter Panel The first stage involves the selection of counties using a stratified random sample based on population. Next within the selected counties there is a random selection of blocks or enumeration districts. These blocks then go through a process called prelisting. A trained field representative visits the selected blocks and creates a li st of all the individual hosing units. This list is then returned to the home office where it is checked for internal consistency and external agreement with other data. Finally, individual household units are randomly selected from each block.
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STRENGTHS AND WEAKNESS OF BASIC SAMPLING TECHNIQUES Techniques
Strengths
Weaknesses
Non probability sampling Convenience sampling
Least
expensive,
tim time
consum nsumin ing, g,
least Selection bias; sample not most ost representative; not
convenient
recommended for descriptive or casual research.
Judgmental sampling
Low cost, convenient, not Does not allow time consuming
Quota sampling
generalization subjective
Sample ca can be be co controlled Selection bias, no for certain characteristics
assurance of representativeness.
Snowball sampling
Can
estimate
rare Time consuming
characteristics
Probability Sampling Simple Simple Random Random Sampling Sampling Easily understood
Difficult to construct
(SRS)
sampling frame;
Result projectable
expensive lower precison; no assurance of
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representativeness Systematic Sa Sampling
Can in increase re representativeness.
Easier
implement
than
sampling
frame
Can decrease
to representativeness SRS not
necessary Stra Strati tifie fied d samp samplin ling g
Incl Includ udes es
all all
impo importa rtant nt Difficult to select relevant
subpopulations; precision
stratification variables; not feasible to stratify on many variable; expensive
Cluster Cluster sampling sampling
Easy to implemen implement, t, cost Imprecise; difficult to effective
compute and interpret results
Choosing Non probability versus Probability Sampling The choice between non probability and probability samples should be based on cons consid ider erat atio ions ns such such as the the natu nature re of the the rese researc arch, h, rela relati tive ve magn magnit itud ude e of non non sampling versus sampling errors, variability in the population, as well as statistical and operational considerations. For example,
Conditions favoring the use of Non probability
Probability
Factors
Sampling
Sampling
Nature of research
Exploratory
Conclusive
Relative ive
magnitude
of Non Non
samplin ling
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errors
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sampling and non-sampling are larger
larger.
errors Vari Variab abil ilit ity y in the the popu popula lati tion on
Hom Homogen ogenou ous s (low (low))
Hete Hetero roge gene neou ous s (hig (high) h)
Statistical consideration
Unfavorable
Favorable
Oper Operat atio iona nall cons consid ider erat atio ion n
Favo Favora rabl ble e
Unfa Unfavo vora rabl ble e
In explor explorato atory ry resear research ch the findin findings gs are treate treated d as prelim prelimina inary ry and the use of prob probab abili ility ty samp samplin ling g may may not not be warra warrant nted ed.. On the the othe otherr hand hand,, in conc conclu lusi sive ve research in which the researcher wishes to use the results to estimate overall market shares shares or the size of the total market, market, probability probability sampling sampling is favored. Probability Probability samples allow statistical projection of the results to a target population.
For some some resear research ch proble problems ms,, highly highly estima estimates tes of popula populatio tion n charac character terist istic ic are requir required. ed. In these these situat situation ions, s, the elimin eliminatio ation n of select selection ion bias bias and the abilit ability y to calculate sampling error make probability sampling desirable. However probability sampling will not always result in more accurate results. If nonsampling errors are likely to be an important factor, then non-probability sampling may be preferable, as the use of judgment may allow greater control over the sampling process.
Anothe Anotherr consi consider derati ation on is the homoge homogene neity ity of the popul populati ation on with with respec respectt to the variab variables les of interes interest. t. A more more hetero heterogen geneou eous s popula populatio tion n would would favor favor probab probabilit ility y samp samplin ling, g, beca becaus use e it woul would d be impo import rtan antt to secu secure re a repr repres esen enta tativ tive e samp sample le.. Probability sampling is preferable from a statistical viewpoint, as it is the basis of most common statistical techniques.
Howeve However, r, probab probabilit ility y samplin sampling g is sophi sophisti sticat cated ed and requir requires es statis statistic ticall ally y traine trained d resear researche cher. r. It genera generally lly costs costs more more and takes takes longer longer than than does does nonpro nonprobab babilit ility y sampling. In many marketing research projects, it is difficult to justify the additional Page 21
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time and expense. Therefore, in practice, the objectives of the study dictate which sampling method will be used.
Methods of determining sample size There are six methods of determining sample size in market research. They are 1.
Unaided Judgement: Judgement: When no specific method is used to determine sample size, it is called Unaided Judgement. Such approach when used to arrive at sample size gives no explicit considerations to either the likely precision of the sample results or the cost of obtaining them (characteristics in which client should have interest). It is an approach to be avoided.
2.
All –You –Can –Afford: In this method, a budget for the project is set by some (generally unspecified) process and, after the estimated fixed costs of designing the project, preparing a questionnaire (if required), analysing the data, and preparing the report are deducted, the remainder of the budget is allocated to sampling. Dividing this remaining amount by the estimated cost per sampling unit gives the sample size.
This method concentrates on the cost of the information and is not concerned about its value. Although cost always has to be considered in any systematic approach to sample size determination, one also needs to give consideration to how much the information to be provided by the sample will be worth. This approach produces sample sizes that are larger than required as well as sizes that are smaller than optimal. 3.
Required Size Per Cell: Cell: This method of determining sample size can be used on simple random, stratified random, purposive and quota samples. For example, in a study of attitudes with respect to fast food establishments in a local marketing area it was decided that information was desired for two occupational groups and for each of the four age groups. This resulted in 2 x 4 = 8 sample cells. A sample size of 30 was needed per cell for the types of statistical analyses that were to be conducted. The overall sample size was therefore 8 x 30 = 240. Page 22
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Use of Traditional Statistical Model: Model: The formula for traditional statistical mode modell depe depend nds s upon upon the the type type of samp sample le to be take taken n and and it alwa always ys incorporates three common variables •
an estimate of the variance in the population from which the sample is to be drawn,
•
the error from sampling that sampling that the researcher will allow, and
•
the desired level of confidence that the actual sampling error will be within the allowable limits.
The statistical models for simple random sampling include estimation of means and estimation of proportion. 5.
Use of Bayesian Statistical Model: Model : The Bayesian model involves finding the difference between the expected value of the information to be provided by the the samp sample le size size.. This This diff differ eren ence ce is know known n as expect expected ed net gain gain from from sampling (ENG (ENGS) S).. The The samp sample le size size with with the the larg larges estt positive ENGS ENGS is chosen.
The Bayesian model is not as widely used as the traditional statistical models for determining sample size, even though it incorporates the cost of sampling and the traditional models do not. The reasons for the relative infrequent use of Bayesian model are related to greater complexity and perceived difficulty of maki making ng the the estim estimat ates es requ require ired d for for Baye Bayesi sian an mode modell as comp compar ared ed to the the traditional models.
The Sampling Distribution Sam Sampling ling theo theory ry res rests on the the conc conce ept of a sampling sampling distributio distribution n. Samp Samplin ling g distribution includes •
Sampling distribution of the mean
•
Sampling distribution of the proportion
Simulated sampling distribution of the mean Page 23
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A sampling distribution of the mean is the relative frequency distribution of the means of all possible samples of size n taken from a population of size N. The definition specifies that all possible samples of size n from population of size N should be taken, and the mean of each sample should be calculated and plotted in relative frequency table. A sampling distribution of the mean for simple random samples that are large (30 or more) has •
a normal distribution
•
a mean equal to the population (M)
•
a standard deviation, called the standard error of the mean( ), that is equal to the popula populatio tion n standard standard deviati deviation( on(
) divide divided d by the square square root root of the
sample size FORMULA:
Standard deviation is called standard error of the mean to indicate to indicate that it applies to a distribution of sample means and not to a single sample or a population. A basic basic charac character terist istic ic of a samplin sampling g distrib distributi ution on is that that the area under under it (between any two points) can be calculated so long as each point is defined by the number of standard errors it is away from the mean. The number of standard error, a point is away from the mean is referred as the Z value for that point.
Sampling Distribution of the Proportion
A sampling distribution of the proportion is the relative frequency distribution of the proportion (p) of all possible samples of size n taken from population of size N . A sampling distribution of a proportion for a simple random sample has a •
normal distribution
•
a mean equal to the population proportion (P)
•
a standard standard error ( ) equal to
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FORMULA:
The estimated standard error of the proportion (given a large sample size that is a small proportion of the population) is FORMULA:
where p where p represents the sample population.
Traditional Statistical Methods of Determining Sample Determination of Sample Size in Problem Involving Means Three kinds of specifications have to be made before the sample size necessary to estimate the population mean can be determined. These are
1.
Specification of error (e) that can be allowed –how –how close must the estimate be (how accurate do we need to be)?
2.
Specification of confidence coefficient –what –what level of confidence is required that the actual sampling error does not exceed that specified (how sure do we want to be that we have achieved our desired accuracy)?
3.
Estimate Estimate of the the populatio population n standard standard deviat deviation( ion(
) –what is the standard
deviation of the population (how “spread out” or diverse is the population)?
The three specifications are related in the following way: Number of standard errors implied by confidence coefficient = allowable error standard error or in symbols,
FORMULA:
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The only unknown variable is sample size (n). A simpler formula for the size of simple random samples can be derived from the above equation. FORMULA:
Determination of Sample Size in Problem Involving Proportions
The specifications that must be made to determine the sample size for an estimation problem involving a proportion are very similar to those for a mean. They are 1.
Specification of error (e) that can be allowed –how –how close must the estimate be?
2.
Specification of confidence coefficient –what –what level of confidence is required that the actual sampling error does not exceed that specified?
3.
Estimate of the population proportion (P) using prior information –what is the approximate or estimated population proportion?
Specif Specifica icatio tions, ns, along along with with the sample sample size, size, colle collecti ctivel vely y determ determine ine the sampli sampling ng distribution for the problem. Because sample size is the only remaining unknown, it can be calculated. The above mentioned three specifications are related as follows: Number of standard errors implied by confidence coefficient = allowable error standard error or in symbols, FORMULA:
The formula for determining n that is sample size directly is FORMULA:
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Determination of Sample Size in Problems Involving Hypothesis Testing
A hypoth hypothes esis is is a propos propositio ition, n, which which the research researcher er wants wants to verify verify.. It may may be mentioned that while a hypothesis is useful, it is not always necessary. Many a time, the researcher is interested in collecting and analysing data, indicating the main charac character terist istics ics withou withoutt a hypoth hypothesi esis s except excepting ing the one, one, which which he may may sugges suggestt incidentally during the course of his study. However, in a problem-oriented research, it is necessary to formulate a hypothesis. In such research, hypothesis are generally concerned with the causes of a certain phenomenon or a relationship between two or more variables under investigation.
In order to determine determine the sample sample the size in a hypothesis hypothesis testing testing problem problem involving involving proportion, the following specifications must be made: 1.
the hypotheses to be tested: A null and an alternate hypothesis are involved in each hypothesis test. A null hypothesis, hypothesis, designated by Ho, is one that, if accepted, will result in no option being formed and/or action being taken that is different from those currently held or being used. The null hypothesis in the problem just described is Ho: order rate = 3.5%
The alternate hypothesis, hypothesis, designated by H1, is one that will lead to opinions being formed and/or actions being taken that are different from those currently held or being used. The alternate hypothesis here is H1: order rate = 5.0% Although null hypothesis is always explicitly stated, this is sometimes not true of the alternate hypothesis. In those instances when it is not stated i t is understood that it consists of all values of the proportion not reserved by the null hypothesis. In this situation if the alternate hypothesis were not explicitly stated, it would be understood that it would be H1: order rate (is not equal to) 3.5% Page 27
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2. the level level of sampli sampling ng error error permit permitted ted in the test of each hypothe hypothesis sis:: Two types of error can be made in hypothesis testing problems. An error is made when null hypothesis is true but the conclusion is reached that the alternate hypothesis should be accepted. This is known as Type I error. The Type II error is made when the alternate hypothesis is accepted 3. the test test stati statisti stic c to be use used. d.
In order to determine determine the sample sample the size in a hypothesi hypothesis-tes s-testing ting problem involving involving means, the following specifications must be made:
1. the hypoth hypothese eses s to be test tested, ed, 2. the level level of sampling sampling error error permitte permitted d in the test test of each hypot hypothesis hesis,, 3. the standard standard deviation deviation of population, population, and 4. the test test stati statisti stic c to be use used. d.
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