STATISTICS REVIEW FOR UPCAT TAKERS. INTRODUCTION TO STATISTICS
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INFERENTIAL STATISTICS
Inferential Statistics statistics that permit inferences on whether relationships observed in a sample are likely to occur in a larger population (Polit and Beck, 2004)
based on the laws of probability
based on the assumption that the sample was randomly selected
2 Purposes of Inferential Statistics 1. Estimating population parameter from
sample data 2. Testing hypothesis about a population
Estimating Population Parameters From Sample Data Sample Error – occurs when the sample does not accurately reflect the population
Sample Distribution – a theoretical frequency distribution that is based on an infinite number of samples
--based on mathematical formulas and logic
Statistical Inference • The process of inferring attributes attri butes about the
population based on information from a sample, using laws of probability • 2 Types of Error in Statistical Inference A. Type I or Alpha Error - the researchers’ rejection of the null hypothesis when it is actually true B. Type II or Beta Error - the researchers’ acceptance of a null hypothesis that is actually false
Level of Significance
also referred as alpha level (α)
is the probability of making a type I error, or the probability of rejecting a true null hypothesis
two most frequently used significance levels are: .05 and .01
Six Steps in Tests of Significance (Gillis, 2002) 1. State the research and the null hypothesis 2. Determine where the outcome will fall in the sampling distribution if the null hypothesis is to be rejected 3. Indicate the chosen significance level to be used in the test ( usually 0.05) 4. Compute the test statistics 5. Note whether the test indicates if you should accept or reject the null hypothesis 6. Interpret the findings
Statistical Tests an analytic tool that estimates the probability that obtained results from a sample reflect true population values
2 Broad Classes of Statistical Tests A. Parametric Tests B. Nonparametric Tests
Parametric Tests characterized by three attributes: 1. they involve the estimation of a parameter 2. they require measurements on at least an interval scale 3. they involve several assumptions, such as the assumption that the variables are normally distributed in the population
t
- Test • sometimes referred to as Student’s t • for testing differences in group means • used when there are 2 independent
groups (ex. male versus female), and when the sample is paired or dependent (ex. when pretreatment and post-treatment scores are compared for a single group
Analysis of Variance (ANOVA) for testing differences between means where there are 3 or more groups, or of 2 or more independent variables
the statistics computed is the F – – ratio statistics
Nonparametric Tests
are used when the data are nominal nom inal or ordinal or when a normal distribution cannot be assumed
Chi-Square Test ( X ( X 2 ) • most commonly used statistics st atistics with nominal data • primarily used in cross-table analysis and is used when: 1. the dependent dependent variable variable is a nominal one 2. you wish to determine determine if frequencies vary across across categories 3. the expected frequencies are above 5 in most cells of the table 4. the variables are normally distributed 5. the measures of the variables variables are independen independentt of one another
Chi-Square Test ( X ( X ) 2
most commonly used statistics with nominal data primarily used in cross-table analysis and is used when: 1. the dependent variable is a nominal one 2. you wish to determine if frequencies vary across categories 3. the expected frequencies are above 5 in most cells of the table 4. the variables are normally distributed 5. the measures of of the variables are independent of one another
Other Nonparametric Tests Fisher’s Exact Test - when the total sample size is small or when there are cells with o frequencies McNemar Test - when proportions being compared are from two paired groups Pearson’s r r - calculated when two variables are measured on at least the interval scale, is both descriptive and inferential Spearman rho - used when the assumptions of Pearson’s analysis cannot be met Kendall’s Tau - used when both variables have been measured at the ordinal level
Guidelines for Critiquing Inferential Statistics Are inferential statistics presented in the research report? 2. If inferential statistics are present, is enough information presented for the reader to determine whether the appropriate tests were used? 3. Is the reader provided with the calculated value of the inferential statistic, the degree of freedom, and the level of significance that was obtained? 4. Were the parametric or nonparametric tests used when the other type would have been more appropriate? 1.
Guidelines for Critiquing Inferential Statistics contd. 1. Are the chosen tests appropriate considering
the level of measurement of the variables, the number of groups that were tested, the size of the sample, etc? 2. Are inferential statistics presented for each hypothesis stated in the study? 3. Are the results of the inferential tests clearly and thoroughly discussed? 4. Are the results presented both in the text and in tables?
