Statistical MethodsUnit 10: Dependent Sample t-Testby Adam J. McKeeUsingF. J. Gravetter and L. B. Wallnau's Essentials of Statistics for the Behavioral Sciences (4th Ed.).Defined A repeated measures study is one in which a single sample of individuals is measured more than once on the same dependent variable. Also called a within subjects study. Advantage The primary advantage is that using the same subjects eliminates the risk that the subjects in one treatment are substantially different from those in another. In an independent subject design, there is always a chance that one group is different than the other group despite randomization Matched Subjects A matched-subjects design tries to mimic the advantages of a repeated measures design by matching subjects on one group to subjects in another group. t-statistic for Related Samples The major distinction between the t for related samples and the t for dependent samples is that the dependent samples t works with difference scores. D Scores Difference scores are calculated by subtracting the second score from the first score:
Note: It is important to keep up with the signs when working with difference scores! Sample Mean The actual analysis utilizes the mean of the difference scores:
Note: The researcher is interested in a population of difference scores The Hypotheses The null can be expressed as:
This is different than the independent null which says the difference between two means is zero—not that the mean of the differences is zero The alternative is the same except for the inequality sign is used. SS We also need to obtain a measure of variance. The sum of squares can be calculated as follows:
Note: n is referring to the number of difference scores Sample Variance Estimated Standard Error Computing t Computing Cohen’s d r-square
Remember that r-square is the proportion of variance in the DV accounted for by the treatment.
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