ABSTRACT
In Chapter 11 we discussed two kinds of t tests. One of these was used with independent groups; the other was used with correlated observations such as might be obtained in a test-retest, or matched pairs, investigation. We mentioned that the matched pairs t test was normally a more powerful test of significance than the independent groups t test because the positive correlation between the paired measurements tended to decrease the variability of the difference scores on which the standard error of the mean difference was based. But we also pointed out that the matched pairs procedure cost n - l degrees of freedom because there were n 1 + n2 - 2 df available for evaluating an independent groups t, and only half that number (n - 1) for evaluating a matched pairs t. (If the section on the independent groups and matched pairs t tests is not familiar from the brief discussion in the preceding paragraph, it would be advisable to return to Chapter 11 for a review before continuing with this chapter.)
The rationale for a matched pairs t test can be extended to comparisons of more than two group means by the use of a procedure called repeated measures analysis of variance. Just as the simple one-way analysis of variance discussed in Chapter 12 is used to compare the means of k independent groups, a repeated measures oneway analysis of variance is used to compare the means resulting from k tests of the same, or matched, subjects.
