27 Assumptions of Repeated Measures Designs

In between-subjects ANOVA, we assume independence (scores for different levels of the independent variable do not influence each other). In the repeated measures design, because the same participants are in all conditions, scores across levels of the independent variable are correlated and so we have violated the assumption of independence. Therefore, we make an extra assumption: the assumption of sphericity. This assumption specifies that the correlation of scores across conditions should not differ. It is tested by testing whether the variances in the differences between conditions are significantly different from one another. To do this, we use Mauchly’s test. Let’s say we have three levels in our design, A, B, and C. Mauchly’s tests whether the the variance of the differences between groups A and B and the variance of the differences between groups A and C and the variance of the differences between groups C and A are significantly different from one another. We want them to be the same (in the population, and not significantly different in our sample), i.e., varianceA-B = varianceA-C = varianceB-C.

If we violate the assumption of sphericity (i.e., if the variances are significantly different from one another), we can apply one of three corrections: Greenhouse-Geisser, Huynh-Feldt, or Lower-bound (the third one is not available in jamovi but is in some other software packages). One problem with Mauchly’s is the same as as arose with our tests of normality and homogeneity of the variance that we discussed in previous chapters: for small samples, the test will not be significant (due to lack of power), even when the assumption is violated; for very large samples, it will be significant even when there are only small differences among the differences in the variances. One approach is to err on the side of caution and apply the Greenhouse-Geisser correction whenever reporting the results of a repeated-measures ANOVA. We shall look at this further in the next section.

 

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Research Methods and Statistics with jamovi Copyright © 2024 by Catharine Ortner, Thompson Rivers University Open Press is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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