Validity conditions in repeated measures designs

This article has 2 objectives. The 1st is to present necessary and sufficient conditions for the validity of traditional within-S F tests in repeated measures designs. It is shown that the Mauchly sphericity criterion ( W ) and possibly the Box test for the equality of covariance matrices are appropriate to judge the validity of these conditions. Valid applications of both tests are conducted on sets of orthogonal normalized variables that are associated with each cluster of within-S mean square ratios. The 2nd objective of the article is to present empirical results on the appropriateness of using the W criterion when the variates are not normally distributed. For light-tailed distributions the W criterion was shown to be moderately conservative, whereas for heavy-tailed distributions, empirical Type I error rates exceeded nominal alpha. Since most social science applications typically involve light-tailed rather than heavy-tailed distributions, the W criterion should provide useful results in most cases. (29 ref)