Analyzing Multivariate Repeated Measures Designs: A Comparison of Two Approximate Degrees of Freedom Procedures.

The approximate degrees of freedom Welch-James (WJ) and Brown-Forsythe (BF) procedures for testing within-subjects effects in multivariate groups by trials repeated measures designs were investigated under departures from covariance homogeneity and normality. Empirical Type I error and power rates were obtained for least-squares estimators and robust estimators based on trimming/Winsorization. The BF and WJ procedures with least-squares estimators produced comparable Type I error rates for the main effect. For the interaction, the former could become conservative, while the latter was liberal when sample sizes were small. When robust estimators were adopted, the WJ test generally controlled the error rate while the BF test was conservative. Both procedures had similar power for the main effect test, while the WJ procedure was more powerful for tests of the interaction when covariances were heterogeneous.