Testing Repeated Measures Hypotheses When Covariance Matrices are Heterogeneous: Revisiting the Robustness of the Welch-James Test Again

Abstract

The Welch-James and Improved General Approximation tests were examined in between-subjects × within-subjects repeated measures designs for their rates of Type I error when data were nonnormal, nonspherical, and heterogeneous and when group sizes were unequal as well. The tests were computed with either least squares or robust estimators of central tendency and variability and assessed with critical values that were obtained either theoretically or through a bootstrapping method. Prior findings indicated that one could only obtain a robust test of the interaction effect with the Welch-James procedure when sample sizes were very large. This study’s results indicate that a robust test of the interaction effect can be obtained with reasonable sample sizes when the Welch-James test is computed with trimmed means and Winsorized covariance matrices.