Repeated measures ANOVA: some new results on comparing trimmed means and means

Abstract

This paper considers the common problem of testing the equality of means in a repeated measures design. Recent results indicate that practical problems can arise when computing confidence intervals for all pairwise differences of the means in conjunction with the Bonferroni inequality. This suggests, and is confirmed here, that a problem might occur when performing an omnibus test of equal means. The problem is that the probability of rejecting is not minimized when the means are equal and the usual univariate F test is used with the Huynh‐Feldt correction (ε) for the degrees of freedom. That is, power can actually decrease as the mean of one group is lowered, although eventually it increases. A similar problem is found when using a multivariate method (Hotelling's T2). Moreover, the probability of a Type I error can exceed the nominal level by a large amount. The paper considers methods for correcting this problem, and new results on comparing trimmed means are reported as well. In terms of both Type I errors and power, simulations reported here suggest that a percentile t bootstrap used with 20% trimmed means and an analogue of the ε‐adjusted F gives the best results. This is consistent with extant theoretical results comparing methods based on means with trimmed means.