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

This paper considers the common problem of testing the equality of means in a repeated measures design. Recent results indicate that practical problem s can arise when computing confidence intervals for all pairwise difference s of the means in conjunction with the Bonferroni inequality. This suggests , and is confirmed here, that a problem might occur when performing an omni bus test of equal means. The problem is that the probability of rejecting i s not minimized when the means are equal and the usual univariate F test is used with the Huynh-Feldt correction (<(epsilon)over tilde>) for the degre es of freedom. That is, power can actually decrease as the mean of one grou p is lowered, although eventually it increases. A similar problem is found when using a multivariate method (Hotelling's T-2). Moreover, the probabili ty of a Type I error can exceed the nominal level by a large amount. The pa per considers methods for correcting this problem, and new results on compa ring trimmed means are reported as well. In terms of both Type I errors and power, simulations reported here suggest that a percentile t bootstrap use d with 20% trimmed means and an analogue of the <(epsilon)over tilde>-adjus ted F gives the best results. This is consistent with extant theoretical re sults comparing methods based on means with trimmed means.