Repeated measures one-way ANOVA based on a modified one-step M-estimator

Wilcox, Keselman, Muska and Cribbie (2000) found a method for comparing the trimmed means of dependent groups that performed well in simulations, in terms of Type I errors, with a sample size as small as 21. Theory and simulations indicate that little power is lost under normality when using trimmed means rather than untrimmed means, and trimmed means can result in substantially higher power when sampling from a heavy-tailed distribution. However, trimmed means suffer from two practical concerns described in this paper. Replacing trimmed means with a robust M-estimator addresses these concerns, but control over the probability of a Type I error can be unsatisfactory when the sample size is small. Methods based on a simple modification of a one-step M-estimator that address the problems with trimmed means are examined. Several omnibus tests are compared, one of which performed well in simulations, even with a sample size of 11.