AbstractTwo common goals when choosing a method for performing all pairwise comparisons of J independent groups are controlling experiment wise Type I error and maximizing power. Typically groups are compared in terms of their means, but it has been known for over 30 years that the power of these methods becomes highly unsatisfactory under slight departures from normality toward heavy‐tailed distributions. An approach to this problem, well‐known in the statistical literature, is to replace the sample mean with a measure of location having a standard error that is relatively unaffected by heavy tails and outliers. One possibility is to use the trimmed mean. This paper describes three such multiple comparison procedures and compares them to two methods for comparing means.