Effect of Very Unequal Group Sizes On Tukey's Multiple Comparison Test

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Abstract
The harmonic mean and Kramer procedures have been recommended for use with the Tukey multiple comparison test when group sizes are unequal. The only study that has compared these procedures maximally varied the disparity between the groups for a 3: 1 difference. The present investigation varied the disparity between the groups, the number of groups and the nominal significance levels. It was found that rarely did the empirical Type I error probabilities exceed their nominal significance levels by more than 1 percent even when the groups differed by 40:1. The Kramer estimates were typically less than the nominal significance levels while the harmonic mean estimates were generally larger than the true alphas.

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