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Tests of mean equality proposed by Alexander and Govern, Box, Brown and Forsythe, James, and Welch, as well as the analysis of variance F test, were compared for their ability to limit the number of Type I errors and to detect true treatment group differences in one-way, completely randomized designs in which the underlying distributions were nonnormal, variances were nonhomogeneous, and groups sizes were unequal. These tests were compared when the usual method of least squares was applied to estimate group means and variances and when Yuen's trimmed means and Winsorized variances were adopted. Based on the variables examined in this investigation, which included number of treatment groups, degree of population skewness, nature of the pairing of variances and group sizes, and nonnull effects of varying sizes, we recommend that researchers use trimmed means and Winsorized variances with either the Alexander and Govern, James, or Welch tests to test for mean equality.
Lix et al. (Mon,) studied this question.