Comparing means from nonnormal distributions: The bisquare-weighted analysis of variance

A new procedure analogous to the analysis of variance (ANOVA), called the bisquare-weighted ANOVA (bANOVA), is described. When a traditional ANOVA is calculated, using samples from a distribution with heavy tails, the Type I error rates remain in check, but the Type II error rates increase, relative to those across samples from a normal distribution. The bANOVA is robust with respect to deviations from a normal distribution, maintaining high power with normal and heavy-tailed distributions alike. The more popular rank ANOVA (rANOVA) is also described briefly. However, the rANOVA is not as robust to large deviations from normality as is the bANOVA, and it generates high Type I error rates when applied to three-way designs.