Statistical significance levels of nonparametric tests biased by heterogeneous variances of treatment groups

The statistical significance levels of the Wilcoxon-Mann-Whitney test and t he Kruskal-Wallis test are substantially biased by heterogeneous variances of treatment groups-even when sample sizes are equal. Under these condition s, the Type I error probabilities of the nonparametric tests, performed at the .01, .05, and .10 significance levels, increase by as much as 40%-50% i n many cases and sometimes as much as 300%. The bias increases systematical ly as the ratio of standard deviations of treatment groups increases and re mains fairly constant for various sample sizes. There is no indication that Type I error probabilities approach the significance level asymptotically as sample size increases.