Some Properties of Preliminary Tests of Equality of Variances in the Two-Sample Location Problem

Abstract

A simulation study was conducted to examine probabilities of Type I errors of the two-sample Student t test, the Wilcoxon–Mann–Whitney test, and the Welch separate-variances t test under violation of homogeneity of variance. Two-stage procedures in which the choice of a significance test in the second stage is determined by the outcome of a preliminary test of equality of variances in the first stage were also examined. Type I error rates of both the t test and the Wilcoxon test were severely biased by unequal population variances combined with unequal sample sizes. The two-stage procedures were not only ineffective, they actually distorted the significance level of the test of location. Furthermore, the distortion was greatest when the discrepancy between variances was slight rather than extreme. Unconditional substitution of the Welch separate-variances t test for the Student t test whenever sample sizes were unequal was the most effective way to counteract modification of the significance level. Conditional substitution of the the Welch test, depending on the outcome of a preliminary test, was far less effective.