Robust tests of equivalence for k independent groups

Abstract

A common question of interest to researchers in psychology is the equivalence of two or more groups. Failure to reject the null hypothesis of traditional hypothesis tests such as the ANOVA F-test (i.e., H0 : μ(1) = ... = μ(k)) does not imply the equivalence of the population means. Researchers interested in determining the equivalence of k independent groups should apply a one-way test of equivalence (e.g., Wellek, 2003). The goals of this study were to investigate the robustness of the one-way Wellek test of equivalence to violations of homogeneity of variance assumption, and compare the Type I error rates and power of the Wellek test with a heteroscedastic version which was based on the logic of the one-way Welch (1951) F-test. The results indicate that the proposed Wellek-Welch test was insensitive to violations of the homogeneity of variance assumption, whereas the original Wellek test was not appropriate when the population variances were not equal.