title: 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.
authors.affiliation: Quantitative Methods Program, Department of Psychology, York University, Toronto, Canada.
authors.forename: Andy
authors.initials: A
authors.lastname: Koh
authors.forename: Robert
authors.initials: R
authors.lastname: Cribbie
mesh_terms: D000704:Analysis of Variance; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D011594:Psychometrics / Q000706:statistics & numerical data*; D018401:Sample Size