Robust tests of equivalence for k independent groups

Area of Science:

• Psychology
• Statistics

Background:

• Determining the equivalence of multiple groups is crucial in psychological research.
• Traditional hypothesis tests, like the ANOVA F-test, do not confirm population mean equivalence when the null hypothesis is not rejected.
• One-way tests of equivalence, such as the Wellek test, are appropriate for assessing group equivalence.

Purpose of the Study:

• To evaluate the robustness of the Wellek equivalence test against violations of the homogeneity of variance assumption.
• To compare the Type I error rates and statistical power of the Wellek test with a novel heteroscedastic version.
• To introduce a Wellek-Welch test adapted from the Welch F-test for heteroscedastic data.

Main Methods:

• Investigated the performance of the Wellek test under conditions violating homogeneity of variance.
• Compared the Wellek test with a proposed Wellek-Welch test, a heteroscedastic adaptation.
• Analyzed Type I error rates and statistical power under various variance conditions.

Main Results:

• The Wellek-Welch test demonstrated insensitivity to violations of the homogeneity of variance assumption.
• The original Wellek test was found to be inappropriate when population variances were unequal.
• The Wellek-Welch test maintained acceptable performance across different variance scenarios.

Conclusions:

• The Wellek-Welch test offers a robust method for assessing the equivalence of independent groups, particularly when variances are unequal.
• Researchers should utilize the Wellek-Welch test for equivalence testing in psychology when the assumption of equal variances is questionable.
• The findings highlight the limitations of the standard Wellek test and the advantages of its heteroscedastic adaptation.