Testing for equivalence of group variances

Abstract

"The purpose of this paper was to situate a test for equality of group variances within the equivalence testing framework. Even though difference-based procedures are appropriate to answer questions about differences in some statistic (e.g., means, variances, etc.), these procedures are not appropriate to address questions related to variance homogeneity. Thus, if a researcher is interested in evaluating the similarity of group variances, it is more appropriate to use a procedure specifically designed to determine equivalence. A simulation study was used to compare newly developed equivalence-based tests to currently recommended difference-based variance homogeneity tests under data conditions common in psychological research. The results of this study provided evidence regarding the problems with assessing equality of variances with traditional difference-based tests. Most notably, traditional difference-based tests assess equality of variances from the wrong perspective, encouraging researchers to ""accept"" the null hypothesis. The results also demonstrated that the newly developed Levene-Wellek- Welch test for equivalence of group variances using the absolute deviations from the median was the best-performing equivalence-based test statistic in terms of accurate Type I error rates and highest power for detecting equivalence across the conditions evaluated. In addition, the use of the Levene-Wellek-Welch median-based test was demonstrated with an applied example, and an R function was provided in order to facilitate use of this newly developed equivalence of group variances test. "