Equivalence of Population Variances: Synchronizing the Objective and Analysis

Researchers are often interested in testing for the equivalence of population variances. Traditional difference-based procedures are appropriate to answer questions about differences in some statistic (e.g., variances, etc.). However, if a researcher is interested in evaluating the equivalence of population 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 difference-based variance homogeneity tests under common data conditions. Results demonstrated that traditional difference-based tests assess equality of variances from the wrong perspective, and that the proposed Levene-Wellek-Welch test for equivalence of group variances using the absolute deviations from the median was the best performing test for detecting equivalence. An R function is provided in order to facilitate use of this test for equivalence of population variances.