Title:  Testing for Homogeneity of Variances: Equivalence-Based Approaches.

 

Abstract: Researchers are often in interested in testing whether the variances of independent groups are equivalent, typically because it is an assumption of the test statistic they are using. Violations of the homogeneity of variances assumption can severely bias the Type I and/or Type II error rates of the test relying on the assumption. There has been substantial research on tests that explore differences in the variances, such as Levene’s test, Brown-Forsythe, and more recent modifications of these tests. However, all of these procedures are fundamentally incorrect in that they are attempting to "accept" the null hypothesis of variance equality. The purpose of this paper is to redefine the problem, situating a test for homogeneity of variances within the equivalence testing framework. Preliminary results comparing the derived statistics with traditional difference-based tests demonstrate that the equivalence-based approach has important statistical properties, such as power increasing with sample size, and trivial differences in variances not being detected with large sample sizes.