Comparing the Statistical Tests for Homogeneity of Variances

Comparing the Statistical Tests for Homogeneity of Variances by Zhiqiang Mu Testing the homogeneity of variances is an important problem in many applications since statistical methods of frequent use, such as ANOVA, assume equal variances for two or more groups of data. However, testing the equality of variances is a difficult problem due to the fact that many of the tests are not robust against non-normality. It is known that the kurtosis of the distribution of the source data can affect the performance of the tests for variance. We review the classical tests and their latest, more robust modifications, some other tests that have recently appeared in the literature, and use bootstrap and permutation techniques to test for equal variances. We compare the performance of these tests under different types of distributions, sample sizes and true variance ratios of the populations. Monte-Carlo methods are used in this study to calculate empirical powers and type I errors under different settings.