Two-Sample Testing for Equality of Variances

To test for equality of variances given two independent random samples from univariate normal populations, popular choices would be the two-sample F test and Levene’s test. The latter is a nonparametric test while the former is parametric: it is the likelihood ratio test, and also a Wald test. Another Wald test of interest is based on the difference in the sample variances. We give a nonparametric analogue of this test and call it the R test. The R, F and Levene tests are compared in an indicative empirical study. For moderate sample sizes when assuming normality the R test is nearly as powerful as the F test and nearly as robust as Levene’s test. It is also an appropriate test for testing equality of variances without the assumption of normality, and so it can be strongly recommended.