Comparing the variances of two independent groups

Comparing the variances of two independent groups is a classic problem. Methods for comparing alternative measures of dispersion have been derived that perform well in simulations, but all methods for comparing variances have been found to be unsatisfactory in terms of Type I error probabilities or power. Currently, it appears that the most successful method, in terms of controlling the probability of a Type I error, is based on the so-called mean half-square successive difference statistic where a bootstrap is used to estimate its standard error, and a calibrated bootstrap is used to control the probability of a Type I error. But the mean half-square successive difference statistic is not permutation-invariant, and it is fairly evident that power can be relatively poor. A slight modification of the percentile bootstrap method for computing a 1 - alpha confidence interval for the difference between the variances is considered that corrects these problems.