Robustness Against Inequality of Variances

Various asymptotic-based criteria are used to assess the robustness against inhomogeneity of variance of various standard and/or distribution-free tests in the two sample problem. The extent of robustness is influenced greatly by the equality or not of the two sample sizes, conforming to an earlier principle of G. E. P. Box. With equal sample sizes, t-tests and related trimmed-mean-like tests are robust, but otherwise, the sign test emerges clearly as the most robust test to variance inequality.