The Chen–Luo test in case of heteroscedasticity

Chen and Luo (2004, Comm. Statist. Simulation Comput. 33, 1007–1020) presented a modification of the Wilcoxon–Mann–Whitney test that can be less conservative than the original test. The results shown here indicate that the possible power advantage of the modification is solely due to its being less conservative. Because the modified statistic is variance adjusted using a variance estimator based on the empirical data situation independent of the null hypothesis, the test may be useful in case of heteroscedasticity. However, it is demonstrated here that the modified test can be much more anticonservative than the Wilcoxon–Mann–Whitney test when the population means are identical, but the population variances differ. Therefore, the modified test cannot be recommended for the nonparametric Behrens–Fisher problem. Possible approaches in that case are the Brunner–Munzel test and Cliff's method.