Robust Rank Procedures for the Behrens-Fisher Problem

The problem of testing for equality of the medians of two populations is considered. The standard distribution-free tests for this problem require that the two populations have the same shape to maintain their nominal significance level under the null hypothesis. A method is given to modify many of these tests so they can be used to test for equality of the medians with fewer assumptions on the shapes of the two populations. The method is demonstrated using the Mann-Whitney-Wilcoxon statistic.