Wilcoxon-Mann-Whitney Test of No Group Discrimination

Abstract

The traditional WMW null hypothesis $H_0: F = G$ is erroneously too broad. WMW actually tests narrower $H_0: AUC = 0.5$. Asymptotic distribution of the standardized $U$ statistic (i.e., the empirical AUC) under the correct $H_0$ is derived along with finite sample bias corrections. The traditional alternative hypothesis of stochastic dominance is too narrow. WMW is consistent against $H_1: AUC \neq 0.5$, as established by Van Dantzig in 1951.