Wilcoxon-Mann-Whitney Test of No Group Discrimination

The traditional WMW null hypothesis H0: F = G is erroneously too broad. WMW actually tests narrower H0: AUC = 0.5. Asymptotic distribution of the standardized U statistic (i.e., the empirical AUC) under the correct H0 is derived along with finite sample bias corrections. The traditional alternative hypothesis of stochastic dominance is too narrow. WMW is consistent against H1: AUC != 0.5, as established by Van Dantzig in 1951.