Wilcoxon-Mann-Whitney Test of No Group Discrimination

2025/11/25 by Marian Grendar, Grendar, Marian
Mathematics · Environmental Science · #Advanced Statistical Methods and Models #Statistical Methods in Clinical Trials #Water Quality and Resources Studies

paper · pdf · doi:10.48550/arxiv.2511.20308

Abstract

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.

Citations

• On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other

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