Editing Mann–Whitney U test (section)

==History==

The statistic appeared in a 1914 article<ref name="Kruskal57">{{cite journal |jstor=2280906 |title=Historical Notes on the Wilcoxon Unpaired Two-Sample Test |last=Kruskal |first=William&nbsp;H. |journal=Journal of the American Statistical Association |date=September 1957 |volume=52 |issue=279 |pages=356–360 |doi=10.2307/2280906}}</ref> by the German Gustav Deuchler (with a missing term in the variance).

In a single paper in 1945, [[Frank Wilcoxon]] proposed <ref name="wilcoxon1945">{{cite journal |doi=10.2307/3001968 |last=Wilcoxon |first=Frank |author-link=Frank Wilcoxon |year=1945 |title=Individual comparisons by ranking methods |journal=[[Biometrics Bulletin]] |volume=1 |issue=6 |pages=80–83 |jstor=3001968 |hdl=10338.dmlcz/135688 |hdl-access=free }}</ref> both the one-sample signed rank and the two-sample rank sum test, in a [[test of significance]] with a point null-hypothesis against its complementary alternative (that is, equal versus not equal). However, he only tabulated a few points for the equal-sample size case in that paper (though in a later paper he gave larger tables).

A thorough analysis of the statistic, which included a recurrence allowing the computation of tail probabilities for arbitrary sample sizes and tables for sample sizes of eight or less appeared in the article by [[Henry Mann]] and his student<!-- source: Olson, cited with url link in Mann article --> Donald Ransom Whitney in 1947.<ref name="mannwhitney1947">{{cite journal |first1=Henry&nbsp;B. |last1=Mann |author-link=Henry Mann |first2=Donald&nbsp;R. |last2=Whitney |title=On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other |journal=[[Annals of Mathematical Statistics]] |volume=18 |issue=1 |year=1947 |pages=50–60 |doi=10.1214/aoms/1177730491 |mr=22058 |zbl=0041.26103 |doi-access=free }}</ref> This article discussed alternative hypotheses, including a [[stochastic ordering]] (where the [[cumulative distribution function]]s satisfied the pointwise inequality {{math|1=''F''<sub>''X''</sub>(''t'') < ''F''<sub>''Y''</sub>(''t'')}}). This paper also computed the first four moments and established the limiting normality of the statistic under the null hypothesis, so establishing that it is asymptotically distribution-free.