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Mann–Whitney U test
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===Example statement of results=== In reporting the results of a Mann–Whitney ''U'' test, it is important to state:<ref>{{Cite journal |last1=Fritz |first1=Catherine O. |last2=Morris |first2=Peter E. |last3=Richler |first3=Jennifer J. |date=2012 |title=Effect size estimates: Current use, calculations, and interpretation. |url=http://doi.apa.org/getdoi.cfm?doi=10.1037/a0024338 |journal=Journal of Experimental Psychology: General |language=en |volume=141 |issue=1 |pages=2–18 |doi=10.1037/a0024338 |pmid=21823805 |issn=1939-2222}}</ref> *A measure of the central tendencies of the two groups (means or medians; since the Mann–Whitney ''U'' test is an ordinal test, medians are usually recommended) *The value of ''U'' (perhaps with some measure of effect size, such as [[#Common language effect size|common language effect size]] or [[#Rank-biserial correlation|rank-biserial correlation]]). *The sample sizes *The significance level. In practice some of this information may already have been supplied and common sense should be used in deciding whether to repeat it. A typical report might run, :"Median latencies in groups E and C were 153 and 247 ms; the distributions in the two groups differed significantly (Mann–Whitney {{math|1=''U'' = 10.5}}, {{math|1=''n''<sub>1</sub> = ''n''<sub>2</sub> = 8}}, {{math|1=''P'' < 0.05}} two-tailed)." A statement that does full justice to the statistical status of the test might run, :"Outcomes of the two treatments were compared using the Wilcoxon–Mann–Whitney two-sample rank-sum test. The treatment effect (difference between treatments) was quantified using the Hodges–Lehmann (HL) estimator, which is consistent with the Wilcoxon test.<ref>{{cite book |title= Nonparametric Statistical Methods |author1=Myles Hollander |author2=Douglas A. Wolfe |publisher= Wiley-Interscience |edition=2 |year=1999 |isbn= 978-0471190455}}</ref> This estimator (HLΔ) is the median of all possible differences in outcomes between a subject in group B and a subject in group A. A non-parametric 0.95 confidence interval for HLΔ accompanies these estimates as does ρ, an estimate of the probability that a randomly chosen subject from population B has a higher weight than a randomly chosen subject from population A. The median [quartiles] weight for subjects on treatment A and B respectively are 147 [121, 177] and 151 [130, 180] kg. Treatment A decreased weight by HLΔ = 5 kg (0.95 CL [2, 9] kg, {{math|1=2''P'' = 0.02}}, {{math|1=''ρ'' = 0.58}})." However it would be rare to find such an extensive report in a document whose major topic was not statistical inference.
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