As with so many tests, the real issue is whether significance testing should be paramount. It should not. Mann-Whitney U easily turns into an index U/mn by dividing by the product of the two sample sizes. U/mn is a very useful effect size measure and is equivalent to the area under the ROC curve. It equals 0.5 on H0 and 0 or 1 if the two samples don’t overlap. Report it with a confidence interval, see
Newcombe RG. Confidence intervals for an effect size measure based on the Mann-Whitney statistic. Part 2: Asymptotic methods and evaluation. Statistics in Medicine 25, 4, 559-573. Feb 2006. DOI: 10.1002/sim.2324
Excel resources for calculating confidence intervals for this and other effect size measures related to proportions are available at
http://profrobertnewcomberesources.yolasite.com/
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