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Abstract:
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The venerable Wilcoxon-Mann-Whitney (WMW) two-sample test has outstanding utility, but is insufficiently understood by many professional statisticians and thus is too often incorrectly taught, interpreted, and reported. Much of this confusion stems from pretending that the two distributions have identical shapes and spread, but possibly different locations, a model that rarely resembles reality. A simple odds parameter, WMWodds, allows us to express the statistical hypotheses correctly and to obtain point estimates and confidence intervals that are directly related to the WMW test, yet are not dependent on the location-shift model. This methodology also yields a new approximation for the WMW p-value and a new noncentrality parameter for performing power/sample-size analyses.
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