WMWprob is identical to the area under the curve (AUC) when using a receiver operator characteristic (ROC) analysis to summarize sensitivity vs. specificity in diagnostic testing in medicine or signal detection in human perception research and other fields. Using the oft-used example of Hanley and McNeil (1982), we cover these analyses and concepts.
WMWprob is identical to the area under the curve (AUC) when using a receiver operator characteristic (ROC) analysis to summarize sensitivity vs. specificity in diagnostic testing in medicine or signal detection in human perception research and other fields. Using the oft-used example of Hanley and McNeil (1982), we cover these analyses and concepts.
Exploiting the Elementary
Wilcoxon-Mann-Whitney Parameters
(under development)
Ralph G. O'Brien
S. Paul Wright
The Wilcoxon-Mann-Whitney (WMW) method compares two groups with respect to an ordered categorical variable, Y. Letting Y1 and Y2 be the Y values for the two groups, the fundamental WMW parameter is
WMWprob = Prob[Y1 > Y2] + Prob[Y1 = Y2]/2
or, using odds scaling,
WMWodds = WMWprob/(1 - WMWprob).
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A major R function, WMW(), computes the estimates and confidence intervals for WMWprob and WMWodds. Optionally, setting a specific null hypothesis begets a p-value congruent with the CI.
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A proposed Bayesian approach yields counterparts to (frequentist) confidence intervals and p-values.
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WMW() returns Qscores (transforms of Y1 and Y2), which enable plotting the individual data values in a manner consistent with WMWprob.
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