Exploiting the Link Between the Wilcoxon-Mann-Whitney Test and a Simple Odds Statistic

Over a quarter-century ago, Alan Agresti (Biometrics, 1980) proposed using the generalized odds ratio (genOR) to summarize the association between two ordinal variables. Unfortunately, genOR is still largely unknown, even though it is elegantly straightforward and fills key voids in the working statistician’s toolbox. An extension of it, a statistic we are calling “WMWodds,” is an ideal effect-size measure for properly interpreting and reporting results based on the common Wilcoxon-Mann-Whitney (WMW) two-group test. In addition, the distribution theory suggests a sound and general way to perform sample-size analyses for the WMW test, an assertion strongly supported by Monte Carlo results. These matters are developed through realistic examples using SAS,  including a downloadable macro. This is an interim report of work still progressing; see www.bio.ri.ccf.org/robrien/WMWodds for later communications.