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Biological and medical investigations often use ordered categorical data. When two groups are to be compared and the data for the groups fall in three or more ordered categories, the Wilcoxon-Mann-Whitney (WMW) test uses information in the ordering to give a test that is usually powerful against shift alternatives. However, such applications of WMW often involve distributions for which extensive ties play an important role. Newly available computer programs for performing exact tests give deeper insights into the characteristics of the exact WMW distributions and the suitability of normal approximations. We offer practical advice, based on experience with published biomedical data sets and on numerical studies of hypothetical ordered tables, for the use of WMW and its normal approximations.
Emerson et al. (Fri,) studied this question.