[The Wilcoxon, Mann and Whitney test: conditions under which and hypotheses for which it is applicable].

Abstract

The test of Wilcoxon, Mann and Whitney is applicable only under the assumption that the two distribution functions FX and FY do not intersect. In case of doubt this assumption should be examined by drawing the estimates of FX and FY. If the assumption is true, the test simultaneously examines whether X and Y have equal means, equal medians, and whether 'X greater than Y' and 'Y greater than X' have the same probability 1/2. Independent of the assumption one concludes 'FX not equal to FY' in case of significance and 'P(X greater than Y) = 1/2 in case of no significance and large sample sizes. If the assumption may be violated, no statement is possible concerning means or medians. The probability P(X greater than Y) can be compared even against some p0 (being possibly different from 1/2), and a confidence interval for P(X greater than Y) can be calculated, when using the large sample modification of the test by Hilgers (1981).