A PECULIARITY OF THE WILCOXON-MANN-WHITNEY RANK-SUM TEST
Robert J. MacG. Dawson
Abstract
Pothoff showed in 1963 that the Wilcoxon-Mann-Whitney test is a test of
relative location whenever the two distributions are symmetric. By contrast,
Steinhaus and Trybula exhibited,in 1959, a set of three distributions for
which the test would yield intransitive cycles. It is shown that the latter
behaviour is usual even within Behrens-Fisher families of distributions.
Sufficient conditions for the test to be acyclic, and hence a test for
relative location, on a Behrens-Fisher family will be given.