ON TESTS THAT ARE UNIFORMLY MORE POWERFUL THAN THE WILCOXON-MANN-WHITNEY TEST

The Wilcoxon-Mann-Whitney rank sum test (U test) is often used in the nonparametric analysis of controlled clinical trials. We suggest a test that is uniformly more powerful than the U test in the following sense: the test will reject H0 whenever the U test rejects H0 and there are situations when the new test will reject H0 but the U test is not able to reject H0. The new test is not a mathematical curiosity, because it is constructed to achieve high power against those alternatives in which the better one of two given treatments has not only higher expectation but also less variability than the other treatment and, furthermore, the reduction in the P-values given by the new test as compared to the U test is often decisive. The principle is rather general and can be applied to practically all nonparametric tests. A table of significance levels is given for continuous distributions and an algorithm is presented that allows the determination of the exact distribution in the general case.