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Biometrika 1979 66(3):645-653; doi:10.1093/biomet/66.3.645
© 1979 by Biometrika Trust
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Modified Wilcoxon test for two different distributions

J. R. GREEN

Department of Computational and Statistical Science, University of Liverpool

Given independent samples from the continuous distributions F(x) and G(y), which may be quite different, we here consider using the Wilcoxon or Mann-Whitney test, with the normal approximation, to test between H0: pr(X > Y) = p0 and H1: pr(X > Y)>p0, especially with p0 = 1/2. A modification of the Wilcoxon test due to Potthoff and to Zaremba is considered. Additional restrictions are introduced to give improved tests. Considerations of asymptotic relative efficiency and Monte Carlo studies show that the power of these tests compare favourably with those of the ordinary t test, the Welch-Aspin t test and a test due to Sen.

Key Words: Location test • Mann-Whitney test • Modified Wilcoron test • Variance of Mann-Whitney U


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