A comparison of some approximations to the Wilcoxon-Mann-Whitney distribution

The following approximations to the exact distribution of the Wilcoxon rank sum test (Mann-Whitney U-test) are compared at or near significance levels .05, .025, .01 and .005: the normal approximation with continuity correction, the simple and complete version of the Edgeworth series approximation proposed by Fix and Hodges (1955), Buckle, Kraft and van Eeden’s (1969a) uniform approximation and Iman’s (1976) recently proposed approximation. The comparison takes into account simplicity of application as well as closeness, and some preference rules are suggested for different user objectives.