A Study of Mann-Whitney Test and Median Test in Several Distributions

The Mann-Whitney test and the Median test are two tests that can be used to test for a difference in location parameters. This paper compared powers of the two tests under a variety of population distributions through a simulation study. Both tests require that two underlying populations have the same variance, but this assumption was relaxed in some of the comparisons. In every cases, equal sizes of 10 and 20 were used. We compared the those two nonparametric tests when underlying distributions were mixed normal, lognormal, beta, gamma and chi-square distributions. Each test was performed 5,000 times and the SAS/MACRO used.