Comparison of some two sample means tests by simulation

The usual t-test for testing that two samples come from a common normal population cannot be used to test H0: μ1 = μ2 for two samples drawn respectively from normal populations if . Many solutions to this problem, known as the two sample or Fisher-Behrens problem after Fisher's (1935b) solution, have been advanced and we examine here the Aspin-Welch (AW) solution and the distribution free Wilcoxon-Mann-Whitney (WMW) test, which latter is commonly, but incorrectly, taught and used as an approximate solution to the problem. It is shown here in a simulation context that the AW test is a highly acceptable practical procedure while the WMW test is definitely not. Some results on testing means when samples are drawn from non-normal populations are also discussed.