Worrying about normality

hypothesis being tested with the WMW test is not easily described; conventional interpretation (including examples provided by statistical packages) would have it that the null hypothesis is one of equal group medians, but such is not the case; rather it is a test for equality of group mean ranks. Because the WMW test is a test of both location and shape, its interpretation as a test of medians is valid when the only distributional difference is a shift in location. That is, for the MWM test to be “distribution free”, under the null hypothesis of equal medians, the two populations being compared are assumed to be continuous and have the same shape. Technically, the above condition will be satisfied if the distribution location parameter is the median (for example a Cauchy distribution); otherwise the location parameter is usually the mean. If the means/medians are similar but the two distributions have different spreads, the WMW test has poor power under the alternative hypothesis. The (Mood) median test also has low power in small samples and is not recommended. That the differences in spread may be as important as (putative) differences in medians is often overlooked. Furthermore, there are different outcomes from WMW test dependent upon the statistical package; these differences relate to the handling of ties, the use of the continuity correction and the use of the asymptotic approximation versus the exact permutation distribution. The latter form of the WMW test would appear to be the preferred option. Point of view