The Relative Power of the Wilcoxon-Mann-Whitney Test and Student t Test Under Simple Bounded Transformations

The Wilcoxon-Mann-Whitney test and related nonparametric statistical methods based on ranks have been found to be more powerful than parametric tests such as the Student t test for various heavy-tailed distributions, including the exponential, Cauchy, and mixed-normal distributions, both in the asymptotic limit and for relatively small sample sizes. The present computer simulation study provided evidence that this power advantage results from reduction of the influence of outliers by transformation of measures to ranks. Random samples were obtained from these heavy-tailed distributions, and the initial sample values were mapped onto several bounded sets of numbers that are not ranks, including a set having a random component in which order was not preserved. An ordinary Student t test performed on the transformed values in most cases was considerably more powerful than one performed on the original values and also as powerful as the Wilcoxon-Mann-Whitney test.