Nonparametric Tests of Differences in Medians: Comparison of the Wilcoxon–Mann–Whitney and Robust Rank-Order Tests

Abstract

The nonparametric Wilcoxon–Mann–Whitney test is commonly used by experimental economists for detecting differences in central tendency between two samples. This test is only theoretically appropriate under certain assumptions concerning the population distributions from which the samples are drawn, and is often used in cases where it is unclear whether these assumptions hold, and even when they clearly do not hold. Fligner and Pollicello's (1981, Journal of the American Statistical Association. 76, 162–168) robust rank-order test is a modification of the Wilcoxon–Mann–Whitney test, designed to be appropriate in more situations than Wilcoxon–Mann–Whitney. This paper uses simulations to compare the performance of the two tests under a variety of distributional assumptions. The results are mixed. The robust rank-order test tends to yield too many false positive results for medium-sized samples, but this liberalness is relatively invariant across distributional assumptions, and seems to be due to a deficiency of the normal approximation to its test statistic's distribution, rather than the test itself. The performance of the Wilcoxon–Mann–Whitney test varies hugely, depending on the distributional assumptions; in some cases, it is conservative, in others, extremely liberal. The tests have roughly similar power. Overall, the robust rank-order test performs better than Wilcoxon–Mann–Whitney, though when critical values for the robust rank-order test are not available, so that the normal approximation must be used, their relative performance depends on the underlying distributions, the sample sizes, and the level of significance used.