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A nonparametric two-sample comparison for skewed data with unequal variances

For practical situations, the pure shift model is probably not very realistic, and it is thus important to assess the robustness of different tests against deviations from this model. It is well established that heteroscedasticity (unequal variances) is at least as deleterious for the properties of the Wilcoxon-Mann-Whitney (WMW) test as for the t -test [1] and that the Welch test should replace the t -test when distributions are approximately normal and variances unequal. It is also worth remembering that the WMW test does not share the asymptotic robustness properties of the t -test. In addition, unequal variance is not the only problem frequently encountered. Distributions can also be skewed, and the skewness of the two distributions may differ. Unfortunately, but not unexpectedly, even the Welch test is unable to maintain the nominal significance level when distributions are skewed [1] .</P>Stochastic simulation is a valuable tool to compare test properties under different conditions. Based on simulation studies, Neuhäuser [2] proposes that the modified or generalized Wilcoxon test by Brunner and Munzel (BM) [3] should be applied when it cannot be assumed that variances are equal and distributions symmetric. In such situations, Skovlund and Fenstad [1] have shown that http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Clinical Epidemiology Elsevier
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