The Wilcoxon-Mann-Whitney test under scrutiny
The Wilcoxon-Mann-Whitney test under scrutiny
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DOI：
10.1002/sim.3561
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发表时间：
2009-05-01
影响因子：
2
通讯作者：
Sandvik, Leiv
中科院分区：
文献类型：
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作者：
Fagerland, Morten W.;Sandvik, Leiv
Wilcoxon-Mann-Whitney(WMW)检验通常用于比较两个独立的、可能是非正态分布的均值或中值。对于这个问题，众所周知，WMW检验的大样本近似版本的真正显著水平对分布形状的差异很敏感。在广泛的仿真研究的基础上，本文表明，这种测试的粗糙性不足的问题比人们想象的要严重得多。特别是，方差的微小差异和中等程度的偏斜度可能会产生与标称类型1错误率的较大偏差。当两种分布具有不同程度的偏度时，这种情况会进一步加剧。其他基于排名的方法，如Fligner-Policello(FP)测试和Brunner-Munzel(BM)测试，表现类似，尽管BM测试通常更好。通过将WMW检验看作是秩上的两样本T检验，我们注意到了秩变换的一些不合需要的性质，从而解释了结果。在实践中，在解释测试结果之前，应对排序的样本进行检查，并发现其充分满足合理的对称性和方差齐性。版权所有(C)2009 John Wiley&Sons，Ltd.
The Wilcoxon-Mann-Whitney (WMW) test is often used to compare the means or medians of two independent, possibly nonnormal distributions. For this problem, the true significance level of the large sample approximate version of the WMW test is known to be sensitive to differences in the shapes of the distributions. Based on a wide ranging simulation study, our paper shows that the problem of lack of roubustness of this test is more serious than is thought to be the case. In particular, small differences in variances and moderate degrees of skewness can produce large deviations from the nominal type 1 error rate. This is further exacerbated when the two distributions have different degrees of skewness. Other rank-based based methods like the Fligner-Policello (FP) test and the Brunner-Munzel (BM) test perform similarly, although the BM test is generally better. By considering the WMW test as a two-sample T test on ranks, we explain the results by noting some undesirable properties of the rank transformation. In practice, the ranked samples should be examined and found to sufficiently satisfy reasonable symmetry and variance homogeneity before the test results are interpreted. Copyright (C) 2009 John Wiley & Sons, Ltd.