Statistical methods for analysis of survey data have been developed to facilitate research. More recently, Lumley and Scott (2013) developed an approach to extend the Mann‐Whitney‐Wilcoxon (MWW) rank sum test to survey data. Their approach focuses on the null of equal distribution. In many studies, the MWW test is called for when two‐sample t‐tests (with or without equal variance assumed) fail to provide meaningful results, as they are highly sensitive to outliers. In such situations, the null of equal distribution is too restrictive, as interest lies in comparing centers of groups. In this article, we develop an approach to extend the MWW test to survey data to test the null of equal mean rank. Although not as popular as the mean and median, the mean rank is also a meaningful measure of the center of a distribution and is the same as the median for a symmetric distribution. We illustrate the proposed approach and show major differences with Lumley and Scott's alternative using both real and simulated data.

中文翻译：

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将Mann-Whitney-Wilcoxon秩和检验扩展到调查数据以比较平均秩

已经开发出用于分析调查数据的统计方法以促进研究。最近，Lumley和Scott（2013）开发了一种方法来将Mann-Whitney-Wilcoxon（MWW）秩和检验扩展到调查数据。他们的方法侧重于均等分布的零。在许多研究中，当两个样本的t检验（假设有或没有相等的方差）无法提供有意义的结果时，就需要进行MWW检验，因为它们对异常值非常敏感。在这种情况下，由于兴趣在于比较组的中心，所以均等分布的零值过于严格。在本文中，我们开发了一种方法，可以将MWW检验扩展到调查数据，以检验均值均等的零值。尽管不如均值和中位数受欢迎，平均等级也是分布中心的有意义的度量，并且与对称分布的中位数相同。我们将说明所提出的方法，并使用实际数据和模拟数据显示与Lumley和Scott的替代方法的主要区别。