Extending the Mann-Whitney-Wilcoxon rank sum test to survey data for comparing mean ranks

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.