Title: Extending the Wilcoxon-Mann-Whitney Test for Latent Variables Author: Heidelinde Dehaene Affiliation: Ghent University Abstract: The most popular statistical tests for comparing two groups are either the two-sample t-test or the Wilcoxon-Mann-Whitney test. The latter can be preferred over the former for various reasons: it is robust to outliers, it has superior power properties for a variety of distributions, it is applicable to ordinal outcomes and the associated effect size is also meaningful for skewed distributions. Because the t-test can be embedded in a structural equation model, it can be extended to the context of latent variables. For the Wilcoxon-Mann-Whitney test such an extension does not exist. In this presentation, we will show how the Wilcoxon-Mann-Whitney test can be modiffed to accommodate for a measurement model. We will discuss the main properties both theoretically and empirically and we illustrate the method on an example in R.