A Wilcoxon–Mann–Whitney Test for Latent Variables

Abstract

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We propose an extension of the Wilcoxon–Mann–Whitney test to compare two groups when the outcome variable is latent. We empirically demonstrate that the test can have superior power properties relative to tests based on Structural Equation Modeling for a variety of settings. In addition, several other advantages of the Wilcoxon–Mann–Whitney test are retained such as robustness to outliers and good small sample performance. We demonstrate the proposed methodology on a case study.

Keywords

• rank test
• measurement error
• indicators
• robustness
• nonparametric inference
• group comparison