Bayesian rank-based hypothesis testing for the rank sum test, the signed rank test, and Spearman's<i>ρ</i>

Abstract

Bayesian inference for rank-order problems is frustrated by the absence of an explicit likelihood function. This hurdle can be overcome by assuming a latent normal representation that is consistent with the ordinal information in the data: the observed ranks are conceptualized as an impoverished reflection of an underlying continuous scale, and inference concerns the parameters that govern the latent representation. We apply this generic data-augmentation method to obtain Bayes factors for three popular rank-based tests: the rank sum test, the signed rank test, and Spearman's <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>ρ</mml:mi> <mml:mi>s</mml:mi></mml:msub> </mml:math> .