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

J. van Doorn, A. Ly, M. Marsman and E.-J. Wagenmakers

Journal of Applied Statistics, 2020, vol. 47, issue 16, 2984-3006

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 $\rho _s $ρs.

Date: 2020
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DOI: 10.1080/02664763.2019.1709053

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