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

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 ρ s .