A simple consistent Bayes factor for testing the Kendall rank correlation coefficient

TL;DR

This paper introduces a simple Bayesian hypothesis test for Kendall's tau, using asymptotic distributions and a closed-form Bayes factor, demonstrating its effectiveness through simulations and real data.

Contribution

It presents a novel, easy-to-implement Bayes factor for testing Kendall's tau, with proven consistency and practical applicability.

Findings

Bayes factor is consistent under certain prior conditions.

The method performs well in simulations.

Effective in real-data analysis.

Abstract

In this paper, we propose a simple and easy-to-implement Bayesian hypothesis test for the presence of an association, described by Kendall's \tau coefficient, between two variables measured on at least an ordinal scale. Owing to the absence of the likelihood functions for the data, we employ the asymptotic sampling distributions of the test statistic as the working likelihoods and then specify a truncated normal prior distribution on the noncentrality parameter of the alternative hypothesis, which results in the Bayes factor available in closed form in terms of the cumulative distribution function of the standard normal distribution. Investigating the asymptotic behavior of the Bayes factor we find the conditions of the priors so that it is consistent to whichever the hypothesis is true. Simulation studies and a real-data application are used to illustrate the effectiveness of the proposed Bayes factor. It deserves mentioning that the proposed method can be easily covered in undergraduate and graduate courses in nonparametric statistics with an emphasis on students' Bayesian thinking for data analysis.