  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.
