R X S Tables From A Bayesian Viewpoint

Abstract

The display of the data by means of contingency tables is used for discussing different approaches to statistical inference. We develop a Bayesian procedure for the homogeneity testing problem of r populations using r × s contingency tables. The posterior probability of the homogeneity null hypothesis is calculated using a mixed prior distribution. The methodology consists of assigning an appropriate prior mass, π0, to the null and spreading the remainder, 1 − π0, over the alternative according to a density function. With this method, it is possible to prove a theorem which shows when the p-value and the posterior probability can give rise to the same conclusion.