Bayesian inference in 2\(\times 2\) and 2\(\times 2\times 2\) contingency tables (Q1061428)

A Bayesian approach to making inferences about the strength of association in \(2\times 2\) and \(2\times 2\times 2\) contingency tables is discussed. Assuming a Dirichlet prior the posterior distributions of the cross-ratio and the second order interaction measures of associations are obtained. It is shown that the distributions are invariant under sampling schemes with fixed margins and with margins not fixed.