Assessing Robustness of Intrinsic Tests of Independence in Two-Way Contingency Tables

For testing nested hypotheses from a Bayesian standpoint, a desirable condition is that the prior for the alternative model concentrates mass around the smaller, or null, model. For testing independence in contingency tables, the intrinsic priors satisfy this requirement. Furthermore, the degree of concentration of the priors is controlled by a discrete parameter, t, the training sample size, which plays an important role in the resulting answer. In this article we report on the robustness of the tests of independence for small or moderate sample sizes in contingency tables with respect to intrinsic priors with different degrees of concentration around the null. We compare these tests to frequentist tests and other robust Bayes tests. For large sample sizes, robustness is achieved because the intrinsic Bayesian tests are consistent. Examples using real and simulated data are given. Supplemental materials (technical details and data sets) are available online.