Enhanced Objective Bayesian Testing for the Equality of two Proportions

WORKING PAPER M10/13, SOUTHAMPTON STATISTICAL SCIENCES RESEARCH INSTITUTE, UNIVERSITY OF SOUTHAMPTON, UK.We develop a new class of prior distributions for Bayesian comparison of nested models, which we call intrinsic moment priors. We aim at testing the equality of two proportions, based on independent samples, and thus focus on discrete data models. We illustrate our methodology in a running Bernoulli example, where we test a sharp null hypothesis, then we implement our procedure to test the equality of two proportions. A detailed analysis of the properties of our method is presented together with an application to a collection of real-world 2*2 tables involving a sensitivity analysis and a crossvalidation study.