Let π=π1-π2 be the difference of two independent proportions related to two populations. We study the test H0:π≥0 against different alternatives, in the Bayesian context. The various Bayesian approaches use standard beta distributions, and are simple to derive and compute. But the more general test H0:π≥η, with η＞0, requires more advanced mathematical tools to carry out the computations. These tools, which include the density of the difference of two general beta variables, are presented in the article, with numerical examples for illustrations to facilitate comprehension of results.
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