Interval estimation of the marginal probability of success for the beta-binomial distribution

Correlated binomial outcomes occur in many areas such as teratology and marketing. We study the problem of confidence interval estimation of the common marginal probability of success for correlated binary observations, focusing on the beta-binomial model. New conservative small sample confidence intervals are proposed for this problem based on extensions of the Tail and Sterne–Crow intervals for independent binomial responses. Some properties of these intervals are derived, comparisons with previously proposed methods are given, and recommendations regarding their use are made.