Confidence intervals for a ratio of two independent binomial proportions.

Several large-sample confidence intervals for the ratio of independent binomial proportions are compared in terms of exact coverage probability and width. A non-iterative approximate Bayesian interval is derived and its frequency properties are superior to all of the non-iterative confidence intervals considered. The approximate Bayesian interval, which is very easy to compute, has performance characteristics that are very similar to the computationally intensive score method. Two sample size determination formulas are presented, one for desired absolute precision and the other for desired relative precision.