Non Iterative Confidence Interval Methods for the Difference between Two Proportions

The construction of a confidence interval for the difference between two independent proportions is one of the most basic analyses in statistical inference. The Wald asymptotic methods, with and without a continuity correction have less than nominal coverage probability characteristics but continue to be used in spite of this known poor behavior. For the equal sample size case, the Wald-z coverage probability is subnominal overall. The Wald-c coverage probability always exceeds the nominal level and has interval width larger than Wald-z. For the unequal sample size case, Wald-z is always subnominal while Wald-c exceeds the nominal level. Newcombe's hybrid method and the Agresti-Caffo methods have coverage probabilities that are near nominal for either the equal or unequal sample sizes. Considering the coverage probability criterion, Newcombe's hybrid method and Agresti-Caffo method demonstrate superior coverage properties.