New intervals for the difference between two independent binomial proportions

Abstract

In this paper we gave an Edgeworth expansion for the studentized difference of two binomial proportions. We then proposed two new intervals by correcting the skewness in the Edgeworth expansion in a direct and an indirect way. Such the bias-correct confidence intervals are easy to compute, and their coverage probabilities converge to the nominal level at a rate of O( n −1/2), where n is the size of the combined samples. Our simulation results suggest that in finite samples the new interval based on the indirect method have the similar performance to the two best existing intervals in terms of coverage accuracy and average interval length and that the another new interval based on the direct method had the best average coverage accuracy but could have poor coverage accuracy when two true binomial proportions are close to the boundary points.