New confidence intervals for the difference between two proportions in two-sample correlated binary data

Asymptotic confidence intervals for the difference between two proportions have been well developed in two-sample correlated binary data. But, the coverage probabilities of such asymptotic confidence intervals are much smaller than the nominal level in small samples, because the asymptotic confidence intervals rely on the large sample theory. The aim of this paper is to construct new confidence intervals whose performance is better than the existing confidence intervals in small samples. Assuming the beta-binomial model, we derive the Edgeworth expansion of the studentized test statistic. Then, we propose new confidence intervals by eliminating the skewness in the Edgeworth expansion. We conduct simulation studies to compare the new confidence intervals with the existing confidence intervals.