Confidence intervals based on some weighting functions for the difference of two binomial proportions

In this paper, we propose two new methods for computing confidence intervals for the difference of two independent binomial proportions in small sample cases. Several test-based exact confidence intervals have been developed to guarantee the nominal coverage probability in small sample cases. However, these methods are sometimes unnecessarily too conservative because they use the exact p-value for constructing confidence intervals by maximizing the tail probability to account for the worst configuration. In order to reduce conservatism, our new methods adopt the p-value weighted by two types of functions instead of the maximum p-value. Our proposed methods can be regarded as quasi-exact methods. The performance evaluation results showed that our methods are much less conservative than the exact method. Compared with other existing quasi-exact methods, generally, our methods possess coverage probabilities closer to the nominal confidence level and shorter expected confidence widths. In particular, the beta weighing method provides the most reasonable balance between accurate coverage probability and short interval width in small sample cases.