A New Exact Confidence Interval for the Difference of Two Binomial Proportions

Abstract

We consider interval estimation of the difference between two binomial proportions. Several methds of constructing such an interval are known. Unfortunately those confidence intervals have poor coverage probability: it is significantly smaller than the nominal confidence level. In this paper a new confidence interval is proposed. The construction needs only information on sample sizes and sample difference between proportions. The coverage probability of the proposed confidence interval is at least the nominal confidence level. The new confidence interval is illustrated by a medical example.