Improving interval estimation of binomial proportions

In this paper, we propose one new confidence interval for the binomial proportion; our interval is based on the Edgeworth expansion of a logit transformation of the sample proportion. We provide theoretical justification for the proposed interval and also compare the finite-sample performance of the proposed interval with the three best existing intervals—the Wilson interval, the Agresti–Coull interval and the Jeffreys interval—in terms of their coverage probabilities and expected lengths. We illustrate the proposed method in two real clinical studies.