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

TL;DR

This paper introduces a new exact confidence interval for the difference between two binomial proportions that guarantees at least the nominal coverage probability, improving over existing methods with poor coverage.

Contribution

A novel confidence interval method for binomial differences that ensures accurate coverage using only sample sizes and observed differences.

Findings

Coverage probability is at least the nominal level.

Method is simple and based on sample sizes and observed differences.

Illustrated with a medical example.

Abstract

We consider interval estimation of the difference between two binomial proportions. Several methods 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.