Better Confidence Intervals for a Binomial Proportion

Abstract

Interval estimation of a binomial proportion is one of the basic problems in statistics. In technical practice a binomial proportion is often used in statistical quality control. The standard Wald interval and the exact Clopper-Pearson interval are the most common and frequently used intervals. They are presented in the majority of statistical literature. It is known that the Wald interval performs poorly and this interval should not be used. In this paper we recommend the alternatives of confidence intervals that have a better performance and are appropriate for practical use. We compare the performance of six alternatives of confidence intervals for a binomial proportion: the Wald interval, the Clopper-Pearson interval, the Wilson score interval, the Wilson score interval with continuity correction, the Agresti-Coull interval and the Jeffreys interval in terms of the coverage probability, the interval length and the root mean square error.

Keywords

• binomial distribution
• binomial proportion
• confidence interval
• coverage probability
• interval length
• root mean square error