Interval Estimators for a Binomial Proportion: Comparison of Twenty Methods

Abstract

In applied statistics it is often necessary to obtain an interval estimate for an unknown proportion (p) based on binomial sampling. This topic is considered in almost every introductory course. However, the usual approximation is known to be poor when the true p is close to zero or to one. To identify alternative procedures with better properties twenty non-iterative methods for computing a (central) two-sided interval estimate for p were selected and compared in terms of coverage probability and expected length. From this study a clear classification of those methods has emerged. An important conclusion is that the interval based on asymptotic normality, but after the arcsine transformation and a continuity correction, and the Add 4 method of Agresti and Coull (1998) yield very reliable results, the choice between the two depending on the desired degree of conservativeness.

Keywords

• confidence interval
• binomial distribution
• proportion test
• normal approximation
• arcsine transformation
• continuity correction