Two-sided confidence intervals for the single proportion: comparison of seven methods

TLDR

Simple interval estimate methods for proportions often have poor coverage and can produce inappropriate intervals, prompting development of methods that align minimum or mean coverage with the nominal level. The authors evaluate seven single‑proportion methods across 96,000 parameter points using criteria such as coverage accuracy, interval placement, width, avoidance of aberrations, and ease of use. Intervals based on tail areas and the simpler score methods are recommended for use. © 1998 John Wiley & Sons, Ltd.

Abstract

Simple interval estimate methods for proportions exhibit poor coverage and can produce evidently inappropriate intervals. Criteria appropriate to the evaluation of various proposed methods include: closeness of the achieved coverage probability to its nominal value; whether intervals are located too close to or too distant from the middle of the scale; expected interval width; avoidance of aberrations such as limits outside [0,1] or zero width intervals; and ease of use, whether by tables, software or formulae. Seven methods for the single proportion are evaluated on 96,000 parameter space points. Intervals based on tail areas and the simpler score methods are recommended for use. In each case, methods are available that aim to align either the minimum or the mean coverage with the nominal 1−α. © 1998 John Wiley & Sons, Ltd.