Statistics Papers

Document Type

Journal Article

Date of this Version

2001

Publication Source

Statistical Science

Volume

16

Issue

2

Start Page

101

Last Page

133

DOI

10.1214/ss/1009213286

Abstract

We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the standard Wald confidence interval has previously been remarked on in the literature (Blyth and Still, Agresti and Coull, Santner and others). We begin by showing that the chaotic coverage properties of the Wald interval are far more persistent than is appreciated. Furthermore, common textbook prescriptions regarding its safety are misleading and defective in several respects and cannot be trusted.

This leads us to consideration of alternative intervals. A number of natural alternatives are presented, each with its motivation and context. Each interval is examined for its coverage probability and its length. Based on this analysis, we recommend the Wilson interval or the equal-tailed Jeffreys prior interval for small n and the interval suggested in Agresti and Coull for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval.

Keywords

Bayes, binomial distribution, confidence intervals, coverage probability, Edgeworth expansion, expected length, Jeffreys prior, normal approximation, posterior

Share

COinS
 

Date Posted: 27 November 2017

This document has been peer reviewed.