Two-tailed asymptotic inferences for a proportion

Abstract

This paper evaluates 29 methods for obtaining a two-sided confidence interval for a binomial proportion (16 of which are new proposals) and comes to the conclusion that: Wilson's classic method is only optimal for a confidence of 99%, although generally it can be applied when n≥50; for a confidence of 95% or 90%, the optimal method is the one based on the arcsine transformation (when this is applied to the data incremented by 0.5), which behaves in a very similar manner to Jeffreys’ Bayesian method. A simpler option, though not so good as those just mentioned, is the classic-adjusted Wald method of Agresti and Coull.

Keywords:

• arcsine transformation
• asymptotic confidence interval
• continuity correction
• Jeffreys' method
• Wald method and adjusted Wald methods
• Wilson score method

This research was supported by the Ministerio de Economía y Competitividad, Spanish, grant number MTM2012-35591.

Notes

1. Supplementary Content may be viewed online at http://10.1080/02664763.2014.881783