Two-tailed asymptotic inferences for a proportion

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.

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CC BY 4.0