The computation of a confidence interval for a binomial proportion is apparently a very elementary problem, considered in almost every introductory statistics textbook. However, there are at least three reasons why it is important to have a closer look at it:
In this talk, 16 simple (non-iterative) methods are considered: exact or Clopper-Pearson interval; score or Wilson interval (with and without continuity correction); Bayesian interval with uniform prior; the usual or Wald interval (with and without continuity correction); four variants of bootstrap intervals which do not need Monte Carlo; three variants based on the arcsin transformation; and three other corrections recently proposed for the Wald interval (Agresti and Coull, 1998; Pan, 2002). The methods are compared based on coverage probabilities and expected lengths numerically computed at 30,000 points in the parameter space. From these comparisons it is possible to have a clear classification of the methods and choose the one that best fits our needs. The implementation of the methods in four major statistical packages is also discussed.
References:
Agresti, A. and Coull, B. A. (1998). Approximate is better than “exact” for interval estimation of binomial proportions. The American Statistician, 52, 119-126.
Newcomb, R. G. (1998). Two-sided confidence intervals for the single proportion: comparison of seven methods. Statistics in Medicine, 17, 857-872.
Pan, W. (2002). Approximate confidence intervals for one proportion and difference of two proportions. Computational Statistics & Data Analysis, 40, 143-157.
Vollset, S. E. (1993). Confidence intervals for a binomial proportion. Statistics in Medicine, 12, 809-827.
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