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Sample size for estimating a binomial proportion: comparison of different methods

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  • Luzia Gonçalves
  • M. Rosário de Oliveira
  • Cláudia Pascoal
  • Ana Pires

Abstract

The poor performance of the Wald method for constructing confidence intervals (CIs) for a binomial proportion has been demonstrated in a vast literature. The related problem of sample size determination needs to be updated and comparative studies are essential to understanding the performance of alternative methods. In this paper, the sample size is obtained for the Clopper--Pearson, Bayesian (Uniform and Jeffreys priors), Wilson, Agresti--Coull, Anscombe, and Wald methods. Two two-step procedures are used: one based on the expected length (EL) of the CI and another one on its first-order approximation. In the first step, all possible solutions that satisfy the optimal criterion are obtained. In the second step, a single solution is proposed according to a new criterion (e.g. highest coverage probability (CP)). In practice, it is expected a sample size reduction, therefore, we explore the behavior of the methods admitting 30% and 50% of losses. For all the methods, the ELs are inflated, as expected, but the coverage probabilities remain close to the original target (with few exceptions). It is not easy to suggest a method that is optimal throughout the range (0, 1) for p . Depending on whether the goal is to achieve CP approximately or above the nominal level different recommendations are made.

Suggested Citation

  • Luzia Gonçalves & M. Rosário de Oliveira & Cláudia Pascoal & Ana Pires, 2012. "Sample size for estimating a binomial proportion: comparison of different methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2453-2473, July.
    • Handle: RePEc:taf:japsta:v:39:y:2012:i:11:p:2453-2473
    DOI: 10.1080/02664763.2012.713919
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    References listed on IDEAS

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    1. Alan Agresti & Yongyi Min, 2005. "Frequentist Performance of Bayesian Confidence Intervals for Comparing Proportions in 2 × 2 Contingency Tables," Biometrics, The International Biometric Society, vol. 61(2), pages 515-523, June.
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    4. Liu, W. & Bailey, B. J. R., 2002. "Sample size determination for constructing a constant width confidence interval for a binomial success probability," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 1-5, January.
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    6. Piegorsch, Walter W., 2004. "Sample sizes for improved binomial confidence intervals," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 309-316, June.
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