Research ArticleOpen AccessGoogle Scholar indexed
Confidence Intervals for the Binomial Proportion: A Comparison of Four Methods
Mathematics Department, Egerton University, Egerton, Kenya
- 1 Mathematics Department, Egerton University, Egerton, Kenya
Open Journal of Statistics·Volume 11 (2021)·Pages 806–816·Published 27 September 2021·DOI10.4236/ojs.2021.115047
Copy link · social · email
Abstract
This paper presents four methods of constructing the confidence interval for the proportion p of the binomial distribution. Evidence in the literature indicates the standard Wald confidence interval for the binomial proportion is inaccurate, especially for extreme values of p . Even for moderately large sample sizes, the coverage probabilities of the Wald confidence interval prove to be erratic for extreme values of p . Three alternative confidence intervals, namely, Wilson confidence interval, Clopper-Pearson interval, and likelihood interval , are compared to the Wald confidence interval on the basis of coverage probability and expected length by means of simulation.
KeywordsBinomial DistributionConfidence IntervalCoverage ProbabilityExpected LengthRelative Likelihood Function
- Matiri, G., Nyongesa, K. and Islam, A. (2017) Sequentially Selecting between Two Experiment for Optimal Estimation of a Trait with Misclassification. American Journal of Theoretical and Applied Statistics, 6, 79-89. https://doi.org/10.11648/j.ajtas.20170602.12
- Vollset, S.E. (1993) Confidence Intervals for a Binomial Proportion. Statistics in Medicine, 12, 809-824. https://doi.org/10.1002/sim.4780120902
- Agresti, A. and Coull, B.A. (1998) Approximate Is Better Than “Exact” for Interval Estimation of Binomial Proportions. The American Statistician, 52, 119-126. https://doi.org/10.1080/00031305.1998.10480550
- Newcombe, R.G. (1998) Two-Sided Confidence Intervals for the Single Proportion: Comparison of Seven Methods. Statistics in Medicine, 17, 857-872. https://doi.org/10.1002/(SICI)1097-0258(19980430)17:8%3C857::AID-SIM777%3E3.0.CO;2-E
- Brown, L.D., Cai, T.T. and DasGupta, A. (2001) Interval Estimation for a Binomial Proportion. Statistical Science, 16, 101-117. https://doi.org/10.1214/ss/1009213286
- Brown, L.D., Cai, T.T. and DasGupta, A. (2002) Confidence Intervals for a Binomial Proportion and Asymptotic Expansions. Annals of Statistics, 30, 160-201. https://doi.org/10.1214/aos/1015362189
- Panagiotis, M. and Konstantinos, Z. (2008) Interval Estimation for a Binomial Proportion. A Bootstrap Approach. Journal of Statistical Computation and Simulation, 78, 1251-1265. https://doi.org/10.1080/00949650701749356
- Kalbfleisch, J.G. (1985) Probability and Statistical Inference, Volume 2: Statistical Inference. 2nd Edition, Springer Verlag, New York. https://doi.org/10.1007/978-1-4612-5136-1
- Clopper, C.J. and Pearson, E.S. (1934) The Use of Confidence Intervals or Fiducial Limits Illustrated in the Case of the Binomial. Biometrika, 26, 404-413. https://doi.org/10.1093/biomet/26.4.404
- Wilson, E.B. (1927) Probable Inference, the Law of Succession, and Statistical Inference. Journal of American Statistical Association, 22, 209-212. https://doi.org/10.1080/01621459.1927.10502953
- Pritz, M.B., Zhou, X.H. and Brizendine, E.J. (1996) Hyperdynamic Therapy for Cerebral Vasospam: A Meta-Analysis of 14 Studies. J. Neurovasc. Dis., 1, 6-8.