Confidence Intervals for the Binomial Proportion: A Comparison of Four Methods
Luke Akong’o Orawo
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.
Topics & Concepts
Binomial proportion confidence intervalConfidence intervalStatisticsTolerance intervalMathematicsRobust confidence intervalsCDF-based nonparametric confidence intervalCredible intervalCoverage probabilityBinomial (polynomial)Confidence distributionNegative binomial distributionConfidence regionPoisson distributionStatistical Distribution Estimation and ApplicationsStatistical Methods and Bayesian InferenceOptimal Experimental Design Methods