Abstract
Interval estimation of a binomial proportion is one of the basic problems in statistics. In technical practice a binomial proportion is often used in statistical quality control. The standard Wald interval and the exact Clopper-Pearson interval are the most common and frequently used intervals. They are presented in the majority of statistical literature. It is known that the Wald interval performs poorly and this interval should not be used. In this paper we recommend the alternatives of confidence intervals that have a better performance and are appropriate for practical use. We compare the performance of six alternatives of confidence intervals for a binomial proportion: the Wald interval, the Clopper-Pearson interval, the Wilson score interval, the Wilson score interval with continuity correction, the Agresti-Coull interval and the Jeffreys interval in terms of the coverage probability, the interval length and the root mean square error.
Highlights
Interval estimation of a binomial proportion is one of the basic problems in statistics
In technical practice the binomial proportion is often used in statistical quality control
In this paper we recommend the alternatives of confidence intervals for binomial proportion that have better performance and are often used in practice, but they are presented sporadically in the basic statistical literature
Summary
Interval estimation of a binomial proportion is one of the basic problems in statistics. The exact Clopper-Pearson interval is based on the exact binomial distribution This interval eliminates overshoot and zero width intervals and it is known that this interval is strictly conservative and too wide (Newcombe, 1998, Brown, Cai, DasGupta, 2001, Pires, Amado, 2008). In this paper we recommend the alternatives of confidence intervals for binomial proportion that have better performance and are often used in practice, but they are presented sporadically in the basic statistical literature. We summarize the results for the coverage probability in terms of the observed minimum coverage probability and the average coverage probability and we classify the alternatives of confidence intervals into two classes of acceptable intervals- strictly conservative intervals and intervals that are not strictly conservative, but conservative on average Our recommendation of these selected alternatives of confidence intervals is based on our investigations of these intervals and on the existing comparative studies that were presented in recent statistical literature, see e. Our recommendation of these selected alternatives of confidence intervals is based on our investigations of these intervals and on the existing comparative studies that were presented in recent statistical literature, see e. g. Newcombe (1998), Brown, Cai, DasGupta (2001) and Pires, Amado (2008)
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