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Abstract

Confidence intervals, in general, have become an important aspect of reporting statistical results. In particular, interval estimators for binomial proportions have been studied extensively in recent literature. The large-sample Wald intervals are known to perform poorly, but the Wilson intervals have been shown to perform well in a variety of situations. One criticism is the relative difficulty of computing the Wilson or quadratic intervals in comparison to the Wald intervals. We offer a computational formula for the Wilson intervals that is a weighted estimator of the observed proportion, p, and that based on an uninformative prior, 1/2. This contribution enhances our understanding of the coverage behavior of the Wilson intervals. In addition, we contrast the Wilson intervals with other well-known intervals for the case of zero successes.

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References

Vollset SE. Confidence intervals for binomial proportions . Statistics in Medicine 1993; 12: 809-824 .

Wilson EB. Probable inference, the law of succession, and statistical inference . Journal of the American Statistical Association 1927; 22: 209-212 .

Newcombe R. Two-sided confidence intervals for the single proportion: Comparison of seven methods . Statistics in Medicine 1998; 17: 857-872 .

Agresti A , Caffo B. Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures . The American Statistician 2000; 54: 280-288 .

Santner TJ. Teaching large-sample binomial confidence intervals . Teaching Statistics 1998; 20: 20-23 .

Agresti A , Coull BA. Approximate is better than ‘exact’ for interval estimation of binomial proportions . The American Statistician 1998; 52: 119-126 .

Chen H. The accuracy of approximate intervals for the binomial parameter . Journal of the American Statistical Association 1990; 85: 514-518 .

Casella G , Berger RL. Statistical Inference, Wadsworth & Brooks/Cole , 1990.

Hanley JA , Lippman-Hand A.

If nothing goes wrong, is everything all right?

Journal of the American Statistical Association 1983; 249: 1743-1745 .

10.

Louis TA. Confidence intervals for a binomial parameter after observing no successes . The American Statistician 1981; 35: 154-154 .

11.

Jovanovic BD , Levy PS. A look at the rule of three . The American Statistician 1997; 51: 137-139 .

Weighted confidence interval construction for binomial parameters

Abstract

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