An exact confidence set for two binomial proportions and exact unconditional confidence intervals for the difference and ratio of proportions

Authors:
Jen Reiczigel;Zsolt Abonyi-Tóth;Júlia Singer
Affiliations:
Szent István University, Faculty of Veterinary Science, Department of Biomathematics and Informatics, Istvan u. 2, Budapest, H-1078, Hungary;Szent István University, Faculty of Veterinary Science, Department of Biomathematics and Informatics, Istvan u. 2, Budapest, H-1078, Hungary;Baxter BioScience, Global Clinical Biostatistics Vienna, Austria
Venue:
Computational Statistics & Data Analysis
Year:
2008

Citing 4
Cited 2

Statistical inference for the risk ratio in 2 x 2 binomial trials with structural zero

Computational Statistics & Data Analysis
Nonconservative exact small-sample inference for discrete data

Computational Statistics & Data Analysis
Small-sample comparisons of confidence intervals for the difference of two independent binomial proportions

Computational Statistics & Data Analysis
Testing general hypotheses under binomial sampling: the two sample case-asymptotic theory and exact procedures

Computational Statistics & Data Analysis

Integrating induction and deduction for finding evidence of discrimination

Artificial Intelligence and Law
Two-tailed approximate confidence intervals for the ratio of proportions

Statistics and Computing

Quantified Score

Hi-index	0.03

Visualization

Abstract

An exact joint confidence set is proposed for two binomial parameters estimated from independent samples. Its construction relies on inverting the minimum volume test, a two-dimensional analogue of Sterne's test for a single probability. The algorithm involves computer-intensive exact computation based on binomial probabilities. The proposed confidence set has good coverage properties and it performs much better than the likelihood-based confidence set for the same problem. Applying the principle of intersection-union tests, the method can be used to derive exact tests and confidence intervals for functions of the two binomial parameters. Based on this, new exact unconditional two-sided confidence intervals are proposed for the risk difference and risk ratio. The performance of the new intervals is comparable to that of certain well-known confidence intervals in small samples. Extension of the methods described to two hypergeometric or two Poisson variables is straightforward.