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

J. Reiczigel, Zsolt Abonyi-Tóth, Júlia Singer

Research output: Contribution to journalArticle

37 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)5046-5053
Number of pages8
JournalComputational Statistics and Data Analysis
Volume52
Issue number11
DOIs
Publication statusPublished - Jul 15 2008

Fingerprint

Confidence Set
Confidence interval
Proportion
Risk Difference
Exact Computation
Exact Test
Small Sample
Likelihood
Siméon Denis Poisson
Coverage
Union
Intersection
Analogue
Interval
Confidence set

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Statistics, Probability and Uncertainty
  • Electrical and Electronic Engineering
  • Computational Mathematics
  • Numerical Analysis
  • Statistics and Probability

Cite this

An exact confidence set for two binomial proportions and exact unconditional confidence intervals for the difference and ratio of proportions. / Reiczigel, J.; Abonyi-Tóth, Zsolt; Singer, Júlia.

In: Computational Statistics and Data Analysis, Vol. 52, No. 11, 15.07.2008, p. 5046-5053.

Research output: Contribution to journalArticle

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