Simultaneous confidence intervals for comparing binomial parameters

Alan Agresti, Matilde Bini, Bruno Bertaccini, Euijung Ryu

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


To compare proportions with several independent binomial samples, we recommend a method of constructing simultaneous confidence intervals that uses the studentized range distribution with a score statistic. It applies to a variety of measures, including the difference of proportions, odds ratio, and relative risk. For the odds ratio, a simulation study suggests that the method has coverage probability closer to the nominal value than ad hoc approaches such as the Bonferroni implementation of Wald or "exact" small-sample pairwise intervals. It performs well even for the problematic but practically common case in which the binomial parameters are relatively small. For the difference of proportions, the proposed method has performance comparable to a method proposed by Piegorsch (1991, Biometrics 47, 45-52).

Original languageEnglish (US)
Pages (from-to)1270-1275
Number of pages6
Issue number4
StatePublished - Dec 2008


  • Bonferroni method
  • Difference of proportions
  • Odds ratio
  • Score test
  • Studentized range distribution
  • Tukey multiple comparisons

ASJC Scopus subject areas

  • Statistics and Probability
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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