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Stat Methods Med Res. 2015 Apr;24(2):224-54. doi: 10.1177/0962280211415469. Epub 2011 Oct 13.

Recommended confidence intervals for two independent binomial proportions.

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  • 1Unit of Biostatistics and Epidemiology, Oslo University Hospital, Norway.
  • 2Department of Neuroscience, Norwegian University of Science and Technology, Trondheim, Norway.
  • 3Department of Biostatistics, University of Oslo, Norway.


The relationship between two independent binomial proportions is commonly estimated and presented using the difference between proportions, the number needed to treat, the ratio of proportions or the odds ratio. Several different confidence intervals are available, but they can produce markedly different results. Some of the traditional approaches, such as the Wald interval for the difference between proportions and the Katz log interval for the ratio of proportions, do not perform well unless the sample size is large. Better intervals are available. This article describes and compares approximate and exact confidence intervals that are - with one exception - easy to calculate or available in common software packages. We illustrate the performances of the intervals and make recommendations for both small and moderate-to-large sample sizes.


2 × 2 table; NNT; odds ratio; relative risk; risk difference

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