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Review of alternative approaches to calculation of a confidence interval for the odds ratio of a 2 × 2 contingency table
Article first published online: 5 OCT 2012
DOI: 10.1111/j.2041-210x.2012.00250.x
© 2012 The Authors. Methods in Ecology and Evolution © 2012 British Ecological Society
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How to Cite
Ruxton, G. D., Neuhäuser, M. (2013), Review of alternative approaches to calculation of a confidence interval for the odds ratio of a 2 × 2 contingency table. Methods in Ecology and Evolution, 4: 9–13. doi: 10.1111/j.2041-210x.2012.00250.x
Publication History
- Issue published online: 24 JAN 2013
- Article first published online: 5 OCT 2012
- Manuscript Accepted: 30 AUG 2012
- Manuscript Received: 8 JUN 2012
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Keywords:
- association;
- conditional approaches;
- Fisher's Exact test;
- Fisher-Boschloo test;
- null hypothesis testing;
- tests of association;
- unconditional approaches
Summary
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A common situation in biology is where we have count data and wish to explore whether there is an association between two categorical variables, each with two levels (a 2 × 2 contingency table). The size of the association can be measured using the odds ratio, with a confidence interval for this measure enclosing unity suggesting no evidence of an association. However, there is no universally agreed method for calculating such a confidence interval.
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Here, we provide a review of some commonly used and recently suggested methods.
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Of all of the methods currently available, the unconditional approach based on the score statistic was consistently closest to the nominal type I error level in our investigations, and this is the method we generally recommend. This method also offers good agreement with P-values from null hypothesis testing using the method of Fisher-Boschloo.
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However, some scientists may prefer the recently developed minlike or Blaker methods, which offered better agreement with P-values calculated using Fisher's Exact test or Blaker's Exact test, respectively.
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Lastly, where calculation without use of a computer is required, we recommend the Woolf method with Haldane-Anscombe correction.