On logit confidence intervals for the odds ratio with small samples
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Updated: Oct 8, 2026

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Published on: September 16, 2022
1Department of Statistics, University of Florida, Gainesville 32611-8545, USA. aa@stat.ufl.edu
Abstract:
Unless the true association is very strong, simple large-sample confidence intervals for the odds ratio based on the delta method perform well even for small samples. Such intervals include the Woolf logit interval and the related Gart interval based on adding .5 before computing the log odds ratio estimate and its standard error. The Gart interval smooths the observed counts toward the model of equiprobability, but one obtains better coverage probabilities by smoothing toward the independence model and by extending the interval in the appropriate direction when a cell count is zero.
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