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Cyrus R. Mehta, Nitin R. Patel, Robert Gray, Computing an Exact Confidence Interval for the Common Odds Ratio in Several 2 × 2 Contingency Tables, Journal of the American Statistical Association, Vol. 80, No. 392 (Dec., 1985), pp. 969-973
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Mehta et al. (1985) studied this question.
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