low`` end of the confidence interval is 0, and there is evidence against the null hypothesis at the chosen `confidence_level` if ``high < OR``. * 'greater': the true odds ratio is greater than ``OR``. The ``high`` end of the confidence interval is ``np.inf``, and there is evidence against the null hypothesis at the chosen `confidence_level` if ``low > OR``. Returns ------- ci : ``ConfidenceInterval`` instance The confidence interval, represented as an object with attributes ``low`` and ``high``. Notes ----- When `kind` is ``'conditional'``, the limits of the confidence interval are the conditional "exact confidence limits" as described by Fisher [1]_. The conditional odds ratio and confidence interval are also discussed in Section 4.1.2 of the text by Sahai and Khurshid [2]_. When `kind` is ``'sample'``, the confidence interval is computed under the assumption that the logarithm of the odds ratio is normally distributed with standard error given by:: se = sqrt(1/a + 1/b + 1/c + 1/d) where ``a``, ``b``, ``c`` and ``d`` are the elements of the contingency table. (See, for example, [2]_, section 3.1.3.2, or [3]_, section 2.3.3). References ---------- .. [1] R. A. Fisher (1935), The logic of inductive inference, Journal of the Royal Statistical Society, Vol. 98, No. 1, pp. 39-82. .. [2] H. Sahai and A. Khurshid (1996), Statistics in Epidemiology: Methods, Techniques, and Applications, CRC Press LLC, Boca Raton, Florida. .. [3] Alan Agresti, An Introduction to Categorical Data Analysis (second edition), Wiley, Hoboken, NJ, USA (2007). )