scipy.stats._result_classes.OddsRatioResult.

confidence_interval#

OddsRatioResult.confidence_interval(confidence_level=0.95, alternative='two-sided')[source]#

Confidence interval for the odds ratio.

Parameters:
confidence_level: float

Desired confidence level for the confidence interval. The value must be given as a fraction between 0 and 1. Default is 0.95 (meaning 95%).

alternative{‘two-sided’, ‘less’, ‘greater’}, optional

The alternative hypothesis of the hypothesis test to which the confidence interval corresponds. That is, suppose the null hypothesis is that the true odds ratio equals OR and the confidence interval is (low, high). Then the following options for alternative are available (default is ‘two-sided’):

  • ‘two-sided’: the true odds ratio is not equal to OR. There is evidence against the null hypothesis at the chosen confidence_level if high < OR or low > OR.

  • ‘less’: the true odds ratio is less than OR. The 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:
ciConfidenceInterval 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] (1,2)

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).

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