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:
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] (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).