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Fisher Exact Test
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Questions to David Rotermund
scipy.stats.fisher_exact
scipy.stats.fisher_exact(table, alternative='two-sided')
Perform a Fisher exact test on a 2x2 contingency table.
The null hypothesis is that the true odds ratio of the populations underlying the observations is one, and the observations were sampled from these populations under a condition: the marginals of the resulting table must equal those of the observed table. The statistic returned is the unconditional maximum likelihood estimate of the odds ratio, and the p-value is the probability under the null hypothesis of obtaining a table at least as extreme as the one that was actually observed. There are other possible choices of statistic and two-sided p-value definition associated with Fisher’s exact test; please see the Notes for more information.
Parameters:
alternative : {‘two-sided’, ‘less’, ‘greater’}, optional Defines the alternative hypothesis. The following options are available (default is ‘two-sided’):
- ‘two-sided’: the odds ratio of the underlying population is not one
- ‘less’: the odds ratio of the underlying population is less than one
- ‘greater’: the odds ratio of the underlying population is greater than one
Returns:
res : SignificanceResult
An object containing attributes:
statistic : float
This is the prior odds ratio, not a posterior estimate.
pvalue : float
The probability under the null hypothesis of obtaining a table at least as extreme as the one that was actually observed.
The input table is a, b], [c, d.
| a | b |
| c | d |
Where N_A = a + c for the elements in group A and N_B = b + d for the elements in group B.
N_A - c |
N_B-d |
| c | d |
Example
| Group A | Group B | |
|---|---|---|
| Yes | 7 | 17 |
| No | 15 | 5 |
This translates in to the table: 7, 17], [15, 5
from scipy.stats import fisher_exact
res = fisher_exact([[7, 17], [15, 5]], alternative="less")
print(res.statistic) # -> 0.13725490196078433
print(res.pvalue) # -> 0.0028841933752349743