# scipy.stats.fisher_exact¶

scipy.stats.fisher_exact(table, alternative='two-sided')[source]

Perform a Fisher exact test on a 2x2 contingency table.

Parameters
tablearray_like of ints

A 2x2 contingency table. Elements should be non-negative integers.

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

Defines the alternative hypothesis. The following options are available (default is ‘two-sided’):

• ‘two-sided’

• ‘less’: one-sided

• ‘greater’: one-sided

Returns
oddsratiofloat

This is prior odds ratio and not a posterior estimate.

p_valuefloat

P-value, the probability of obtaining a distribution at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.

chi2_contingency

Chi-square test of independence of variables in a contingency table.

Notes

The calculated odds ratio is different from the one R uses. This scipy implementation returns the (more common) “unconditional Maximum Likelihood Estimate”, while R uses the “conditional Maximum Likelihood Estimate”.

For tables with large numbers, the (inexact) chi-square test implemented in the function chi2_contingency can also be used.

Examples

Say we spend a few days counting whales and sharks in the Atlantic and Indian oceans. In the Atlantic ocean we find 8 whales and 1 shark, in the Indian ocean 2 whales and 5 sharks. Then our contingency table is:

        Atlantic  Indian
whales     8        2
sharks     1        5


We use this table to find the p-value:

>>> import scipy.stats as stats
>>> oddsratio, pvalue = stats.fisher_exact([[8, 2], [1, 5]])
>>> pvalue
0.0349...


The probability that we would observe this or an even more imbalanced ratio by chance is about 3.5%. A commonly used significance level is 5%–if we adopt that, we can therefore conclude that our observed imbalance is statistically significant; whales prefer the Atlantic while sharks prefer the Indian ocean.

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