Performs a Fisher exact test on a 2x2 contingency table.
Parameters :  table : array_like of ints
alternative : {‘twosided’, ‘less’, ‘greater’}, optional


Returns :  oddsratio : float
p_value : float

See also
Notes
The calculated odds ratio is different from the one R uses. In R language, this implementation returns the (more common) “unconditional Maximum Likelihood Estimate”, while R uses the “conditional Maximum Likelihood Estimate”.
For tables with large numbers the (inexact) chisquare 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 pvalue:
>>> 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.