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# scipy.stats.fisher_exact

`scipy.stats.``fisher_exact`(table, alternative='two-sided')

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

  Parameters:

  table : array_like of ints

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

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

  > Which alternative hypothesis to the null hypothesis the test uses. Default is ‘two-sided’.

  Returns:

  oddsratio : float

  > This is prior odds ratio and not a posterior estimate.

  p_value : float

  > 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.

  See also

  `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.