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chi2_contingency(observed, correction=True, lambda_=None)

This function computes the chi-square statistic and p-value for the hypothesis test of independence of the observed frequencies in the contingency table observed. The expected frequencies are computed based on the marginal sums under the assumption of independence; see scipy.stats.contingency.expected_freq. The number of degrees of freedom is (expressed using numpy functions and attributes)

dof = observed.size - sum(observed.shape) + observed.ndim - 1

Notes

An often quoted guideline for the validity of this calculation is that the test should be used only if the observed and expected frequencies in each cell are at least 5.

This is a test for the independence of different categories of a population. The test is only meaningful when the dimension of observed is two or more. Applying the test to a one-dimensional table will always result in expected equal to observed and a chi-square statistic equal to 0.

This function does not handle masked arrays, because the calculation does not make sense with missing values.

Like scipy.stats.chisquare, this function computes a chi-square statistic; the convenience this function provides is to figure out the expected frequencies and degrees of freedom from the given contingency table. If these were already known, and if the Yates' correction was not required, one could use scipy.stats.chisquare. That is, if one calls

res = chi2_contingency(obs, correction=False)

then the following is true

(res.statistic, res.pvalue) == stats.chisquare(obs.ravel(),
                                               f_exp=ex.ravel(),
                                               ddof=obs.size - 1 - dof)

The lambda_ argument was added in version 0.13.0 of scipy.

Parameters

observed : array_like: The contingency table. The table contains the observed frequencies (i.e. number of occurrences) in each category. In the two-dimensional case, the table is often described as an "R x C table".
correction : bool, optional: If True, and the degrees of freedom is 1, apply Yates' correction for continuity. The effect of the correction is to adjust each observed value by 0.5 towards the corresponding expected value.
lambda_ : float or str, optional: By default, the statistic computed in this test is Pearson's chi-squared statistic . lambda_ allows a statistic from the Cressie-Read power divergence family to be used instead. See scipy.stats.power_divergence for details.

Returns

res : Chi2ContingencyResult

An object containing attributes:

statistic: statistic
pvalue: pvalue
dof: dof
expected_freq: expected_freq

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

Examples

A two-way example (2 x 3):

import numpy as np
from scipy.stats import chi2_contingency
obs = np.array([[10, 10, 20], [20, 20, 20]])
res = chi2_contingency(obs)
res.statistic

res.pvalue

res.dof

res.expected_freq

Perform the test using the log-likelihood ratio (i.e. the "G-test") instead of Pearson's chi-squared statistic.

res = chi2_contingency(obs, lambda_="log-likelihood")
res.statistic

res.pvalue

A four-way example (2 x 2 x 2 x 2):

obs = np.array(
    [[[[12, 17],
       [11, 16]],
      [[11, 12],
       [15, 16]]],
     [[[23, 15],
       [30, 22]],
      [[14, 17],
       [15, 16]]]])
res = chi2_contingency(obs)
res.statistic

res.pvalue

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.stats.contingency:association scipy.stats._hypotests:boschloo_exact scipy.stats._hypotests:barnard_exact scipy.stats._morestats:median_test scipy.stats._stats_py:fisher_exact

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