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scipy.stats.

# chi2_contingency

scipy.stats.chi2_contingency(observed, correction=True, lambda_=None, *, method=None)

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

  This function computes the chi-square statistic and p-value for the hypothesis test of independence of the observed frequencies in the contingency table [1] 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

  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 [2]. lambda_ allows a statistic from the Cressie-Read power divergence family [3] to be used instead. See `scipy.stats.power_divergence` for details.

    method ResamplingMethod, optional

      Defines the method used to compute the p-value. Compatible only with correction=False, default lambda_, and two-way tables. If method is an instance of `PermutationMethod`/`MonteCarloMethod`, the p-value is computed using `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the provided configuration options and other appropriate settings. Otherwise, the p-value is computed as documented in the notes. Note that if method is an instance of `MonteCarloMethod`, the `rvs` attribute must be left unspecified; Monte Carlo samples are always drawn using the `rvs` method of `scipy.stats.random_table`.

      Added in version 1.15.0.

  Returns:
    res Chi2ContingencyResult

      An object containing attributes:

      statisticfloat

        The test statistic.

      pvaluefloat

        The p-value of the test.

      dofint

        The degrees of freedom. NaN if method is not `None`.

      expected_freqndarray, same shape as observed

        The expected frequencies, based on the marginal sums of the table.

  See also

  `scipy.stats.contingency.expected_freq`
  `scipy.stats.fisher_exact`
  `scipy.stats.chisquare`
  `scipy.stats.power_divergence`
  `scipy.stats.barnard_exact`
  `scipy.stats.boschloo_exact`
  Chi-square test of independence of variables in a contingency table

    Extended example

  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.

  References

  [1]

  “Contingency table”, https://en.wikipedia.org/wiki/Contingency_table

  [2]

  “Pearson’s chi-squared test”, https://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test

  [3]

  Cressie, N. and Read, T. R. C., “Multinomial Goodness-of-Fit Tests”, J. Royal Stat. Soc. Series B, Vol. 46, No. 3 (1984), pp. 440-464.

  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
      2.7777777777777777
      >>> res.pvalue
      0.24935220877729619
      >>> res.dof
      2
      >>> res.expected_freq
      array([[ 12.,  12.,  16.],
             [ 18.,  18.,  24.]])

  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
      2.7688587616781319
      >>> res.pvalue
      0.25046668010954165

  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
      8.7584514426741897
      >>> res.pvalue
      0.64417725029295503

  When the sum of the elements in a two-way table is small, the p-value produced by the default asymptotic approximation may be inaccurate. Consider passing a `PermutationMethod` or `MonteCarloMethod` as the method parameter with correction=False.

      >>> from scipy.stats import PermutationMethod
      >>> obs = np.asarray([[12, 3],
      ...                   [17, 16]])
      >>> res = chi2_contingency(obs, correction=False)
      >>> ref = chi2_contingency(obs, correction=False, method=PermutationMethod())
      >>> res.pvalue, ref.pvalue
      (0.0614122539870913, 0.1074)  # may vary

  For a more detailed example, see Chi-square test of independence of variables in a contingency table.