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 :ref:`hypothesis_chi2_contingency`. r