scipy.stats.chi2_contingency¶

scipy.stats.
chi2_contingency
(observed, correction=True, lambda_=None)[source]¶ Chisquare test of independence of variables in a contingency table.
This function computes the chisquare statistic and pvalue 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 twodimensional 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 chisquared statistic [2]. lambda_ allows a statistic from the CressieRead power divergence family [3] to be used instead. See
power_divergence
for details.
Returns:  chi2 : float
The test statistic.
 p : float
The pvalue of the test
 dof : int
Degrees of freedom
 expected : ndarray, same shape as observed
The expected frequencies, based on the marginal sums of the table.
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 onedimensional table will always result in expected equal to observed and a chisquare statistic equal to 0.
This function does not handle masked arrays, because the calculation does not make sense with missing values.
Like stats.chisquare, this function computes a chisquare 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 stats.chisquare. That is, if one calls:
chi2, p, dof, ex = chi2_contingency(obs, correction=False)
then the following is true:
(chi2, p) == 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] (1, 2) “Contingency table”, https://en.wikipedia.org/wiki/Contingency_table [2] (1, 2) “Pearson’s chisquared test”, https://en.wikipedia.org/wiki/Pearson%27s_chisquared_test [3] (1, 2) Cressie, N. and Read, T. R. C., “Multinomial GoodnessofFit Tests”, J. Royal Stat. Soc. Series B, Vol. 46, No. 3 (1984), pp. 440464. Examples
A twoway example (2 x 3):
>>> from scipy.stats import chi2_contingency >>> obs = np.array([[10, 10, 20], [20, 20, 20]]) >>> chi2_contingency(obs) (2.7777777777777777, 0.24935220877729619, 2, array([[ 12., 12., 16.], [ 18., 18., 24.]]))
Perform the test using the loglikelihood ratio (i.e. the “Gtest”) instead of Pearson’s chisquared statistic.
>>> g, p, dof, expctd = chi2_contingency(obs, lambda_="loglikelihood") >>> g, p (2.7688587616781319, 0.25046668010954165)
A fourway 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]]]]) >>> chi2_contingency(obs) (8.7584514426741897, 0.64417725029295503, 11, array([[[[ 14.15462386, 14.15462386], [ 16.49423111, 16.49423111]], [[ 11.2461395 , 11.2461395 ], [ 13.10500554, 13.10500554]]], [[[ 19.5591166 , 19.5591166 ], [ 22.79202844, 22.79202844]], [[ 15.54012004, 15.54012004], [ 18.10873492, 18.10873492]]]]))