Help on function chi2_contingency in module scipy.stats.contingency:
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`.
.. versionadded:: 1.15.0
Returns
-------
res : Chi2ContingencyResult
An object containing attributes:
statistic : float
The test statistic.
pvalue : float
The p-value of the test.
dof : int
The degrees of freedom. NaN if `method` is not ``None``.
expected_freq : ndarray, 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
:ref:`hypothesis_chi2_contingency` : 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 :ref:`hypothesis_chi2_contingency`.
None