scipy.stats.chisquare¶

scipy.stats.
chisquare
(f_obs, f_exp=None, ddof=0, axis=0)[source]¶ Calculate a oneway chi square test.
The chi square test tests the null hypothesis that the categorical data has the given frequencies.
Parameters:  f_obs : array_like
Observed frequencies in each category.
 f_exp : array_like, optional
Expected frequencies in each category. By default the categories are assumed to be equally likely.
 ddof : int, optional
“Delta degrees of freedom”: adjustment to the degrees of freedom for the pvalue. The pvalue is computed using a chisquared distribution with
k  1  ddof
degrees of freedom, where k is the number of observed frequencies. The default value of ddof is 0. axis : int or None, optional
The axis of the broadcast result of f_obs and f_exp along which to apply the test. If axis is None, all values in f_obs are treated as a single data set. Default is 0.
Returns:  chisq : float or ndarray
The chisquared test statistic. The value is a float if axis is None or f_obs and f_exp are 1D.
 p : float or ndarray
The pvalue of the test. The value is a float if ddof and the return value chisq are scalars.
See also
Notes
This test is invalid when the observed or expected frequencies in each category are too small. A typical rule is that all of the observed and expected frequencies should be at least 5.
The default degrees of freedom, k1, are for the case when no parameters of the distribution are estimated. If p parameters are estimated by efficient maximum likelihood then the correct degrees of freedom are k1p. If the parameters are estimated in a different way, then the dof can be between k1p and k1. However, it is also possible that the asymptotic distribution is not a chisquare, in which case this test is not appropriate.
References
[1] Lowry, Richard. “Concepts and Applications of Inferential Statistics”. Chapter 8. https://web.archive.org/web/20171022032306/http://vassarstats.net:80/textbook/ch8pt1.html [2] “Chisquared test”, https://en.wikipedia.org/wiki/Chisquared_test Examples
When just f_obs is given, it is assumed that the expected frequencies are uniform and given by the mean of the observed frequencies.
>>> from scipy.stats import chisquare >>> chisquare([16, 18, 16, 14, 12, 12]) (2.0, 0.84914503608460956)
With f_exp the expected frequencies can be given.
>>> chisquare([16, 18, 16, 14, 12, 12], f_exp=[16, 16, 16, 16, 16, 8]) (3.5, 0.62338762774958223)
When f_obs is 2D, by default the test is applied to each column.
>>> obs = np.array([[16, 18, 16, 14, 12, 12], [32, 24, 16, 28, 20, 24]]).T >>> obs.shape (6, 2) >>> chisquare(obs) (array([ 2. , 6.66666667]), array([ 0.84914504, 0.24663415]))
By setting
axis=None
, the test is applied to all data in the array, which is equivalent to applying the test to the flattened array.>>> chisquare(obs, axis=None) (23.31034482758621, 0.015975692534127565) >>> chisquare(obs.ravel()) (23.31034482758621, 0.015975692534127565)
ddof is the change to make to the default degrees of freedom.
>>> chisquare([16, 18, 16, 14, 12, 12], ddof=1) (2.0, 0.73575888234288467)
The calculation of the pvalues is done by broadcasting the chisquared statistic with ddof.
>>> chisquare([16, 18, 16, 14, 12, 12], ddof=[0,1,2]) (2.0, array([ 0.84914504, 0.73575888, 0.5724067 ]))
f_obs and f_exp are also broadcast. In the following, f_obs has shape (6,) and f_exp has shape (2, 6), so the result of broadcasting f_obs and f_exp has shape (2, 6). To compute the desired chisquared statistics, we use
axis=1
:>>> chisquare([16, 18, 16, 14, 12, 12], ... f_exp=[[16, 16, 16, 16, 16, 8], [8, 20, 20, 16, 12, 12]], ... axis=1) (array([ 3.5 , 9.25]), array([ 0.62338763, 0.09949846]))