Chi-square test for normality python

Test whether a sample differs from a normal distribution.

This function tests the null hypothesis that a sample comes from a normal distribution. It is based on D’Agostino and Pearson’s [1], [2] test that combines skew and kurtosis to produce an omnibus test of normality.

The array containing the sample to be tested.

Axis along which to compute test. Default is 0. If None, compute over the whole array a.

Defines how to handle when input contains nan. The following options are available [default is ‘propagate’]:

• ‘propagate’: returns nan

• ‘raise’: throws an error

• ‘omit’: performs the calculations ignoring nan values

s^2 + k^2, where s is the z-score returned by skewtest and k is the z-score returned by kurtosistest.

A 2-sided chi squared probability for the hypothesis test.

References

D’Agostino, R. B. [1971], “An omnibus test of normality for moderate and large sample size”, Biometrika, 58, 341-348

D’Agostino, R. and Pearson, E. S. [1973], “Tests for departure from normality”, Biometrika, 60, 613-622

Examples

>>> from scipy import stats
>>> rng = np.random.default_rng[]
>>> pts = 1000
>>> a = rng.normal[0, 1, size=pts]
>>> b = rng.normal[2, 1, size=pts]
>>> x = np.concatenate[[a, b]]
>>> k2, p = stats.normaltest[x]
>>> alpha = 1e-3
>>> print["p = {:g}".format[p]]
p = 8.4713e-19
>>> if p >> 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 2-D, 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 p-values is done by broadcasting the chi-squared 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 chi-squared 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]]]