SciPy

scipy.stats.normaltest

scipy.stats.normaltest(a, axis=0, nan_policy='propagate')[source]

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 [R655], [R656] test that combines skew and kurtosis to produce an omnibus test of normality.

Parameters:

a : array_like

The array containing the sample to be tested.

axis : int or None, optional

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

nan_policy : {‘propagate’, ‘raise’, ‘omit’}, optional

Defines how to handle when input contains nan. ‘propagate’ returns nan, ‘raise’ throws an error, ‘omit’ performs the calculations ignoring nan values. Default is ‘propagate’.

Returns:

statistic : float or array

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

pvalue : float or array

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

References

[R655](1, 2) D’Agostino, R. B. (1971), “An omnibus test of normality for moderate and large sample size”, Biometrika, 58, 341-348
[R656](1, 2) D’Agostino, R. and Pearson, E. S. (1973), “Tests for departure from normality”, Biometrika, 60, 613-622

Examples

>>> from scipy import stats
>>> pts = 1000
>>> np.random.seed(28041990)
>>> a = np.random.normal(0, 1, size=pts)
>>> b = np.random.normal(2, 1, size=pts)
>>> x = np.concatenate((a, b))
>>> k2, p = stats.normaltest(x)
>>> alpha = 1e-3
>>> print("p = {:g}".format(p))
p = 3.27207e-11
>>> if p < alpha:  # null hypothesis: x comes from a normal distribution
...     print("The null hypothesis can be rejected")
... else:
...     print("The null hypothesis cannot be rejected")
The null hypothesis can be rejected

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