`scipy.stats._stats_py:normaltest`

source: /scipy/stats/_stats_py.py :1811

Signature

   def     normaltest (    a    ,    axis    =  0   ,    nan_policy    =  propagate   ,  * ,     keepdims    =  False     )

Summary

Test whether a sample differs from a normal distribution.

Extended Summary

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.

Parameters

a : array_like

The array containing the sample to be tested. Must contain at least eight observations.

axis : int or None, default: 0

If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If None, the input will be raveled before computing the statistic.

nan_policy : {'propagate', 'omit', 'raise'}

Defines how to handle input NaNs.

propagate: if a NaN is present in the axis slice (e.g. row) along which the statistic is computed, the corresponding entry of the output will be NaN.
omit: NaNs will be omitted when performing the calculation. If insufficient data remains in the axis slice along which the statistic is computed, the corresponding entry of the output will be NaN.
raise: if a NaN is present, a ValueError will be raised.

keepdims : bool, default: False

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.

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.

Notes

Beginning in SciPy 1.9, np.matrix inputs (not recommended for new code) are converted to np.ndarray before the calculation is performed. In this case, the output will be a scalar or np.ndarray of appropriate shape rather than a 2D np.matrix. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or np.ndarray rather than a masked array with mask=False.

Array API Standard Support

normaltest has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ✅                   
JAX                   ✅                     ✅                   
Dask                  ✅                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

import numpy as np
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))
res = stats.normaltest(x)

✓

res.statistic
res.pvalue

✗

For a more detailed example, see :ref:`hypothesis_normaltest`.

Aliases

scipy.stats.normaltest