`scipy.stats._morestats:shapiro`

source: /scipy/stats/_morestats.py :2003

Signature

   def     shapiro (    x    ,  * ,     axis    =  None   ,    nan_policy    =  propagate   ,    keepdims    =  False     )

Summary

Perform the Shapiro-Wilk test for normality.

Extended Summary

The Shapiro-Wilk test tests the null hypothesis that the data was drawn from a normal distribution.

Parameters

x : array_like

Array of sample data. Must contain at least three observations.

axis : int or None, default: None

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: The test statistic.
p-value : float: The p-value for the hypothesis test.

Notes

The algorithm used is described in ^[4] but censoring parameters as described are not implemented. For N > 5000 the W test statistic is accurate, but the p-value may not be.

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

shapiro 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()
x = stats.norm.rvs(loc=5, scale=3, size=100, random_state=rng)
shapiro_test = stats.shapiro(x)

✓

shapiro_test
shapiro_test.statistic
shapiro_test.pvalue

✗

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

Aliases

scipy.stats.shapiro