shapiro#
- scipy.stats.shapiro(x, *, axis=None, nan_policy='propagate', keepdims=False)[source]#
Perform the Shapiro-Wilk test for normality.
The Shapiro-Wilk test tests the null hypothesis that the data was drawn from a normal distribution.
- Parameters:
- xarray_like
Array of sample data. Must contain at least three observations.
- axisint 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, aValueError
will be raised.
- keepdimsbool, 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:
- statisticfloat
The test statistic.
- p-valuefloat
The p-value for the hypothesis test.
See also
anderson
The Anderson-Darling test for normality
kstest
The Kolmogorov-Smirnov test for goodness of fit.
- Shapiro-Wilk test for normality
Extended example
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 tonp.ndarray
before the calculation is performed. In this case, the output will be a scalar ornp.ndarray
of appropriate shape rather than a 2Dnp.matrix
. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar ornp.ndarray
rather than a masked array withmask=False
.References
[2]Shapiro, S. S. & Wilk, M.B, “An analysis of variance test for normality (complete samples)”, Biometrika, 1965, Vol. 52, pp. 591-611, DOI:10.2307/2333709
[3]Razali, N. M. & Wah, Y. B., “Power comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling tests”, Journal of Statistical Modeling and Analytics, 2011, Vol. 2, pp. 21-33.
[4]Royston P., “Remark AS R94: A Remark on Algorithm AS 181: The W-test for Normality”, 1995, Applied Statistics, Vol. 44, DOI:10.2307/2986146
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 ShapiroResult(statistic=0.9813305735588074, pvalue=0.16855233907699585) >>> shapiro_test.statistic 0.9813305735588074 >>> shapiro_test.pvalue 0.16855233907699585
For a more detailed example, see Shapiro-Wilk test for normality.