normaltest#
- scipy.stats.normaltest(a, axis=0, nan_policy='propagate', *, keepdims=False)[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 [1], [2] test that combines skew and kurtosis to produce an omnibus test of normality.
- Parameters:
- aarray_like
The array containing the sample to be tested. Must contain at least eight observations.
- axisint 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, 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 or array
s^2 + k^2
, wheres
is the z-score returned byskewtest
andk
is the z-score returned bykurtosistest
.- pvaluefloat or array
A 2-sided chi squared probability for the hypothesis test.
See also
- Normal test
Extended example
Notes
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
[1]D’Agostino, R. B. (1971), “An omnibus test of normality for moderate and large sample size”, Biometrika, 58, 341-348
[2]D’Agostino, R. and Pearson, E. S. (1973), “Tests for departure from normality”, Biometrika, 60, 613-622
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 53.619... # random >>> res.pvalue 2.273917413209226e-12 # random
For a more detailed example, see Normal test.