`scipy.stats._morestats:levene`

source: /scipy/stats/_morestats.py :3191

Signature

   def     levene (  *  samples    ,    center    =  median   ,    proportiontocut    =  0.05   ,    axis    =  0   ,    nan_policy    =  propagate   ,    keepdims    =  False     )

Summary

Perform Levene test for equal variances.

Extended Summary

The Levene test tests the null hypothesis that all input samples are from populations with equal variances. Levene's test is an alternative to Bartlett's test bartlett in the case where there are significant deviations from normality.

Parameters

sample1, sample2, ... : array_like

The sample data, possibly with different lengths.

center : {'mean', 'median', 'trimmed'}, optional

Which statistics to use to center data points within each sample. Default is 'median'.

proportiontocut : float, optional

When center is 'trimmed', this gives the proportion of data points to cut from each end. (See scipy.stats.trim_mean.) Default is 0.05.

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

Notes

Three variations of Levene's test are possible. The possibilities and their recommended usages are:

'median'Recommended for skewed (non-normal) distributions>
'mean'Recommended for symmetric, moderate-tailed distributions.
'trimmed'Recommended for heavy-tailed distributions.

The test version using the mean was proposed in the original article of Levene (^[2]) while the median and trimmed mean have been studied by Brown and Forsythe (^[3]), sometimes also referred to as Brown-Forsythe test.

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

levene 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

Test whether the lists `a`, `b` and `c` come from populations with equal variances.

import numpy as np
from scipy import stats
a = [8.88, 9.12, 9.04, 8.98, 9.00, 9.08, 9.01, 8.85, 9.06, 8.99]
b = [8.88, 8.95, 9.29, 9.44, 9.15, 9.58, 8.36, 9.18, 8.67, 9.05]
c = [8.95, 9.12, 8.95, 8.85, 9.03, 8.84, 9.07, 8.98, 8.86, 8.98]
stat, p = stats.levene(a, b, c)

✓

✗

The small p-value suggests that the populations do not have equal variances. This is not surprising, given that the sample variance of `b` is much larger than that of `a` and `c`:

[np.var(x, ddof=1) for x in [a, b, c]]

✗

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

Aliases

scipy.stats.levene