scipy.stats.

levene#

scipy.stats.levene(*samples, center='median', proportiontocut=0.05, axis=0, nan_policy='propagate', keepdims=False)[source]#

Perform Levene test for equal variances.

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. Only one-dimensional samples are accepted.

center{‘mean’, ‘median’, ‘trimmed’}, optional

Which function of the data to use in the test. The default is ‘median’.

proportiontocutfloat, 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.

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, a ValueError 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.

pvaluefloat

The p-value for the test.

See also

fligner

A non-parametric test for the equality of k variances

bartlett

A parametric test for equality of k variances in normal samples

Levene test for equal variances

Extended example

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.

References

[2]

Levene, H. (1960). In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling, I. Olkin et al. eds., Stanford University Press, pp. 278-292.

[3]

Brown, M. B. and Forsythe, A. B. (1974), Journal of the American Statistical Association, 69, 364-367

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)
>>> p
0.002431505967249681

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]]
[0.007054444444444413, 0.13073888888888888, 0.008890000000000002]

For a more detailed example, see Levene test for equal variances.

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