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Module « scipy.stats »

Fonction levene - module scipy.stats

Signature de la fonction levene

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

Description

help(scipy.stats.levene)

    


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'.
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.

See Also
--------

:func:`fligner`
    A non-parametric test for the equality of k variances
:func:`bartlett`
    A parametric test for equality of k variances in normal samples
:ref:`hypothesis_levene`
    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
----------
.. [1] https://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm
.. [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 :ref:`hypothesis_levene`.

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