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Module « scipy.stats »

Fonction bartlett - module scipy.stats

Signature de la fonction bartlett

def bartlett(*samples, axis=0, nan_policy='propagate', keepdims=False) 

Description

help(scipy.stats.bartlett)

    


Perform Bartlett's test for equal variances.

Bartlett's test tests the null hypothesis that all input samples
are from populations with equal variances.  For samples
from significantly non-normal populations, Levene's test
`levene` is more robust.

Parameters
----------
sample1, sample2, ... : array_like
    arrays of sample data.  Only 1d arrays are accepted, they may have
    different lengths.
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 of the test.

See Also
--------

:func:`fligner`
    A non-parametric test for the equality of k variances
:func:`levene`
    A robust parametric test for equality of k variances
:ref:`hypothesis_bartlett`
    Extended example


Notes
-----
Conover et al. (1981) examine many of the existing parametric and
nonparametric tests by extensive simulations and they conclude that the
tests proposed by Fligner and Killeen (1976) and Levene (1960) appear to be
superior in terms of robustness of departures from normality and power
([3]_).

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/eda357.htm
.. [2]  Snedecor, George W. and Cochran, William G. (1989), Statistical
          Methods, Eighth Edition, Iowa State University Press.
.. [3] Park, C. and Lindsay, B. G. (1999). Robust Scale Estimation and
       Hypothesis Testing based on Quadratic Inference Function. Technical
       Report #99-03, Center for Likelihood Studies, Pennsylvania State
       University.
.. [4] Bartlett, M. S. (1937). Properties of Sufficiency and Statistical
       Tests. Proceedings of the Royal Society of London. Series A,
       Mathematical and Physical Sciences, Vol. 160, No.901, pp. 268-282.

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.bartlett(a, b, c)
>>> p
1.1254782518834628e-05

The very 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_bartlett`.

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