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Module « scipy.stats »

Fonction ansari - module scipy.stats

Signature de la fonction ansari

def ansari(x, y, alternative='two-sided', *, axis=0, nan_policy='propagate', keepdims=False) 

Description

help(scipy.stats.ansari)

    


Perform the Ansari-Bradley test for equal scale parameters.

The Ansari-Bradley test ([1]_, [2]_) is a non-parametric test
for the equality of the scale parameter of the distributions
from which two samples were drawn. The null hypothesis states that
the ratio of the scale of the distribution underlying `x` to the scale
of the distribution underlying `y` is 1.

Parameters
----------
x, y : array_like
    Arrays of sample data.
alternative : {'two-sided', 'less', 'greater'}, optional
    Defines the alternative hypothesis. Default is 'two-sided'.
    The following options are available:
    
    * 'two-sided': the ratio of scales is not equal to 1.
    * 'less': the ratio of scales is less than 1.
    * 'greater': the ratio of scales is greater than 1.
    
    .. versionadded:: 1.7.0
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 Ansari-Bradley test statistic.
pvalue : float
    The p-value of the hypothesis test.

See Also
--------

:func:`fligner`
    A non-parametric test for the equality of k variances
:func:`mood`
    A non-parametric test for the equality of two scale parameters


Notes
-----
The p-value given is exact when the sample sizes are both less than
55 and there are no ties, otherwise a normal approximation for the
p-value is used.

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] Ansari, A. R. and Bradley, R. A. (1960) Rank-sum tests for
       dispersions, Annals of Mathematical Statistics, 31, 1174-1189.
.. [2] Sprent, Peter and N.C. Smeeton.  Applied nonparametric
       statistical methods.  3rd ed. Chapman and Hall/CRC. 2001.
       Section 5.8.2.
.. [3] Nathaniel E. Helwig "Nonparametric Dispersion and Equality
       Tests" at http://users.stat.umn.edu/~helwig/notes/npde-Notes.pdf

Examples
--------
>>> import numpy as np
>>> from scipy.stats import ansari
>>> rng = np.random.default_rng()

For these examples, we'll create three random data sets.  The first
two, with sizes 35 and 25, are drawn from a normal distribution with
mean 0 and standard deviation 2.  The third data set has size 25 and
is drawn from a normal distribution with standard deviation 1.25.

>>> x1 = rng.normal(loc=0, scale=2, size=35)
>>> x2 = rng.normal(loc=0, scale=2, size=25)
>>> x3 = rng.normal(loc=0, scale=1.25, size=25)

First we apply `ansari` to `x1` and `x2`.  These samples are drawn
from the same distribution, so we expect the Ansari-Bradley test
should not lead us to conclude that the scales of the distributions
are different.

>>> ansari(x1, x2)
AnsariResult(statistic=541.0, pvalue=0.9762532927399098)

With a p-value close to 1, we cannot conclude that there is a
significant difference in the scales (as expected).

Now apply the test to `x1` and `x3`:

>>> ansari(x1, x3)
AnsariResult(statistic=425.0, pvalue=0.0003087020407974518)

The probability of observing such an extreme value of the statistic
under the null hypothesis of equal scales is only 0.03087%. We take this
as evidence against the null hypothesis in favor of the alternative:
the scales of the distributions from which the samples were drawn
are not equal.

We can use the `alternative` parameter to perform a one-tailed test.
In the above example, the scale of `x1` is greater than `x3` and so
the ratio of scales of `x1` and `x3` is greater than 1. This means
that the p-value when ``alternative='greater'`` should be near 0 and
hence we should be able to reject the null hypothesis:

>>> ansari(x1, x3, alternative='greater')
AnsariResult(statistic=425.0, pvalue=0.0001543510203987259)

As we can see, the p-value is indeed quite low. Use of
``alternative='less'`` should thus yield a large p-value:

>>> ansari(x1, x3, alternative='less')
AnsariResult(statistic=425.0, pvalue=0.9998643258449039)

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