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Module « scipy.stats »

Fonction mood - module scipy.stats

Signature de la fonction mood

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

Description

help(scipy.stats.mood)

    


Perform Mood's test for equal scale parameters.

Mood's two-sample test for scale parameters is a non-parametric
test for the null hypothesis that two samples are drawn from the
same distribution with the same scale parameter.

Parameters
----------
x, y : array_like
    Arrays of sample data. There must be at least three observations
    total.
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.
alternative : {'two-sided', 'less', 'greater'}, optional
    Defines the alternative hypothesis. Default is 'two-sided'.
    The following options are available:
    
    * 'two-sided': the scales of the distributions underlying `x` and `y`
      are different.
    * 'less': the scale of the distribution underlying `x` is less than
      the scale of the distribution underlying `y`.
    * 'greater': the scale of the distribution underlying `x` is greater
      than the scale of the distribution underlying `y`.
    
    .. versionadded:: 1.7.0
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
-------
res : SignificanceResult
    An object containing attributes:
    
    statistic : scalar or ndarray
        The z-score for the hypothesis test.  For 1-D inputs a scalar is
        returned.
    pvalue : scalar ndarray
        The p-value for the hypothesis test.

See Also
--------

:func:`fligner`
    A non-parametric test for the equality of k variances
:func:`ansari`
    A non-parametric test for the equality of 2 variances
:func:`bartlett`
    A parametric test for equality of k variances in normal samples
:func:`levene`
    A parametric test for equality of k variances


Notes
-----
The data are assumed to be drawn from probability distributions ``f(x)``
and ``f(x/s) / s`` respectively, for some probability density function f.
The null hypothesis is that ``s == 1``.

For multi-dimensional arrays, if the inputs are of shapes
``(n0, n1, n2, n3)``  and ``(n0, m1, n2, n3)``, then if ``axis=1``, the
resulting z and p values will have shape ``(n0, n2, n3)``.  Note that
``n1`` and ``m1`` don't have to be equal, but the other dimensions do.

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] Mielke, Paul W. "Note on Some Squared Rank Tests with Existing Ties."
    Technometrics, vol. 9, no. 2, 1967, pp. 312-14. JSTOR,
    https://doi.org/10.2307/1266427. Accessed 18 May 2022.

Examples
--------
>>> import numpy as np
>>> from scipy import stats
>>> rng = np.random.default_rng()
>>> x2 = rng.standard_normal((2, 45, 6, 7))
>>> x1 = rng.standard_normal((2, 30, 6, 7))
>>> res = stats.mood(x1, x2, axis=1)
>>> res.pvalue.shape
(2, 6, 7)

Find the number of points where the difference in scale is not significant:

>>> (res.pvalue > 0.1).sum()
78

Perform the test with different scales:

>>> x1 = rng.standard_normal((2, 30))
>>> x2 = rng.standard_normal((2, 35)) * 10.0
>>> stats.mood(x1, x2, axis=1)
SignificanceResult(statistic=array([-5.76174136, -6.12650783]),
                   pvalue=array([8.32505043e-09, 8.98287869e-10]))

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