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Module « scipy.stats »

Fonction kendalltau - module scipy.stats

Signature de la fonction kendalltau

def kendalltau(x, y, *, nan_policy='propagate', method='auto', variant='b', alternative='two-sided') 

Description

help(scipy.stats.kendalltau)

Calculate Kendall's tau, a correlation measure for ordinal data.

Kendall's tau is a measure of the correspondence between two rankings.
Values close to 1 indicate strong agreement, and values close to -1
indicate strong disagreement. This implements two variants of Kendall's
tau: tau-b (the default) and tau-c (also known as Stuart's tau-c). These
differ only in how they are normalized to lie within the range -1 to 1;
the hypothesis tests (their p-values) are identical. Kendall's original
tau-a is not implemented separately because both tau-b and tau-c reduce
to tau-a in the absence of ties.

Parameters
----------
x, y : array_like
    Arrays of rankings, of the same shape. If arrays are not 1-D, they
    will be flattened to 1-D.
nan_policy : {'propagate', 'raise', 'omit'}, optional
    Defines how to handle when input contains nan.
    The following options are available (default is 'propagate'):

    * 'propagate': returns nan
    * 'raise': throws an error
    * 'omit': performs the calculations ignoring nan values

method : {'auto', 'asymptotic', 'exact'}, optional
    Defines which method is used to calculate the p-value [5]_.
    The following options are available (default is 'auto'):

    * 'auto': selects the appropriate method based on a trade-off
      between speed and accuracy
    * 'asymptotic': uses a normal approximation valid for large samples
    * 'exact': computes the exact p-value, but can only be used if no ties
      are present. As the sample size increases, the 'exact' computation
      time may grow and the result may lose some precision.

variant : {'b', 'c'}, optional
    Defines which variant of Kendall's tau is returned. Default is 'b'.
alternative : {'two-sided', 'less', 'greater'}, optional
    Defines the alternative hypothesis. Default is 'two-sided'.
    The following options are available:

    * 'two-sided': the rank correlation is nonzero
    * 'less': the rank correlation is negative (less than zero)
    * 'greater': the rank correlation is positive (greater than zero)

Returns
-------
res : SignificanceResult
    An object containing attributes:

    statistic : float
       The tau statistic.
    pvalue : float
       The p-value for a hypothesis test whose null hypothesis is
       an absence of association, tau = 0.

Raises
------
ValueError
    If `nan_policy` is 'omit' and `variant` is not 'b' or
    if `method` is 'exact' and there are ties between `x` and `y`.

See Also
--------
spearmanr : Calculates a Spearman rank-order correlation coefficient.
theilslopes : Computes the Theil-Sen estimator for a set of points (x, y).
weightedtau : Computes a weighted version of Kendall's tau.
:ref:`hypothesis_kendalltau` : Extended example

Notes
-----
The definition of Kendall's tau that is used is [2]_::

  tau_b = (P - Q) / sqrt((P + Q + T) * (P + Q + U))

  tau_c = 2 (P - Q) / (n**2 * (m - 1) / m)

where P is the number of concordant pairs, Q the number of discordant
pairs, T the number of ties only in `x`, and U the number of ties only in
`y`.  If a tie occurs for the same pair in both `x` and `y`, it is not
added to either T or U. n is the total number of samples, and m is the
number of unique values in either `x` or `y`, whichever is smaller.

References
----------
.. [1] Maurice G. Kendall, "A New Measure of Rank Correlation", Biometrika
       Vol. 30, No. 1/2, pp. 81-93, 1938.
.. [2] Maurice G. Kendall, "The treatment of ties in ranking problems",
       Biometrika Vol. 33, No. 3, pp. 239-251. 1945.
.. [3] Gottfried E. Noether, "Elements of Nonparametric Statistics", John
       Wiley & Sons, 1967.
.. [4] Peter M. Fenwick, "A new data structure for cumulative frequency
       tables", Software: Practice and Experience, Vol. 24, No. 3,
       pp. 327-336, 1994.
.. [5] Maurice G. Kendall, "Rank Correlation Methods" (4th Edition),
       Charles Griffin & Co., 1970.

Examples
--------

>>> from scipy import stats
>>> x1 = [12, 2, 1, 12, 2]
>>> x2 = [1, 4, 7, 1, 0]
>>> res = stats.kendalltau(x1, x2)
>>> res.statistic
-0.47140452079103173
>>> res.pvalue
0.2827454599327748

For a more detailed example, see :ref:`hypothesis_kendalltau`.

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