Kendall tau

src.meliora.core.kendall_tau(x, y, variant='b')[source]

Calculate Kendall’s tau, a correlation measure for ordinal data. This is a wrapper around SciPy kendalltau function. 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. :param x: Arrays of rankings, of the same shape. If arrays are not 1-D, they

will be flattened to 1-D.

Parameters

y (array_like) – Arrays of rankings, of the same shape. If arrays are not 1-D, they will be flattened to 1-D.
variant ({'b', 'c'}, optional) – Defines which variant of Kendall’s tau is returned. Default is ‘b’.

Returns

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

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.

Scipy: https://github.com/scipy/scipy/blob/v1.8.1/scipy/stats/_stats_py.py#L4666-L4875

Examples

>>> from scipy import stats
>>> x1 = [12, 2, 1, 12, 2]
>>> x2 = [1, 4, 7, 1, 0]
>>> tau, p_value = kendall_tau(x1, x2)
>>> tau
-0.47140452079103173
>>> p_value
0.2827454599327748