scipy.stats.kendalltau

scipy.stats.kendalltau(x, y, initial_lexsort=None, nan_policy='propagate', method='auto')

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, values close to -1 indicate strong disagreement. This is the 1945 “tau-b” version of Kendall’s tau [2], which can account for ties and which reduces to the 1938 “tau-a” version [1] in absence of ties.

Parameters

x, yarray_like

Arrays of rankings, of the same shape. If arrays are not 1-D, they will be flattened to 1-D.

initial_lexsortbool, optional

Unused (deprecated).

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

Returns

correlationfloat

The tau statistic.

pvaluefloat

The two-sided p-value for a hypothesis test whose null hypothesis is an absence of association, tau = 0.

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.

Notes

The definition of Kendall’s tau that is used is [2]:

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

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.

References

1

Maurice G. Kendall, “A New Measure of Rank Correlation”, Biometrika Vol. 30, No. 1/2, pp. 81-93, 1938.

2(1,2)

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]
>>> tau, p_value = stats.kendalltau(x1, x2)
>>> tau
-0.47140452079103173
>>> p_value
0.2827454599327748