scipy.stats.kendalltau(x, y, initial_lexsort=None, nan_policy='propagate')[source]

Calculates 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 [R559], which can account for ties and which reduces to the 1938 “tau-a” version [R558] in absence of ties.


x, y : array_like

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

initial_lexsort : bool, optional

Unused (deprecated).

nan_policy : {‘propagate’, ‘raise’, ‘omit’}, optional

Defines how to handle when input contains nan. ‘propagate’ returns nan, ‘raise’ throws an error, ‘omit’ performs the calculations ignoring nan values. Default is ‘propagate’. Note that if the input contains nan ‘omit’ delegates to mstats_basic.kendalltau(), which has a different implementation.


correlation : float

The tau statistic.

pvalue : float

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

See also

Calculates a Spearman rank-order correlation coefficient.
Computes the Theil-Sen estimator for a set of points (x, y).


The definition of Kendall’s tau that is used is [R559]:

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.


[R558](1, 2) Maurice G. Kendall, “A New Measure of Rank Correlation”, Biometrika Vol. 30, No. 1/2, pp. 81-93, 1938.
[R559](1, 2, 3) Maurice G. Kendall, “The treatment of ties in ranking problems”, Biometrika Vol. 33, No. 3, pp. 239-251. 1945.
[R560]Gottfried E. Noether, “Elements of Nonparametric Statistics”, John Wiley & Sons, 1967.
[R561]Peter M. Fenwick, “A new data structure for cumulative frequency tables”, Software: Practice and Experience, Vol. 24, No. 3, pp. 327-336, 1994.


>>> from scipy import stats
>>> x1 = [12, 2, 1, 12, 2]
>>> x2 = [1, 4, 7, 1, 0]
>>> tau, p_value = stats.kendalltau(x1, x2)
>>> tau
>>> p_value