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 tau-b version of Kendall’s tau which accounts for ties.
x, y : array_like
initial_lexsort : bool, optional
Kendall’s tau : float
p-value : float
The definition of Kendall’s tau that is used is:
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.
W.R. Knight, “A Computer Method for Calculating Kendall’s Tau with Ungrouped Data”, Journal of the American Statistical Association, Vol. 61, No. 314, Part 1, pp. 436-439, 1966.
>>> x1 = [12, 2, 1, 12, 2] >>> x2 = [1, 4, 7, 1, 0] >>> tau, p_value = sp.stats.kendalltau(x1, x2) >>> tau -0.47140452079103173 >>> p_value 0.24821309157521476