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 taub version of Kendall’s tau which accounts for ties.
Parameters :  x, y : array_like
initial_lexsort : bool, optional


Returns :  Kendall’s tau : float
pvalue : float

Notes
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.
References
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. 436439, 1966.
Examples
>>> 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