.. _docs-meteoinfolab-numeric-stats-kendalltau: ********** kendalltau ********** .. currentmodule:: numeric.stats .. function:: kendalltau(x, y) 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 [2]_, which can account for ties and which reduces to the 1938 "tau-a" version [1]_ in absence of ties. :param x: (*array_like*) x data array. :param y: (*array_like*) y data array. :returns: Correlation. 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] 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. Examples:: from mipylib.numeric import stats x1 = [12, 2, 1, 12, 2] x2 = [1, 4, 7, 1, 0] tau = stats.kendalltau(x1, x2) print tau Result:: >>> run script... -0.471404520791