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kendalltau

numeric.stats.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.

Parameters:
  • x – (array_like) x data array.
  • y – (array_like) y data array.
Returns:

Correlation.

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.

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