
KENDALLS TAUName:
\( \frac{Y_j  Y_i}{X_j  X_i} \) < 0  pair is discordant \( \frac{Y_j  Y_i}{X_j  X_i} \) = 0  pair is considered a tie X_{i} = X_{j}  pair is not compared Kendall's tau is computed as
with N_{c} and N_{d} denoting the number of concordant pairs and the number of discordant pairs, respectively, in the sample. Ties add 0.5 to both the concordant and discordant counts. There are \( \left( \begin{array}{c} n \\ 2 \end{array} \right) \) possible pairs in the bivariate sample. Kendall's tau is an alternative to the Spearman's rho rank correlation. Kendall's tau or the rank correlation may be preferred to the standard correlation coefficient in the following cases:
<SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable; <y2> is the second response variable; <par> is a parameter where the computed Kendall's tau is stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.
LET A = KENDALLS TAU Y1 Y2 SUBSET TAG > 2
. Following data from page 320 of Conover, "Practical . Nonparametric Statistics", Third Edition, 1999, Wiley. LET Y1 = DATA 7 8 4 5.5 4.5 4 5 3 2 0.5 1 LET Y2 = DATA 4 2 5 0.5 1.5 2 0 1 0 1.5 0 LET A1 = KENDELLS TAU Y1 Y2 The computed value of Kendell's tau is 0.4355.  
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Date created: 12/22/2004 