Measures of association in R — Kendall's tau-b and tau-c

Question

Are there any R packages for the calculation of Kendall\'s tau-b and tau-c, and their associated standard errors? My searches on Google and Rseek have turned up nothing, but su

Answer 1

I have been doing a bit research on Kendall's tau. Directly using cor(x, y, method="kendall") will give you Kendall's tau-b, which is a little different from the original definition, i.e., Kendall's tau-a. Kendall's tau-b is more commonly used as it takes into account ties, hence, most available software packages (e.g. cor(), Kendall()) all calculate Kendall's tau-b.

The difference between Kendall's tau-a and tau-b is essentially the denominator. Specifically, for Kendall's tau-a, the denominator D=n*(n-1)/2, which is fixed, while for Kendall's tau-b, the denominator D=sqrt(No. pairs of Var1 excluding tied pairs)*sqrt(No. pairs of Var2 excluding tied pairs). The value of tua-b is usually larger than tau-a.

As a simple example, consider X=(1,2,3,4,4), Y=(2,3,4,4,4). Kendall's tau-b=0.88, while tau-a=0.7.

For Kendall's tau-c, I didn't see too much on it, so no comments.