Re: [R] R/S-Plus/SAS yield different results for Kendall-tau and Spearman nonparametric regression

From: Peter Dalgaard <>
Date: Mon 15 Aug 2005 - 13:18:20 EST

Dennis Fisher <> writes:

> Colleagues,
> I ran some nonparametric regressions in R (run in RedHat Linux), then
> a colleague repeated the analyses in SAS. When we obtained different
> results, I tested S-Plus (same Linux box). And, got yet different
> results. I replicated the results with a small dataset:
 (They came across somewhat garbled, but we'll believe you...)


> Each of the programs yields some differences, possibly because of how
> ties are handled (R warns about this). Can anyone enlighten me?

Ties are certainly involved in the Spearman case. There are more accurate expressions for the variance of the test statistic in the tied case, than the formula that R is using. As you see, the difference is not exactly huge (at least for a small number of ties), but it is something that we should get around to fixing.

I assume that there is a similar issue with Kendall's tau. In addition, S-PLUS appears to modify the actual definition of the test statistic, which might be a matter of taste. (K's tau relies on counting concordant and discordant pairs relative to the total number of pairs, and with ties, some pairs will be undecided. You can either discard such pairs or count them as zeros. S-PLUS appears to be doing the latter. A quick test is to notice that x <- y <- rep(0:1,4) gives a tau that is less than 1 in S-PLUS but gives 1 in R.)

   O__  ---- Peter Dalgaard             ุster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph:  (+45) 35327918
~~~~~~~~~~ - (                  FAX: (+45) 35327907

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Received on Mon Aug 15 13:30:47 2005

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