[R] Bug in Kendall for n<4?

[Martin Maechler]

>>>>> "SM" == Stavros Macrakis <macrakis at alum.mit.edu>
>>>>>     on Fri, 21 Nov 2008 14:44:37 -0500 writes:

    >> library(Kendall) Kendall(1:3,1:3)
    SM> WARNING: Error exit, tauk2. IFAULT = 12 <<<<<< tau = 1,
    SM> 2-sided pvalue =1

    SM> I believe Kendall tau is well-defined for this case and
    SM> the reported value is correct; isn't it a bug to give a
    SM> warning?  (And if, e.g., the pvalue is not well-defined
    SM> in this case, wouldn't it be better to return NA or NaN
    SM> or something?) Also, shouldn't the error code be given
    SM> in plain English -- or at least the meaning of "IFAULT =
    SM> 12" documented on the help page?

The real question is  *WHY* there needs to be a separate package
'Kendall'  when R itself does everything you want and does not
show any problems ?

     cor()
     cov()
     cor.test()

all have a method = "kendall"  and seem to work alright,
even for  n=2

  > cor(1:3, c(3,1,2), method="kendall")
  [1] -0.3333333
  > cov(1:3, c(3,1,2), method="kendall")
  [1] -2
  > cor(1:3, 1:3, method="kendall")
  [1] 1
  > cor.test(1:3, 1:3, method="kendall")

	  Kendall's rank correlation tau

  data:  1:3 and 1:3 
  T = 3, p-value = 0.3333
  alternative hypothesis: true tau is not equal to 0 
  sample estimates:
  tau 
    1 


Questions about the 'Kendall' package should typically first go
to its author ...
But those on  cor(), cor.test() etc do belong here.

Best regards,
Martin Maechler, ETH Zurich


    SM> A somewhat less clear case is Kendall(1:2,1:2), which
    SM> gives the same error.  Though the usual formula for
    SM> Kendall tau has a zero in the denominator in this case,
    SM> I'd think the correct generalization is 1 if the two
    SM> elements are in the same order, and -1 if they are not
    SM> (the only possibilities). But perhaps I don't fully
    SM> understand the interpretation of this statistic.

    SM>           -s

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