[R] about spearman and kendal correlation coefficient calculation in "cor"

[Baoqiang Cao]

Hi,

I have the following two measurements stored in mat:

> print(mat)
           [,1]     [,2]
 [1,] -14.80976 -265.786
 [2,] -14.92417  -54.724
 [3,] -13.92087  -58.912
 [4,]  -9.11503 -115.580
 [5,] -17.05970 -278.749
 [6,] -25.23313 -219.513
 [7,] -19.62465 -497.873
 [8,] -13.92087 -659.486
 [9,] -14.24629 -131.680
[10,] -20.81758 -604.961
[11,] -15.32194  -18.735

To calculate the ranking correlation, I used "cor":
> cor(mat[,1], mat[,2], method="spearman")
[1] 0.2551259
> cor(mat[,1], mat[,2], method="kendal")
[1] 0.1834940

However, when I tried to reproduce the two correlation coefficients by
following their "defination", I got different results than from "cor".
For Spearman, I got:
 
od1 = order(mat[,1], decreasing=T)
od2= order(mat[,2], decreasing=T)  
> 1-6*sum((od1-od2)^2)/(length(od1)^3-length(od1))
[1] -0.2909091

This is different with from "cor", which is 0.255.

For Kendal, I got:

accord=0
disaccord=0

experi=mat[,1]
target=mat[,2]
N= length(experi)
for(i in 1:(N-1)) {
   for(j in (i+1):N) {
      if((target[i] < target[j]) && (experi[i] < experi[j])) {
         accord=accord+1
      } else if ((target[i] > target[j]) && (experi[i] > experi[j])) {
         disaccord=disaccord+1
      }
   }
}

> (accord-disaccord)/(N*(N-1)/2)
[1] -0.2181818

This is also different with from "cor", which is 0.183.

Anybody could help me out explaining the right answer? Thanks in
advance!

Baoqiang