Kendall's Tau

Can someone explain to me how to calculate the discordant and condordant pairs? I don't know how the C(++) or D(-+) etc are really derived. Sweeting doesn't show it. page 132

 

Don't you guys think there is an error in ActEd notes on the empirical calculation of C and D? page 15 of chapter 11.

Example is ok until I get to the calculation of

(64 - 72) - this gives me a negative sign (-)
(85 - 45) - this gives me a positve sign (+)

so the answer should be D(-,+) instead of C(+,+).

 

Let X and Y be random variables.

Then for a sample x, y of X and Y the paid are concordant is

x-E(X) >=0 and y-E(Y)>=0 or x-E(X) <=0 and y-E(Y)<=0

and discordant otherwise.

 

Thanks, I understand the definition, but can you refer to my example in the post? I think the ActEd contains an error....

 

Actually, it would be helpful if someone could show a numerical example, as I can't work it out from Sweeting page 132.

 

This example is very simple. I just don't agree with the ActEd calculation in ActEd notes.

With the example in sweeting, I don't know how he is getting his C and D.

But I googled another method of calculation where

Kendall's Tau = (C-D)/(C+D) and the calculation is by re-ranking one variable in ascending or descending order. AcdEd excercises also show this method.

Is that acceptable for an exam?

 

Thank you. This is clear now. I was doing my calc. differently at first.