V
Viki2010
Member
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
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V
Viki2010
Member
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(+,+).
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(+,+).
S
Shillington
Member
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
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.
V
Viki2010
Member
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....
V
Viki2010
Member
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.
Simon James
Senior Member
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(+,+).
The pairs you are quoting are t=4 vs t=3 hence the bottom right cell in the table which is indeed D(-,+)?
Simon James
Senior Member
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
A concordant pair is one where the pairs are in the same order relative to each other, so if we consider the ranks:
X Y
1 4
2 6
Then for X: 1-2=-1 and for Y: 4-6=-2 so we have (-,-) and a concordant pair
If we have:
X Y
3 4
2 6
Then for X: 3-2=+1 and for Y: 4-6=-2 so we have (+,-) and a discordant pair.
V
Viki2010
Member
A concordant pair is one where the pairs are in the same order relative to each other, so if we consider the ranks:
X Y
1 4
2 6
Then for X: 1-2=-1 and for Y: 4-6=-2 so we have (-,-) and a concordant pair
If we have:
X Y
3 4
2 6
Then for X: 3-2=+1 and for Y: 4-6=-2 so we have (+,-) and a discordant pair.
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?
Simon James
Senior Member
It would be fine to sort first (as this simplifies the process somewhat!)
I hope I dealt with that one in an earlier post? Let me know if you still disagree.
(p132) He is using the same method.
eg t=3 vs t=2
t X Y
2 95 25
3 15 10
15-95 = neg
10-25 = neg
hence C(-,-)
eg t=4 vs t=1
t X Y
1 10 20
4 35 15
35-10 = pos
15-20 = neg
hence D(+,-)
This example is very simple. I just don't agree with the ActEd calculation in ActEd notes.
I hope I dealt with that one in an earlier post? Let me know if you still disagree.
With the example in sweeting, I don't know how he is getting his C and D.
(p132) He is using the same method.
eg t=3 vs t=2
t X Y
2 95 25
3 15 10
15-95 = neg
10-25 = neg
hence C(-,-)
eg t=4 vs t=1
t X Y
1 10 20
4 35 15
35-10 = pos
15-20 = neg
hence D(+,-)
V
Viki2010
Member
It would be fine to sort first (as this simplifies the process somewhat!)
I hope I dealt with that one in an earlier post? Let me know if you still disagree.
(p132) He is using the same method.
eg t=3 vs t=2
t X Y
2 95 25
3 15 10
15-95 = neg
10-25 = neg
hence C(-,-)
eg t=4 vs t=1
t X Y
1 10 20
4 35 15
35-10 = pos
15-20 = neg
hence D(+,-)
Thank you. This is clear now. I was doing my calc. differently at first.