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Re: st: Difference in correlation coefficients
At 09:03 17/07/02 +0100, Winston Banya wrote:
I don't know about the difference between 2 Pearson correlations. However,
you can do this with Kendall's tau-a correlations using my -somersd-
package, downloadable from SSC. Type -ssc describe somersd- inside
Web-aware Stata for a description.
I have used the pwcorr command to get correlation coefficients and I am
interested in finding the difference in the coefficients and the
significance of the difference.
For example if I have 3 variables y1 y2 and x2 and then I do
pwcorr y1 x2 to get r1 and pwcorr y1/y2 x2 to get r2. If there is an
improvement in r as a result of using y1/y2 then how to account for the
improvement together with its significance. Is there anyway way I can do so
In this case, you might type
somersd x2 y1 yratio,taua tdist
The first command generates the ratio in -yratio-, the second command
calculates the Kendall tau-as between -x2- and -y1- and between -x2- and
-yratio-, and the third command calculates a confidence interval for
(tau(x2,y1)-tau(x2,yratio))/2. If -x2-, -y1- and -yratio- are continuous,
and you sample 2 trivariate data points (x2,y1,y2) independently from the
same trivariate distribution, then (tau(x2,y1)-tau(x2,yratio))/2 is the
difference between 2 probabilities, namely the probability that the
x2-values are concordant with the y1-values and discordant with the
yratio-values and the probability that the x2-values are concordant with
the yratio-values and discordant with the y1-values. We expect the
difference to be positive if -y1- is the better predictor, and negative if
-yratio- is the better predictor. No linearity assumption is required.
Kendall's tau-a values, and differences between them, are discussed in
Newson (2002) and in references found there.
I hope this helps.
Newson R. Parameters behind "nonparametric" statistics: Kendall's tau,
Somers' D and median differences. The Stata Journal 2002; 2(1): 45-64.
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
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Opinions expressed are those of the author, not the institution.
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