Re: st: Difference in correlation coefficients

[Roger Newson <roger.newson@kcl.ac.uk>]

At 09:03 17/07/02 +0100, Winston Banya wrote:
> Dear All,
>
> 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
> using STATA?
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.

In this case, you might type

gene yratio=y1/y2
somersd x2 y1 yratio,taua tdist
lincom (y1-yratio)/2

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.

Best wishes

Roger

References

Newson R. Parameters behind "nonparametric" statistics: Kendall's tau, 
Somers' D and median differences. The Stata Journal 2002; 2(1): 45-64.


--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
Fax: 020 7848 6620 International +44 20 7848 6620
  or 020 7848 6605 International +44 20 7848 6605
Email: roger.newson@kcl.ac.uk

Opinions expressed are those of the author, not the institution.

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