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From |
Roger Newson <roger.newson@kcl.ac.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Difference in correlation coefficients |

Date |
Wed, 17 Jul 2002 10:04:46 +0100 |

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.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?

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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**References**:**st: Difference in correlation coefficients***From:*"Banya, Winston" <w.banya@ic.ac.uk>

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