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Re: st: Can Spearman's rho be used to measure of the degree of association between two binary variables ?


From   "Roger B. Newson" <r.newson@imperial.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Can Spearman's rho be used to measure of the degree of association between two binary variables ?
Date   Mon, 21 May 2012 09:57:43 +0100

Yes, Spearman'd rho can be used to measure the association between 2 binary variables. However, I would prefer to use Somers' D and/or Kendall's tau-a. These are estimated (with confidence limits) using the -somersd- package, downloadable from SSC. Both of them can be used for continuous, discrete ordinal and binary variables, and are expressed on a scale from -1 to 1, and are interpreted as differences between 2 probabilities, namely a probability of concordance and a probability of discordance. In the case of 2 binary variables X and Y, Somers' D is equal to the difference between 2 proportions. D(Y|X) is the difference between P(Y==1|X==1) and P(Y==1|X==0). Another advantage is that, in general, the Central Limit Theorem works a lot faster for Somers' D and Kendall's tau-a than for Spearman's rho.

I hope this helps.

Best wishes

Roger


Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

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

On 20/05/2012 21:31, Marcos Vinicius wrote:
Hello,
Can Spearman's rho be used to measure of the degree of association between two binary variables ?
I was wondering if Spearman's rho could be adequate  because I have used the phi coefficient to quantify association among several  binary variables and the results are identifical compared with Spearman's rho coefficient .
Best regards,
Marcos Vinicius

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