Re: st: is Kendall's tau the best correlation coeficient for binary varibles?

[Roger Newson <r.newson@imperial.ac.uk>]

Yes, Kendall's correlation is a reasonable coefficient to use with 
binary variables. However, it is usually more informative to use the 
corresponding regression coefficient, Somers' D, which, if the 2 
variables are binary, is simply the difference between proportions. Both 
Somers' D and Kendall's tau-a can be calculated (with confidence limits 
as well as P-values) using the -somersd- package, which can be 
downloaded from SSC (using the -ssc- command).

So, if -x- and -y- are 2 binary variables, with values 0 for a negative 
outcome and 1 for a positive outcome, then you can type

somersd x y, transf(z) tdist

to get a confidence interval for the difference between the proportion 
of y-positives in the x-positives and the proportion of y-positives in 
the x-negatives. And you can type

somersd y x, transf(z) tdist

to get a confidence interval for the difference between the proportion 
of x-positives in the y-positives and the proportion of x-positives in 
the y-negatives. Both of these confidence intervals are defined using 
the Normalizing and variance-stabilizing hyperbolic arctangent or 
z-transformation, to define symmetric confidence intervals for the 
z-transformed differences between proportiions, and the more useful 
asymmetric confidence intervals for the untransformed differences 
between proportions.

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 08/09/2010 17:16, jl591164@albany.edu wrote:
> Dear Statalist,
> I need to do a correlation matrix of all my study variables. Most of them
> are binary variable, and two are continuous variables. Is Kenall's tau the
> test coefficient to use to get the correlation matrix of my study
> variables? Any advice is highly appreciated.
> Junqing
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