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

 From Roger Newson To "statalist@hsphsun2.harvard.edu" Subject Re: st: is Kendall's tau the best correlation coeficient for binary varibles? Date Wed, 8 Sep 2010 17:43:00 +0100

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
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:

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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