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

 From jl591164@albany.edu To statalist@hsphsun2.harvard.edu Subject Re: st: is Kendall's tau the best correlation coeficient for binary varibles? Date Wed, 8 Sep 2010 13:07:34 -0400 (EDT)

```Hi Roger,
paper on somersd and confidence intervals of the coeficients. This is
perfect. Thanks a lot.
Junqing

> 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
>
> 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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```