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


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: Can Spearman's rho be used to measure of the degree of association between two binary variables ?
Date   Mon, 21 May 2012 18:06:50 +0100

The last equivalence between Spearman and Pearson correlations in this
case can be understood without doing calculations. If two variables
are 0 and 1, that means up to 4 blobs of identical points on a scatter
plot, namely as many of (0, 0), (0, 1), (1, 0) and (1, 1) as occur.
You can assign ranks to both variables, but the blobs are same: you
are just labelling them differently. So the correlation between ranked
values is identical to the correlation between values; there is a
linear transformation for each variable from values to ranks that
drops out of the correlation calculation, so the same numerical result
is guaranteed.

All that said, multicollinearity is centred on calculations such as
those that produce a covariance matrix, and so are clearly based on
the original measured values. Thus it seems to me that Pearson
correlation is the natural concept of correlation here if there is
one. The model calculations don't use the ranks, nor are they related
to latent variables, except in your head perhaps. So although Spearman
correlation does not differ here, if it did differ, it would certainly
be the wrong way to think about what is going on.

Nick

On Mon, May 21, 2012 at 5:23 PM, Visintainer, Paul
<Paul.Visintainer@baystatehealth.org> wrote:
>
> Yes, in fact many of the contingency coefficients will give equivalent results for 2x2 tables:
>
> .sysuse auto
> .gen pricecat=cond(price>=5000,1,0)
> .tab foreign pricecat, all
> .corr foreign pricecat
> .spearman foreign pricecat
>
>
> Cramer's V, Spearman rho, and Pearson's correlation all give the same value.  Another is called the "phi" coefficient, which can be computed as the sqrt(chisquare/N)
>
> .di sqrt(2.3287/74)
>
Marcos Vinicius

> 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 .

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