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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 . * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Can Spearman's rho be used to measure of the degree of association between two binary variables ?***From:*Marcos Vinicius <bioestatistico@inbox.com>

**st: RE: Can Spearman's rho be used to measure of the degree of association between two binary variables ?***From:*"Visintainer, Paul" <Paul.Visintainer@baystatehealth.org>

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