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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: difference between "Spearman" and "pwcorr / correlate" |

Date |
Thu, 8 Oct 2009 16:13:08 +0100 |

(a) is on all fours with "the problem with pink is that it isn't blue". That is, (a) amounts to saying that the problem with Spearman's rank is that it's not Kendall's tau. True, but the reverse is equally true. That aside, I think most users of rank correlation would be happy to acknowledge advantages and disadvantages of each such measure, and indeed to note that they should give similar results in practice. For example, given the property emphasised earlier in the thread that Spearman(x, y) = Pearson(rank(x), rank(y)) one of many possibilities for Spearman correlations is that they offer a route to a robustified PCA. (You can be sure that the eigenproperties are OK.) Nick n.j.cox@durham.ac.uk Newson, Roger B There IS an interpretation of the Spearman correlation for continuous variables in an infinite population. In that case, if the random variables are X and Y, then the Spearman rho(X,Y) is simply the Pearson correlation of F_X(X) and F_Y(Y), where F_X(.) and F_Y(.) are the population cumulative distribution functions of X and Y respectively. And a Pearson correlation, as always, is a measure of linearity. The two main problems with the Spearman rho are that (a) it is ONLY a measure of linearity between 2 cumulative distribution functions (with no interpretation as a difference between concordance and discordance probabilities), and that (b) the Central Limit Theorem works a lot less quickly for the sample Spearman rho than for the sample Kendall tau-a, especially under the null hypothesis of zero correlation (see Kendall and Gibbons, 1990). References Kendall, M. G., and J. D. Gibbons. 1990. Rank Correlation Methods. 5th ed. Oxford, UK: Oxford University Press. * * 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**:**Re:st: difference between "Spearman" and "pwcorr / correlate"***From:*Mike Lacy <Michael.Lacy@colostate.edu>

**Re: st: difference between "Spearman" and "pwcorr / correlate"***From:*Stas Kolenikov <skolenik@gmail.com>

**RE: st: difference between "Spearman" and "pwcorr / correlate"***From:*"Newson, Roger B" <r.newson@imperial.ac.uk>

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