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


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 17:33:17 +0100

There's a tacit criterion here, that techniques must have simple verbal
interpretations. I am as much in favour of simple verbal interpretations
as the next person -- nay, on average, more so -- but while they're a
bonus when available insisting on them would deprive you of much that is
indispensable. 

What's the simple verbal interpretation of (say) eigenvectors or an SVD?


Nick 
n.j.cox@durham.ac.uk 

Stas Kolenikov

If you have a finite population, then of course you will have Spearman
correlation for it. Although if you want to set up any asymptotic
framework, you will be trying to hit a moving target. I don't think
there is a meaningful definition of Spearman correlation for infinite
populations/continuous variables, although I might be mistaken. On the
other hand, Kendall's tau, as Nick Cox quoted from Roger Newson, has
explicit population analogues in probabilities of concordant and
discordant pairs of observations.

The question is: if the correlation estimate is 0.5, what does it say?
For Pearson moment correlation, it means that the proportion of
explained variance in a bivariate regression is 0.25. For Kendall's
tau, it means that for every discordant pair of observations, there
are three concordant pairs (i.e., Prob[ concordant ] = 3 Prob[
discordant ] = 3/4 ). For Spearman rank correlation, you can only say
that the variables are positively associated, but not much more.

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