Dear Ian,
I absolutely agree - Spearman is a special case of Pearson but not
vice-versa.
All the best,
Will.
Ian Nimmo-Smith wrote:
> Dear Will,
>
> > Esa Wallius wrote:
> >
> > > Our covariate is clearly ordinal. Wouldn't it be better to use ordinal
> > > correlation (e.g Spearman)? Does SPM (or some toolbox) provide a
> > > solution for this?
> > >
> > > Esa
> >
> > Dear Esa,
> >
> > Spearman's rank order correlation coefficient (corrected for
> > ties, if there are any) will give you EXACTLY THE SAME correlation value as
> > Pearson's product-moment correlation coefficient (ie. the usual one).
>
> This is true so long as the variables being correlated are the rank
> order values.
>
> In general if you take variables X and Y and compute their (Pearson's
> product moment) correlation coefficient PPMCC(X,Y), it is not the same
> as the Spearman's rank order correlation coefficient of X and Y,
> SROCCC(X,Y).
>
> However if RX and RY are the rank order equivalents (ranks) of X and Y
> then PPMCC(RX,RY) = SROCC(X,Y) (with correction for ties).
>
> > So why do people bother using Spearman ? Because, if there
> > are'nt any ties, the Spearman formula is
> > quicker to evaluate - this was important before we had computers.
>
> What this refers to is the formula based on the sum of squares of
> diferences of ranks (RX-RY)'*(RX-RY). The ranks had to be calculated
> previously by hand.
>
> > This correspondence is described, for example, in Chaper 23 of D.J. Sheskin
> > (1997) The handbook of parametric and nonparametric statistical procedures,
> > CRC Press.
>
> > Therefore, as SPM performs a regression, and regression and correlation
> > are two sides of the same coin (for multiple regression read
> > multiple and partial correlation), then SPM is already implicitly doing a
> > Spearman type computation.
>
> I think the analogy breaks down here as I am not aware of any coherent rank regression model in which the regression coefficients might be thought to correspond to effect sizes. The 'slopes' in non-parametric rank regression partly depend on the number of data points that are being ranked. There is a burgeoning field of 'non-parametric regression models' but it is not based on simple ranks.
>
> Ian Nimmo-Smith
> MRC Cognition and Brain Sciences Unit
> Cambridge, UK
--
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