[NOTE: 3-way interaction talk.politics.drugs removed from Newsgroups] In article <[EMAIL PROTECTED]>, Brian Sandle <[EMAIL PROTECTED]> writes: ... >How can he say that Spearman's rank order correlation given by > >rho = 1 - [6sigmaD^2]/[N(N^2-1)] > > is just Pearson's product moment correlation given by > >r =[NsigmaXY -(sigmaX)(sigmaY)]/SQRT{[NsigmaX^2-(sigmaX)^2][ > NsigmaY^2-(sigmaY)^2]} > > using ranks instead of scores?
Quite easily. If X & Y are ranks (with no ties) then (e.g.) sigmaX^2 involves SUM_(i=1)^N i^2, which is just N(N+1)(2N+1)/6. The formula for r then simplifies to give rho. Note that if there are tied ranks (are there ever not?) then Pearson's r on the ranks is different from Spearman's rho with the "standard" correction for ties (whatever that may be). If you really really want to calculate a nonparametric correlation, then I'd suggest using Kendall's tau, which has a natural probabilistic interpretation and also a smoother distribution than Spearman's rho. -- J.E.H.Shaw [Ewart Shaw] [EMAIL PROTECTED] TEL: +44 2476 523069 Department of Statistics, University of Warwick, Coventry CV4 7AL, U.K. http://www.warwick.ac.uk/statsdept/Staff/JEHS/ 3 ((4&({*.(=+/))++/=3:)@([:,/0&,^:(i.3)@|:"2^:2))&.>@]^:(i.@[) <#:3 6 2 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
