[R] Test statistic for Spearman correlation

[Peter Dalgaard BSA]

Thomas W Blackwell <tblackw at umich.edu> writes:

> Brett  -
> 
> I can give you a further reference, but you may not
> find it much help !
> 
> E. G. Olds.  Distribution of sums of squares of rank
> differences for small numbers of individuals.  Annals
> of Mathematical Statistics, v.9, pp. 133-148, 1938.
> 
> My source says that "Olds (1938) tabulated the exact
> distribution of a quantity S related to rho by the
> equation
> 
>     R = 1 - 6 * S / (n^3 - n) ."
> 
> Olds must have been using a Comptometer or a Marchant
> calculator, so presumably, this construct guarantees
> always to be an integer.  Algorithm AS 89 is certainly
> available on line from Statlib.

The title of Olds paper might have given you a hint:

> x <- rank(rnorm(10))
> y <- rank(rnorm(10))
> cor(x,y)
[1] -0.2242424
> 990/6*(1-cor(x,y))
[1] 202
> sum((x-y)^2)
[1] 202

BTW, the identity breaks down when there are ties, something that we
probably ought to look into at some point. The code does say that the
p values may be incorrect, but I suspect they may be more incorrect
than need be.

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907