[R] Test statistic for Spearman correlation

[Thomas W Blackwell]

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.

HTH  -  tom blackwell  -  u michigan medical school  -  ann arbor  -

On Thu, 1 May 2003, Brett Magill wrote:

> In the ouput below, what is the "S" statistic (S = 96) that
> is used for Spearman?  I don't have easy access to the books
> cited on the help page.  Other texts and web sources that I
> have found use t or z as a test for Spearman, perhaps
> inappropriately.  Can anyone tell me how S is computed or
> refer to a web resource?
>
> I see from the code for that:
>
>   q <- as.integer((n^3 - n) * (1 - ESTIMATE)/6)
>   STATISTIC <- c(S = q)
>
> I couldn't decipher the next part.  Would appreciate some help.
>
> R 1.7.0 Windows 98.
> _________________________________________
>         Spearman's rank correlation rho
>
> data:  x and y
> S = 96, p-value = 0.2324
> alternative hypothesis: true rho is not equal to 0
> sample estimates:
>       rho
> 0.4181818
>