[R] Test statistic for Spearman correlation
Thomas W Blackwell
tblackw at umich.edu
Thu May 1 17:40:30 CEST 2003
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
>
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