"It has long been an axiom of mine that the little things are infinitely the most important" (Sherlock Holmes)

Spearman's rank correlation coefficient - using R

Spearman's rank correlation coefficient

The R output for the Spearman correlation test is as follows:

> cor.test (x,y,method = "spearman")
Spearman's rank correlation rho
data: x and y
S = 2063.483, p-value = 1.697e-06
alternative hypothesis: true rho is not equal to 0
sample estimates:
rho
0.7109968
Warning message:
In cor.test.default(x, y, method = "spearman") :
Cannot compute exact p-values with ties

The test statistic S given in the R output is estimated from:

S = (n^{3}-n) × (1-r_{s})/6

where n is the number of bivariate observations and r_{s} is Spearman's rank correlation coefficient.

Olds (1938)
tabulated the exact distribution of S using 'algorithm AS 89'. R uses this algorithm to test the significance of r_{s}. Values are only exact when there are no ties.