*
* Example 11.3, page 407
* Spearman's Rank Correlation test
*
data(unit=input,org=columns) 1 10 avgret stddev
 12.4 12.1
 14.4 21.4
 14.6 18.7
 16.0 21.7
 11.3 12.5
 10.0 10.4
 16.2 20.8
 10.4 10.2
 13.1 16.0
 11.3 12.0

linreg avgret
# constant stddev
*
*  Spearman's rank correlation test.
*  Get the ranks for |u| and x.
*  Compute the difference in the ranks.
*  Compute r using %dot(d,d) (will be sum of squares) and
*  the %nobs variable, and the t statistic generated from it.
*  Use cdf to show the significance.
*
set absu = abs(%resids)
order(ranks=urank) absu
order(ranks=srank) stddev
*
sstats / (urank-srank)**2>>dd
compute r=1-6*dd/(%nobs*(%nobs**2-1))
compute rt=r*sqrt(%nobs-2)/sqrt(1-r**2)
*
* The CDF instruction produces a two-tailed significance level, testing a null of
* no correlation in the ranks vs non-zero correlation. If you want a one-tailed
* test (that is, that the alternative is positive correlation, not just
* non-zero), divide the reported significance level by 2.
*
cdf(title="Spearman Rank Correlation Test") ttest rt %nobs-2