1. Sampling Distribution of Pearson Correlation

2. IMLMLIB Some IML functions and a subroutine
The RANDNORMAL function The corr function
The QNTL subroutine

3. Generate random samples bivariate normal and calculate correlation for each sample
%let obs = 20; /* size of each sample */
%let reps = 1000; /* number of samples*/
proc iml;
call randseed(54321);
mu = {0 0}; /*mean*/
print mu;
Sigma = {1 0.3, 0.3 1};/*covariance*/
print sigma;
rho = j(&reps, 1); /* allocate vector for results*/
do i = 1 to &reps; /* simulation loop*/
/* simulated data */
x = RandNormal(&obs, mu, Sigma);
/* corr returns a matrix, get Pearson correlation for ith sample*/
rho[i] = corr(x)[1,2];
end;
print x;
print (rho[1:5,]);

4. Compute quantiles, create data set
call qntl(q, rho, { });
print (q`)[colname={"P5" "P25" "Median" "P75" "P95"}];
create corr var {"Rho"};
append;
close;
quit;

5. Visualize approx. sampling distribution
proc univariate data=Corr;
label Rho = "Pearson Correlation Coefficient";
histogram Rho / kernel;
ods select Histogram;
run;

6. Find the percentage of negative correlations in the approximate sampling distribution.
proc sql;
select sum(Rho<0)/count(*) as pctneg "Percent negative" format=percent6.1
from corr ;
quit;