Suppose that two English tests--a long one on paragraph comprehension and s short one on vocabulary--were given to three classes of high school seniors, pursuing three different curricular programs. Prior testing the significance of differences among the three centroids, we wish to test the tenability of the assumptions of equal covariance matrices in the three populations. Given the following:

n1 = 33, n2 = 37, and n3 = 24

s1 = [3352.71 100.09, 100.09 286.97]
s2 = [2647.87 149.22, 149.22 251.57]
s3 = [2948.02 61.00, 61.00 181.83]
Test the null hypothesis that the three population covariance matrices are equal, using alpha = .10.

/* H0: sigma1 = sigma2 = sigma3 */
proc iml;
start;
k = 3;
p = 2;
n1 = 33;
n2 = 37;
n3 = 24;
s1 = {3352.71 100.09, 100.09 286.97};
s2 = {2647.87 149.22, 149.22 251.57};
s3 = {2948.02 61.00, 61.00 181.83};
c1 = (1/(n1-1))#s1;
c2 = (1/(n2-1))#s2;
c3 = (1/(n3-1))#s3;
print c1;
print c2;
print c3;
n = n1+n2+n3;
c = (s1+s2+s3)/(n-k);
print c;
d = det(c);
d1 = det(c1);
d2 = det(c2);
d3 = det(c3);
m = ((n-k)#log(d))-((n1-1)#log(d1) + (n2-1)#log(d2) + (n3-1)#log(d3));
print m;
h = 1 - ((2#p#p+3#p-1)/(6#(p+1)#(k-1))#(1/(n1-1)+1/(n2-1)+1/(n3-1)-1/(n-k)));
print h;
chi = m#h;
df = p#(p+1)#(k-1)/2;
print chi;
print df;
finish;
run;

updated