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;