OPTIONS LINESIZE=75 PAGESIZE=54 NODATE PAGENO=1;
TITLE
 'Ex. 10.2 - A test for sphericity of the variance-covariance matrix.';
DATA DAT;
 INPUT ID X1-X3;
 CARDS;
 1 1 3 5
 2 2 3 5
 3 1 4 6
 4 1 4 4
 5 3 4 7
 6 2 5 6
DATA XX; SET DAT; DROP ID;
PROC IML;
 RESET NOLOG;
 USE XX;  READ ALL INTO X;
 PRINT "The Data Matrix is" X;
N=NROW(X);  P=NCOL(X);
 XBAR = X(|+,|)`/N;
PRINT, "XBAR = " XBAR;
SUMSQ=X`*X-(XBAR*XBAR`)#N;
S=SUMSQ/(N-1);
PRINT , "The Variance-Covariance Matrix is " S;
NU=N-1;
W=NU#S;
LAMDA = DET(W)/((1/P)#TRACE(W))##P;
PRINT, "LAMDA = " LAMDA;
M = NU - (2#P#P+P+2)/6/P;
L = -M#LOG(LAMDA);
PRINT, "L = " L;
A = (P+1)#(P-1)#(P+2)#(2#P#P#P+6#P#P+3#P+2)/288/P/P;
F=P#(P+1)/2-1;
A1 = 1-PROBCHI(L,F);
A3 = 1-PROBCHI(L,F+4);
ALPHA = A1+(A/M/M)#(A3-A1);
PRINT, "ALPHA = ", ALPHA;
QUIT;