* Timm: Table 3.4.1
  Two instructors use different methods to teach algebra;
  
title 'Two-Sample Hotelling T2';
data mathscor;
   input group BM WP;
   label BM='Basic Math'
         WP='Word Problems';
datalines;
1 190  90
1 170  80
1 180  80
1 200 120
1 150  60
1 180  70
2 160 120
2 190 150
2 150  90
2 160 130
2 140 110
2 145 130
;
proc print;
/* (1) Standard analysis with GLM
Note: Hotelling's T**2 is equivalent to the MANOVA tests
  - all have the same F-approximation and p-value.
  - T**2 = dfe * Hotelling-Lawley trace
*/
proc glm data=mathscor  outstat=stats;
   class group;
   model BM WP = group / nouni;
   manova H=group / printH printE;
run;
/* (2) Similar analysis produced by DISCRIM or CANDISC, but
   gives discriminant function coefficients and output scores
*/
proc discrim data=mathscor
     pool=test noclassify
     MANOVA canonical ncan=1 out=scores;
   class group;
   var BM WP;
proc print data=scores;
   var group BM WP CAN1;
run;
/* (3) T**2 = t**2 based on discriminant scores */
proc ttest data=scores;
   class group;
   var can1; title2 'Univariate t-test on Discrim scores';
run;