options ls=78;

data one;
  input subject l1 l2 l3 l4 r1 r2 r3 r4;
  cards;
1 116 119 116 124 120 117 114 122
2 110 110 114 115 106 112 110 110
3 117 118 120 120 120 120 120 124
4 112 116 115 113 115 116 116 119
5 113 114 114 118 114 117 116 112
6 119 115  94 116 100  99  94  97
7 110 110 105 118 105 105 115 115
;
run;

proc transpose data=one out=two(rename=(_name_=eyelens col1=y));
  by subject;
run;

data two;
  set two;
  if (eyelens in ("l1","l2","l3","l4")) then eye="L";
  else eye="R";
  if (eyelens in ("l1","r1")) then lens=1;
  else if (eyelens in ("l2","r2")) then lens=2;
  else if (eyelens in ("l3","r3")) then lens=3;
  else lens=4;
run;

proc print data=two; 
run;

/* The models fit with proc mixed make no adjustments for
   non-sphericity. For those models the G-G or H_F adjustment would have to be done by hand. */
title 'Model 1: the RCBD model with random subject (block) effects';
title2 'No adjustment for non-sphericity'; 
proc mixed data=two method=type3;
  class subject lens eye;
  model y=lens|eye /ddfm=satterth;
  random subject;
  lsmeans lens eye lens*eye;
run;

title 'Model 1 refit with PROC GLM';
title2 'Here, adjustments for non-sphericity are done in RM-ANOVA'; 
* but only for overall treatment effect, without decomposing it into lens effect, eye effect and
  interaction. The call to PROC GLM below will give G-G and H-F estimates of epsilon
  based on the 8x8 within-subject var-cov matrix.;
proc glm data=one;
  model l1 l2 l3 l4 r1 r2 r3 r4= /nouni;
  repeated  eyelens/printe nom;

* The manova statements below will not be tested with the RM-ANOVA procedure, but rather
  as multivariate hypotheses assuming an unstructured within-subject var-cov matrix. So,
  these really shouldn't be used in this problem where you were asked to implement RM-ANOVA,
  not he unstructure multivariate approach to the analysis. 
  However,  I misled some students in office hours who asked about this. I told them to do these
  contrasts this way (using the C matrix in the multivariate linear hypothesis ABC=D, 
  not realizing that the problem asked for RM-ANOVA, not the unstructured 
  approach. Therefore, it you did the hypothesis tests this way, I will accept your answer
  without marking it wrong.;

  manova h=intercept m=(1 1 1 1 -1 -1 -1 -1);
  manova h=intercept m=(3 -1 -1 -1 3 -1 -1 -1,
                        0 2 -1 -1 0 2 -1 -1,
                        0 0 1 -1 0 0 1 -1);
  manova h=intercept m=(3 -1 -1 -1 -3 1 1 1,
                        0 2 -1 -1 0 -2 1 1,
                        0 0 1 -1 0 0 -1 1);

run;



title 'Model 2: the RCBD model with random subj, subj*lens and subj*eye effects';
title2 'No adjustment for non-sphericity'; 
proc mixed data=two method=type3;
  class subject lens eye;
  model y=lens|eye /ddfm=satterth;
  random subject subject*lens subject*eye;
  lsmeans lens eye lens*eye;
run;

/* The second model above can be fit with PROC GLM, which will make adjustments 
   for non-sphericity */
title 'Model 2 refit with PROC GLM';
title2 'Here, adjustments for non-sphericity are done in RM-ANOVA';
proc glm data=one;
  model l1 l2 l3 l4 r1 r2 r3 r4= /nouni;
  repeated  eye 2, lens 4/printe nom;
run;