Date:         Mon, 13 Apr 1998 17:46:29 GMT
Reply-To:     chuck@BARNEY.PMEH.UIOWA.EDU
Sender:       "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From:         chuck@BARNEY.PMEH.UIOWA.EDU
Organization: The University of Iowa
Subject:      Analysis of Covariance with Repeated Measures

Someone recently asked me a question about the repeated measures
analysis of covariance example on pp. 805-808 of Winer, 1971,
Statistical Principles in Experimental Design.
 
The example has three groups with three subjects/group.  A response
(Y) and a covariate (X) are measured two times for each subject.
Neither one of us can determine how to produce Winer's analysis of
covariance (panel (iii) of Table 10.6-7).
 
It seems evident that the "multivariate" data organization of proc glm
can't be used, since there's no way to account for the repeated
measurements of the covariate.  The "univariate" data organization
gives some of Winer's sums of squares, but doesn't give Winer's
estimate for the group sum of squares (factor A).
 
Although I'm not an SPSS user, the person who asked me the question is
able to reproduce Winer's results using SPSS.
 
If anyone in this group has previously considered this type of
example, I'd appreciate your comments.
 
Thanks,
 
Chuck
 
The SAS statements I've considered follow:
 
 data covar;
   input subject group time x y;
   cards;
1 1 1 3 8
1 1 2 4 14
2 1 1 5 11
2 1 2 9 18
3 1 1 11 16
3 1 2 14 22
4 2 1 2 6
4 2 2 1 8
5 2 1 8 12
5 2 2 9 14
6 2 1 10 9
6 2 2 9 10
7 3 1 7 10
7 3 2 4 10
8 3 1 8 14
8 3 2 10 18
9 3 1 9 15
9 3 2 12 22
;
 proc glm; class subject group time;
   model y=group subject(group) time group*time x;
   test H=group  E=subject(group);