Date:         Wed, 15 Apr 1998 15:41:30 -0600
Reply-To:     mgonen@ALOGIC.COM
Sender:       "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From:         mgonen@ALOGIC.COM
Organization: Deja News - The Leader in Internet Discussion
Subject:      Re: Analysis of Covariance with Repeated Measures

In article <6gtj1l$f9o$1@flood.weeg.uiowa.edu>,
  chuck@barney.pmeh.uiowa.edu wrote:
>
> 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);
>
>
 
You can use PROC MIXED to work with univariate repeated measures. Check
documentation for Release 6.11 for a comprehensive account of different
covariance structures it offers.
 
Mithat Gonen
mgonen@alogic.com
 
 
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