From: Prof Brian Ripley <ripley_at_stats.ox.ac.uk>

Date: Thu 10 Mar 2005 - 21:38:20 EST

Date: Thu 10 Mar 2005 - 21:38:20 EST

On Thu, 10 Mar 2005, Peter Dalgaard wrote:

> Prof Brian Ripley <ripley@stats.ox.ac.uk> writes:

*>
**>> On Wed, 9 Mar 2005, Darren Weber wrote:
**>>
**>>> How do we specify a contrast interaction matrix for an ANOVA model?
**>>>
**>>> We have a two-factor, repeated measures design, with
**>>
**>> Where does `repeated measures' come into this? You appear to have
**>> repeated a 2x2 experiment in each of 8 blocks (subjects). Such a
**>> design is usually analysed with fixed effects. (Perhaps you averaged
**>> over repeats in the first few lines of your code?)
**>
**> Actually, that's not "usual" in SAS (and not SPSS either, I believe)
**> in things like
**>
**> proc glm;
**> model y1-y4= ;
**> repeated row 2 col 2;
**>
**> [Not that SAS/SPSS is the Gospel, but they do tend to set the
**> terminology in these matters.]
*

That seems to be appropriate only if the four treatments are done in a particular order (`repeated') and one expects correlations in the responses. However, here the measurements seem to have been averages of replications.

It may be "usual" to (mis?)specify experiments in SAS that way: I don't know what end users do, but it is not the only way possible in SAS.

> There you'd get the analysis split up as analyses of three contrasts

*> corresponding to the main effects and interaction, c(-1,-1,1,1),
**> c(-1,1,-1,1), and c(-1,1,1,-1) in the 2x2 case (up to scale and sign).
**> In the 2x2 case, this corresponds exactly to the 4-stratum model
**> row*col + Error(block/(row*col)).
**>
**> (It is interesting to note that it is still not the optimal analysis
**> for arbitrary covariance patterns because dependence between contrasts
**> is not utilized - it is basically assumed to be absent.)
*

It also assumes that there is a difference between variances of the contrasts, that is there is either correlation between results or a difference in variances under different treatments. Nothing in the description led me to expect either of those, but I was asking why it was specified that way. (If the variance does differ with the mean then there are probably more appropriate analyses.)

-- Brian D. Ripley, ripley@stats.ox.ac.uk Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595 ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.htmlReceived on Thu Mar 10 21:47:55 2005

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