Date: Wed, 12 Feb 1997 18:02:52 +0100
Reply-To: Hans-Peter Piepho <piepho@WIZ.UNI-KASSEL.DE>
Sender: "SAS(r) Discussion" <SAS-L@UGA.CC.UGA.EDU>
From: Hans-Peter Piepho <piepho@WIZ.UNI-KASSEL.DE>
Subject: Re: Interaction contrasts
Content-Type: text/plain; charset="us-ascii"
>Hans-Peter,
>
>Thanks for your response. The SAS manual is confusing in this area but
>your explanation helped a great deal.
>
>Regards,
>
>Joe
Someone else posted a response to sas-l saying it is necessary to be
familiar with Type I thru Type III SS estimable functions as described in
the manual in order to define estimable functions using the CONTRAST
statement. I think this is unnecessary, as is all the fuzz that is being
made about the different types of SS. This is made very clear in two papers
by Nelder:
Nelder JA, Lane PW 1995 The computer analysis of factorial experiments. In
memoriam - Frank Yates.
Nelder JA 1994 The statistics of linear models: back to basics. Statistics
and computing 4, 221-234
One main point of the papers is that marginality relations have to be
considered when testing effects in ANOVA. In the two way model with unequal
subclass numbers, this means that a test of main effects is pointless when
the interactions are significant (or deemed present, despite
non-significance of the interaction MS). In this case, both Type I and Type
III SS test uninteresting hypotheses. In the absence of interaction, main
effects may be tested by either Type I or Type II or Type III SS. In fact,
the Type I analysis is more powerful than Type III (For Type I analysis two
model sequences have to be considered. (a b a*b) and (b a a*b) the first
gives the test for a, the second that for b, provided interaction is not
significant. A simpler way of obtaining this analysis is to specify Type II
SS).
What is most helpful in putting up appropriate CONSTAST statements, I think,
is to get familiar with the cell means model. The book "Analysis of messy
data. Volume I. designed experiments" by Milliken GA and Johnson DA (1992,
Chapman and Hall) does a very good job explaining this model (Chapters 9 to
11) (though it does not seem to agree with Nelder on the usefulness of Type
III SS). The book discusses use of SAS PROC GLM.
Hans-Peter
_______________________________________________________________________
Hans-Peter Piepho
Institut f. Nutzpflanzenkunde WWW: http://www.wiz.uni-kassel.de/fts/
Universitaet Kassel Mail: piepho@wiz.uni-kassel.de
Steinstrasse 19 Fax: +49 5542 98 1230
37213 Witzenhausen, Germany Phone: +49 5542 98 1248
