On 4/11/2008, at 6:29 PM, Edna Bell wrote:
Dear R Gurus: I vaguely remember reading that if interaction was present in a factorial design, then the main effect results were suspect. However, I was reading a text which now uses the tests for main effects even if interaction is present. Which is correct, please?
Both, neither, whatever. You have to specify what you mean by ``main effect'' if interaction is present. One possible definition is to average the response of factor A (at each level) over all levels of factor B. There is an ``A main effect'' (by this definition) if these averages are different. E.g. (1): mu(1,1) = 1, mu(1,2) = -1, mu(2,1) = -1, mu(2,2) = 1 where mu(i,j) is the population mean when factor A is at level i and factor B is at level j. Factor A averages out to 0 at both levels so there is no main A effect in the sense defined. (And likewise there is no main B effect either.) ``Clearly'' there is interaction! E.g. (2): mu(1,1) = 1, mu(1,2) = 2, mu(2,1) = -1, mu(2,2) = -2. Here factor A averages to 1.5 at level 1 and to -1.5 at level 2 so there *is* a main A effect ***in the sense defined***. Note that factor B averages to 0 at both levels so there is no main B effect in the sense defined. This is the sort of thing that the much maligned ``Type III'' sums of squares test for. But is it *really* what you are interested in? Probably NOT. Read Bill Venables' ``Exegesis on Linear Models'' for more discussion of why such things are a bad idea: http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf The important thing is to get it clear in your head what you want to know about, and then conduct your analysis in such a way as to find about that. This is sometimes not so easy. But there's no avoiding it if you want to do a sensible analysis. Doing tests mindlessly without a clear understanding of exactly what it is that you are testing is a recipe for nonsense if not disaster. cheers, Rolf Turner ###################################################################### Attention:\ This e-mail message is privileged and confid...{{dropped:9}} ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
