contrast matrix for aov
As an R newbie (formerly SPSS), I was pleased to find some helpful notes on ANOVA here: http://personality-project.org/r/r.anova.html In my case, I believe the relevant section is: Example 4. Two-Way Within-Subjects ANOVA This is where I noted and copied the error notation. Sorry for any confusion about terms - I did mean "within-subjects" factors, rather than repeated measures (although, as noted earlier, we do have both in this experiment).
Prof Brian Ripley wrote:
On Thu, 10 Mar 2005, Christophe Pallier wrote:
Prof Brian Ripley wrote:
On Wed, 9 Mar 2005, Darren Weber wrote: 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?)
roi.aov <- aov(roi ~ (Cue*Hemisphere) + Error(Subject/(Cue*Hemisphere)), data=roiDataframe)
I think the error model should be Error(Subject). In what sense are `Cue' and `Cue:Hemisphere' random effects nested inside `Subject'?
I do not understand this, and I think I am probably not the only one. That is why I would be grateful if you could give a bit more information. My understanding is that the fixed factors Cue and Hemisphere are crossed with the random factor Subject (in other words, Cue and Hemisphere are within-subjects factors, and this is probably why Darren called it a "repeated measure" design).
The issue is whether the variance of the error really depends on the
treatment combination, which is what the
Error(Subject/(Cue*Hemisphere)) assumes. With that model
Error: Subject:Cue
Df Sum Sq Mean Sq F value Pr(>F)
Cue 1 0.2165 0.2165 0.1967 0.6708
Residuals 7 7.7041 1.1006
Error: Subject:Hemisphere
Df Sum Sq Mean Sq F value Pr(>F)
Hemisphere 1 0.0197 0.0197 0.0154 0.9047
Residuals 7 8.9561 1.2794
Error: Subject:Cue:Hemisphere
Df Sum Sq Mean Sq F value Pr(>F)
Cue:Hemisphere 1 0.0579 0.0579 0.0773 0.789
Residuals 7 5.2366 0.7481
you are assuming different variances for three contrasts.
In this case, it seems to me from the various textbooks I read on Anova, that the appropriate MS to test the interaction Cue:Hemisphere is Subject:Cue:Hemisphere (with 7 degress of freedom, as there are 8 independent subjects). If you input Error(Subject/(Cue*Hemisphere)) in the aov formula, then the test for the interaction indeed uses the Subject:Cue:Hemisphere source of variation in demoninator. This fits with the ouput of other softwares. If you include only 'Subjet', then the test for the interaction has 21 degrees of Freedom, and I do not understand what this tests.
It uses a common variance for all treatment combinations.
I apologize in if my terminology is not accurate. But I hope you can clarify what is wrong with the Error(Subject/(Cue*Hemisphere)) term, or maybe just point us to the relevant textbooks.
Nothing is `wrong' with it, it just seems discordant with the description of the experiment.