From: Darren Weber <DarrenLeeWeber_at_gmail.com>

Date: Fri 11 Mar 2005 - 06:07:44 EST

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.html Received on Fri Mar 11 13:39:36 2005

Date: Fri 11 Mar 2005 - 06:07:44 EST

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.
**>
*

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Fri Mar 11 13:39:36 2005

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