Re: [R] contrast matrix for aov

From: Darren Weber <DarrenLeeWeber_at_gmail.com>
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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