[R-lang] Odd summary(aov()) result

[Francisco Torreira]

Dear Adam,

> I'm just surprised
> that commutativity doesn't hold.

A*B is is not the equivalent notation of any combination of A, B and
A:B. It is only the equivalent of A+B+A:B. When your design is
completely balanced, the output should be the same regardless of the
order. However, with unbalanced/incomplete designs you will get
different outputs. This is because of the famous Type I / Type III
sums of squares issue. To be honest I don't think this is the answer
to your problem, since repeated-measures designs require only 1 data
point per cell. Is any data point missing?

Francisco

On 5/14/07, Adam Baker <adamb924 at gmail.com> wrote:
> I wonder if somebody could comment on why I get different summaries
> with these two commands, which differ only in the order of the
> variables.
>
> summary(aov(MidAvg ~ Ccon*Rpres + Error(Subject/Ccon*Rpres),data=nr))
> summary(aov(MidAvg ~ Rpres*Ccon + Error(Subject/Ccon*Rpres),data=nr))
>
> With the first command, R doesn't report the main effect of Rpres.
> With the second command, it does (code & output below). It's not very
> important since the interaction is significant; I'm just surprised
> that commutativity doesn't hold.
>
> Thanks,
> Adam
>
>
> > summary(aov(MidAvg ~ Ccon*Rpres + Error(Subject/Ccon*Rpres),data=nr))
>
> Error: Subject
>           Df   Sum Sq  Mean Sq F value   Pr(>F)
> Ccon       1 13245765 13245765  17.767 0.002256 **
> Residuals  9  6709794   745533
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Error: Rpres
>      Df   Sum Sq  Mean Sq
> Ccon  1 38923433 38923433
>
> Error: Subject:Ccon
>            Df   Sum Sq  Mean Sq F value    Pr(>F)
> Ccon        2 16646448  8323224 239.589 3.334e-14 ***
> Ccon:Rpres  1   906946   906946  26.107 6.229e-05 ***
> Residuals  19   660053    34740
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Error: Subject:Rpres
>            Df Sum Sq Mean Sq F value  Pr(>F)
> Ccon:Rpres  1 645835  645835  9.5416 0.01295 *
> Residuals   9 609176   67686
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Error: Subject:Ccon:Rpres
>            Df  Sum Sq Mean Sq F value    Pr(>F)
> Ccon:Rpres  2 7636019 3818009  676.48 < 2.2e-16 ***
> Residuals  20  112879    5644
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Error: Within
>            Df  Sum Sq Mean Sq F value Pr(>F)
> Residuals 499 9862093   19764
>
>
>
>
>
>
> > summary(aov(MidAvg ~ Rpres*Ccon + Error(Subject/Ccon*Rpres),data=nr))
>
> Error: Subject
>           Df   Sum Sq  Mean Sq F value   Pr(>F)
> Rpres      1 13245765 13245765  17.767 0.002256 **
> Residuals  9  6709794   745533
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Error: Rpres
>       Df   Sum Sq  Mean Sq
> Rpres  1 38923433 38923433
>
> Error: Subject:Ccon
>            Df   Sum Sq  Mean Sq F value    Pr(>F)
> Ccon        2 16646448  8323224 239.589 3.334e-14 ***
> Rpres:Ccon  1   906946   906946  26.107 6.229e-05 ***
> Residuals  19   660053    34740
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Error: Subject:Rpres
>            Df Sum Sq Mean Sq F value  Pr(>F)
> Rpres:Ccon  1 645835  645835  9.5416 0.01295 *
> Residuals   9 609176   67686
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Error: Subject:Ccon:Rpres
>            Df  Sum Sq Mean Sq F value    Pr(>F)
> Rpres:Ccon  2 7636019 3818009  676.48 < 2.2e-16 ***
> Residuals  20  112879    5644
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Error: Within
>            Df  Sum Sq Mean Sq F value Pr(>F)
> Residuals 499 9862093   19764
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-- 
Francisco Torreira
PhD Candidate in Romance Linguistics
University of Illinois at Urbana-Champaign

https://netfiles.uiuc.edu/ftorrei2/www/index.html
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