[R] another aov results interpretation question

[Spencer Graves]

	  I commend you to (a) the recent article by Doug Bates on "Fitting 
nonlinear mixed models in R" pp. 27-30 in the latest issue of "R News" 
available from "www.r-project.org" -> Newsletter and (b) Doug's book 
with Pinheiro (2000) Mixed-Effects Models in S and S-PLUS (Springer).  I 
suggest you try the same analysis using in "lmer", library(lme4), and 
"lme", library(nlme), with method = "ML", as explained in Pinheiro and 
Bates.  If you have trouble with this, please post another question on 
this, preferably using either a standard data set distributed with R or 
one of the standard packages or a very simple made-up data set with very 
few observations that you can distribute with your question in a short 
sequence of R commands illustrating something you tried that either 
didn't work or that gave results you don't understand.  I can't do much 
more with the example you've provided below, because I don't know how to 
access the your data.  (And PLEASE do read the posting guide! 
http://www.R-project.org/posting-guide.html if you haven't already.)

	  hope this helps.
	  spencer graves

RenE J.V. Bertin wrote:

> Hello,
> 
> I'm trying to understand how to interpret the differences in results between two versions of a 2-factor ANOVA with (slightly?) different models, of an observable y, a within-subject factor 'indep' and a grouping factor 'cond' (and a subject 'factor' Snr):
> 
> 
>>summary( aov( y~cond + indep + Error(Snr/indep) ) )
> 
> # example results:
> Error: Snr
>           Df Sum Sq Mean Sq F value Pr(>F)
> cond       1  103.1   103.1   1.425  0.248
> indep      5  159.8    32.0   0.442  0.813
> Residuals 18 1301.6    72.3               
> 
> Error: Snr:indep
>            Df Sum Sq Mean Sq F value Pr(>F)  
> indep       5  20.81    4.16   3.167 0.0104 *
> Residuals 111 145.89    1.31                 
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> 
> Error: Within
>            Df Sum Sq Mean Sq F value Pr(>F)
> Residuals 137 22.178   0.162               
> 
> 
>>summary( aov( y~cond * indep + Error(Snr/indep) ) )
> 
> # example results:
> Error: Snr
>            Df Sum Sq Mean Sq F value Pr(>F)
> cond        1  174.6   174.6   1.689  0.213
> indep       5  201.9    40.4   0.391  0.848
> cond:indep  5  124.0    24.8   0.240  0.939
> Residuals  15 1550.8   103.4               
> 
> Error: Snr:indep
>             Df Sum Sq Mean Sq F value Pr(>F)    
> indep        5  73.16   14.63   8.601  5e-07 ***
> cond:indep   5  21.32    4.26   2.507 0.0336 *  
> Residuals  125 212.64    1.70                   
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> 
> Error: Within
>            Df Sum Sq Mean Sq F value Pr(>F)
> Residuals 464  507.5     1.1               
> 
> 
> I would like to understand a bit better what the cond:indep line under the second Error:Snr:indep can mean. If I understood correctly, this represents some "higher-order" interaction, but not a real indep/cond interaction. What I also do not grasp is why the indep effect's F and significance is so different between the two models.
> Finally, what does it mean when significant effects are listed under the Error:Within line?
> 
> Is there a good resource available (web, or if not printed) which discusses this kind of question in a way accessible to non statisticians? The last time I checked, manuals like "R for Psychologists" do not really enter into this level of detail...
> 
> Thanks very much in advance,
> R. Bertin
> 
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