[R] effect size

[David A. van Leeuwen]

Prof Brian Ripley wrote:

>I think you want to call summary.lm on the aov object, but this depends on 
>what you mean by `effect size'.
>
>  
>
I guess this is what we wanted.

>Given that, I wonder if you are used to standard terminology.
>  
>
No, I am not, unfortunately.  We are doing lots of statistical analyses, 
using R because it is fab and such, but reviewers are looking for SPSS 
output using terminology that we can't find in the R bundle---but our 
general impression is that R does things way more cleverer and better 
than click-until-you-seed-red-signifficant-effect tools found elsewhere. 

Reactions on r-help caused us to request for a better specification of 
the `effect size' that people wanted, and it turns out to be
$$ SS(effect) / \Sum SS $$ (SS being sums-of-squares).  To me, a simple 
physicist, that sounds as `the fraction of explained variance' by the 
factor.  Looking at the formulas in help(summary.lm) is seems that 
summary.lm()$r.squared  is exactly what we want (for a one-way aov).

Is there a way to quickly tabulate the expression $$ SS(effect) / 
(\Sum_{effects} SS(effect) + SS(residuals)) $$ ?

The numbers are practically there in the summary.aov() table.  Only the 
grand total SS needs to be calculated.

>For example, R does have an effects() function, and that might be what you 
>want.
>
>  
>
I don't really understand the effects()---it must be related to 
coefficients() but it obviously is different. There is 
model.tables.aov() which is also enlightening, but I think it is really 
the $ r^2 $ that we were looking for (our reviewers calling this an $ 
\eta^2 $---if that clarifies things).

Thanks,

---david

>On Mon, 15 Mar 2004, David A. van Leeuwen wrote:
>
>  
>
>>Having searched google '[R] aov effect size' without any results I 
>>wonder if I not completely miss something. 
>>
>>Is there any R function that calculates the effect size of an AOV's main 
>>effect or interaction effect?  It should be related to the F's and the 
>>degree of freedom of the error, but the multitude in numbers in aov() 
>>baffle me a bit.
>>    
>>