[R] In fact this is a Stats question, but...

[Peter Dalgaard]

Ben Bolker wrote:
>  <eesteves <at> ualg.pt> writes:
>
>   
>> Dear All,
>> I'me having (much) trouble understanding why it happened and answering  
>> a referee's comment to part of a submitted manuscript. I've tried to  
>> google for help but... I'm really confident that although this is a  
>> R-Help list someone can help me!
>>
>> I used R to do an ANCOVA w/ RNA/DNA as the dep var, sl as the indep  
>> var and gut (a factor w/ levels: prey and empty) as the covariate:
>>
>>     
>>> RNADNA.sl.gut<-lm(sqrt(RNADNA)~gut*sl,subset=gut!="Yolk-sac",data=cond)
>>> summary(RNADNA.sl.gut)
>>>       
>> The results from this are:
>>
>> (...)
>> Coefficients:
>>               Estimate Std. Error t value Pr(>|t|)
>> (Intercept)  0.856266   0.052252  16.387  < 2e-16 ***
>> gutPrey     -0.009568   0.092170  -0.104    0.917
>> sl           0.030575   0.004648   6.578 6.35e-11 ***
>> gutPrey:sl   0.002285   0.007313   0.313    0.755
>> ---
>> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>>
>> Residual standard error: 0.3312 on 1692 degrees of freedom
>> Multiple R-Squared: 0.05847,    Adjusted R-squared: 0.0568
>> F-statistic: 35.02 on 3 and 1692 DF,  p-value: < 2.2e-16
>>
>> (...)
>>
>> The question raised by referee is related to the "incompatibility" of  
>> the low r2 (0.057) and the high significance (p<<0.0001) of the model.  
>> I've interpreted/used this result in the following way: although  
>> there's a significant relationship between RNA/DNA and sl, it's very  
>> weak; besides, no gut effect on the relationship as been found!
>>
>> Sorry for the off-topic question but...
>>
>> Sincerely, Eduardo Esteves
>>
>>     
>
>    With 1696 data points, a relatively low r^2 can indeed
> give a high degree of statistical significance.  It's up to
> you to convince the reviewers that an increase of 0.03 in
> sqrt(RNA/DNA) per unit of sl (whatever
> that is) is indeed *biologically* significant and worth
> discussing ... 
Agreed, basically.

Notice though that, as I read it, the discussion already says that it is 
statistically significant but biologically irrelevant, which sounds 
sensible thing.

Another way of arguing that there is no contradiction is that the 
_expected_ r^2 in the absence of any true effects is 3/1695=.00177, more 
than 30 times less than the observed (which is, of course essentially 
what the F statistic is measuring).

> but the observed pattern (or one more
> extreme, in either direction) is certainly unlikely
> by chance if there were no effect of sl on sqrt(RNA/DNA).
> (Is sl "standard length" by chance? Is this a size correction?)
>
>   


-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
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