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

[Ben Bolker]

 <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 ... 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?)

  Ben Bolker