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

From: Ben Bolker <bolker_at_ufl.edu>
Date: Thu, 29 May 2008 13:03:56 +0000 (UTC)

 <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



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