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

From: S Ellison <S.Ellison_at_lgc.co.uk>
Date: Thu, 29 May 2008 14:51:55 +0100

The low R2 says the model does not explain much of the variance. But the high significance arises from the very large number of degrees of freedom.
This is not an 'incompatibility'; just what happens with large dispersion, small effects and a very large number of observations.

But you clearly have a small, real effect that in practice would be barely detectable compared to 'natural' variation (or whatever is causing the residual variance), so there may well be a difference between 'statistically significant' and 'large enough to matter'. You may want to comment on the 'practical' significance of your effect.

Another - more serious? - worry would be whether your degrees of freedom are real or not. Do you really have about 1700 entirely independent observations? How many experiments did you really do?

Steve E

>>> <eesteves_at_ualg.pt> 05/29/08 1:00 PM >>>
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:

>

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

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