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
<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
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:>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 ______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ******************************************************************* This email and any attachments are confidential. Any use...{{dropped:8}}