[R-sig-ME] How to test if two gamm-predictions are significantly different?

[Chris Howden]

Rather than using 95% CI'S for the 2 curves U can try using a 90% CI
for them. If 2 90% CI'S don't overlap it's closer to a 5% t-test than
if 2 95% CI's don't.

But I think your other method for a 95% CI for the difference may be better.

Chris Howden
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On 30/05/2012, at 0:09, Karel Viaene <karel.viaene at ugent.be> wrote:

> Dear R community,
>
> A quick sketch of my situation:
>
> I have two continuous explanatory variables ("concentration" and "time")
> and a continuous response variable, "biomass".
>
> I've fitted a gamm model to these data using the package mgcv and want
> to predict at what concentration the biomass is significantly different
> from the control treatment (i.e. a concentration of 0) for a given point
> in time.
>
> I've done this by predicting the biomass for a series of 1000
> concentrations at a given point in time (using "predict"), constructing
> 95% confidence intervals for these predictions by adding and subtracting
> 1.96*SE and then selecting the lowest concentration where the two CI
> show no overlap.
>
> However I've realized that this technique is not adequate because two
> points can also be significantly different at the 5% significance level
> when the 95% CI do overlap and I want to calculate the lowest possible
> concentration. I've read some literature about this and am considering
> the following method:
>
> * Calculate the difference between the control (C0) and a predicted
> point (e.g. C1), thus C0-C1.
> * Construct a 95% CI for this difference by adding and subtracting
> 1.96*sqrt(SE0^2 + SE1^2).
> * Do this for all predictions.
> * Select the lowest concentration where the 95% CI does not include 0.
>
> Could you give me some feedback about this as I'm unsure if this method
> can be used for gamms. Any comments or suggestions are much appreciated.
>
> Many thanks in advance & kind regards
>
> Karel
>
> --
> Karel Viaene
> Ghent University
> Laboratory of Environmental Toxicology and Aquatic Ecology
> Plateaustraat 22
> 9000 Ghent, Belgium
> tel: +32 (0) 9 264 3779
>
>
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>
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