# TukeyHSD with factorial ANCOVA

I'm trying to run post-hoc comparisons on a factorial ANCOVA model for a project of mine and I'm having some difficulty. First off, lets start with the experimental design:

1. Factors include: Focal plants infection status (2 levels), Competition (2 levels) and Damage (2 levels) crossed in a fully factorial design (i.e. 8 treatments)
2. Response variable is simply total biomass of focal plants.
3. Competitor plant biomass and Initial focal plant biomass are being included as continuous covariates.

The model that I ran was as follows:

model1<-aov(TotalFB~Focal*Competition*Grazing+TotalIB+TotalBB, data=dat2)


I realize I cannot use the TukeyHSD function as it does not handle continuous covariates. I have played around with the ghlt from the multcomp package and cannot seem to get it to work correctly.

I am specifically interested in the significant Focal*Grazing interaction and was wondering how I could see if there are significant differences within the levels of focal plant infection status but across the levels of grazing. Any help would be greatly appreciated. Feel free to ask me if you require additional information. Thanks

What you're describing is an interaction. If Focal:Grazing is significant that is the effect you want. It's in your model output and easily found using summary(model1).

In a 2 x 2 x 2 ANOVA there is never any need to run a post hoc test. As for what you're planning to do, how would looking at the individual levels of Focal across Grazing tell you anything other than what your ANOVA does? I'm guessing that what you were planning to do falls under the disparaged practices in Gelman and Stern (2006).

• My thinking was that there may be differences between infected and uninfected plants within one level of damage but not the other. That's why i figured post-hoc tests would be appropriate as they would allow the to see those differences immediately (it's hard to see by plotting because the scale of the response variable differs greatly across the levels of damage). I'm really just looking for a way to do post-hoc tests on interaction when there are multiple covariates present. If at all possible of course. Thanks for the reference also :) – James Feb 16 '14 at 2:38