I have an issue I cannot solve myself and hope I can get some pointers here:
I have a RCB design with 10 tree species each replicated 5 times in 5 blocks. I classified all species according to their height and assigned them to 3 groups (A, B and C). Then, I chose 2 species from each group and take my measurements on 8 individuals of that species, making sure to get at least one individual from each block. That gives me sample size of 48. In the end I want compare the groups with each other. Then I take a measurement for each individual in autumn, winter and spring and call this variable 'season'.
My hypothesis is that the groups are different with respect to the measurement I took, as well as the season will change the outcome of the measurement, e.g. the measures will be 'ideal' in autumn, ' very low' in winter and 'high' in spring.
My data looks similar to this made up example:
mydat<-data.frame(species=rep(1:6, 3, each=8), block=rep(sample(1:5,replace=T,8), 18), individual=rep(1:8,18), group=rep(as.factor(sample(LETTERS[1:3],48, replace=T)),3), season=rep(as.factor(c('autumn','winter','spring')),each=48), outcome=rep(rnorm(144,10,1)))
Here is the model I fit:
But I guess this is not 100% correct, since I cannot treat block as a random factor in aov(), can I? How can I proceed here? I tried to do it with lmer but I don't really understand what I am doing there. I know how do add the random term but how can treat the season now as a repeated measures, so that I get the right total degrees of freedom of 47? Also can I run TukeyHSD() on a lmer model afterwards since I'd like to compare the means.
Thanks for any help!!