[R-sig-eco] Doing repeated measures on a randomized block design

[Richard Boyce]

I’m measuring chlorophyll fluorescence (FvFm), my measured variable, on N and S exposures (treatment variable) of 4 red cedar trees. Here’s what the beginning of the data file looks like: 

head(perm.fvfm).

  Tree Exposure   Date  FvFm
1    1        S 13.Feb 0.775
2    1        N 13.Feb 0.795
3    2        S 13.Feb 0.737
4    2        N 13.Feb 0.759
5    3        S 13.Feb 0.615
6    3        N 13.Feb 0.712

If I were just doing this one time, this would be a randomized block design, where trees were the blocks (random variable) and exposure was the treatment variable (fixed variable). Actually, since there are only two treatment levels, it would be a paired t-test.

However, I’ve repeated this on many dates (18 so far this year). So this also requires a repeated-measures design, with trees as subjects. 

Repeated-measures, however, usually have time (date) as a within-subject variable and then some other treatment that is a between-subjects variable. I don’t have have a between-subjects variable, however, as all subjects (trees) get both levels of exposure and all levels of time (date).

I’ve searched the web, but there is not a lot out there for this kind of design. It looks like lm, lme, lmer, and permuco in R might all work, but advice for how to set up the Error() or random variable designations are confusing and sometimes contradictory. Any advice would be much appreciated!

Thanks,
Rick Boyce