Well, it's clearly not pseudoreplication if it's not replication! But the observations within animal could well be associated. You seem to have a straightforward experiment with multiple treatment combinations on multiple subjects.
You could do several things. The most obvious is probably to consider 'animal' (or 'subject') as a random effect. You can do that with lme or lmer: lme(y~trt1*trt2, random=1|animal, data=...) or lmer(y~trt1*trt2+(1|animal), data=...) If you have a balanced design (all treatment combinations on all animals) and the treatments can reasonably be considered as fixed effects, you have a blocked design that can be analysed with a model of the form y~trt1*trt2+block (it is, under those circumstances, valid to compare treatment effects directly with the residual term; the 'block' effect just drops out as long as it's additive) or, using aov, with summary(aov(y~trt1*trt2+Error(block), data=.. )) That would make me nervous if different animals were given different sets of treatment combinations unless you'd been really clever and used a balanced incomplete block design (you'd certainly know if you had planned it that way!) The other obvious questions are whether treatments were applied in a consistent order, as a cross-over design or in randomised order, and whether there is carry-over. Carry-over and the related cross-over designs are distinctly outside my experience, though; chemists can normally ignore carry-over. I assume there's a biostatistician in the house... ... and of course I'm naively assuming that the treatments are factors and that you aren't studying dose-response curves or other things that need gradient terms. If you are, I suppose you'll want to look at Pinheiro and Bates rather carefully... Steve e >>> nat_h <fbs...@leeds.ac.uk> 29/04/2009 13:43 >>> Hi, I have an experiment with 2 independant factors which I have been trying to analyse in R. The problem is that there are several data points recorded on the same animal. However, no combination of treatments is repeated on the same animal. All possible combinations of treatments are done in a random order with as many points as possible being done on 1 animal before moving onto the next. The suggested way to remove pseudoreplication is to average the points from the same animal. However, as my measures on the same animal are of different treatment combinations so this makes no sense. It is also suggested that as I have random and fixed effects I should use a mixed effects model. However, given that my independant variables are factorial I am not sure how to incorporate this. I would be very grateful for any advice on methods of getting round this problem or whether I have sufficiently accounted from my none independant measures experimentally. Many thanks, Natalie -- View this message in context: http://www.nabble.com/2-way-ANOVA-with-possible-pseudoreplication-tp23295845p23295845.html Sent from the R help mailing list archive at Nabble.com. ______________________________________________ R-help@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}} ______________________________________________ R-help@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.
