[R] 2 way ANOVA with possible pseudoreplication

[S Ellison]

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 <fbsnch at 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
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