2 way ANOVA with possible pseudoreplication

Hi Natalie,

The fact that there's a non-linear relationship between frequency and power
does not matter if you treat power as a categorical variable rather than
continuous.

So like Steve suggested above:

Using the lme4 package

lmer(power~freq*short+(1|animal), data=...)

would seem a good starting point. Make sure that frequency and shortening
are treated as factors.

Alternatively the nlme package

lme(power~freq*short, random=1|animal, data=...)

Andy.

---------- Forwarded message ----------
From: Natalie Holt <fbsnch at leeds.ac.uk>
Date: 2009/5/1
Subject: Re: [R] 2 way ANOVA with possible pseudoreplication
To: Andrew Dolman <andydolman at gmail.com>

Hi Andy,

Thanks ever so much for your reply. I have attached the general layout of my
data with some more infomation on how it was collected. If you have any
ideas they would be much appreciated.

Many thanks,
Natalie

 So I?ve measured muscle power output (continuous) for 3 different shapes of
contraction cycle (25, 50 and 75% shortening) at 3 different frequencies. So
I have 9 possible combinations. I have several replicates of each treatment.
I randomized the order in which I did all 9 treatments and did as many as
possible on one animal before moving on to the next. There are between 1 and
4 treatments on any one animal. There is only ever 1 replicate of any 1
treatment on a single animal.

I could do a mixed effect model however it is well established that the
power frequency relationship is non-liner with an optimum value at around 5.
I believe it is possible to do a non-linear mixed effects model. However I
do not have an equation describing this non-linear relationship. Is this
still possible to do??

Quoting Andrew Dolman <andydolman at gmail.com>:

 Hi Natalie,