[R-sig-ME] Interpreting 2-way aov interaction

Brandstätter Christian bran.chri at gmail.com
Fri Feb 13 09:58:08 CET 2015

Dear community,

I encountered a problem with an experimental setup; we had one treatment
step and a few mixing steps in a laboratory experiment.
The data was stored in a usual dataframe (df as below, long format) with
the categorial variables as factors left.
We could clearly observe an interaction between mixing (f2) and treatment
(meas) by applying aov as in the (extreme) example below.

f2 <- factor(c(rep(seq(1,4),each=20)))
meas <- factor(c(rep(1,18),c(rep(2,44),c(rep(1,18)))))
res <- 15*as.numeric(f2)*as.numeric(meas)
df <- data.frame(f2,meas,res)

My question is, would there be a way to somehow "exclude" the variation
from the mixing step?
Would it be correct to include an error term as follows:

And would that mean, what I am thinking it does: the treatment is still
significant, even if the variation through mixing (f2) is considered?
One obvious alternative I could think of would be to separate the mixing
steps, but of course in the experiment there were a few of them.

Another option would be a lmer-model I found, but the interpretation of the
output is harder to interpret:
mix.model = lmer(res ~ meas + (1|f2),data=df)

I am unfortunately not very familiar with mixed anova-setups and available
sources usually mention rather catchy examples from psychology which I find
hard to translate for this case.

Best regards
Brandstätter Christian

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