I am trying to fully understand the trade-offs between the two analyses and
if one method is superior in the case of only two observations per random
effect.

Full experimental set-up: I have 6 field plots and three of them receive a
treatment (applied to the plot) and three serve as controls.  In each plot,
I have measurements from 2 individual plants.  Since this is a desert
ecosystem, the variance within a plot is quite large compared the the
variance from plot to plot.

The 'old-school' analysis method would be to calculate plot average for each
plot and do an ANOVA using those plot means as data and accept that my
inference is only at the plot level.  If I go with a fancy mixed model
approach, my inference is on the level of an individual plant, and I get an
estimate of within plot variability.

But the rub is this:  the plot means approach gives me a fairly significant
treatment effect (p = .014) while the mixed model approach gives me a
non-significant result (p=.34).  My feeling is that trying to estimate the
random effect (in addition to the treatment effect) is taking a large amount
of our statistical power in a relatively data poor problem.  I did a quick
simulation study and it appears that in the case of high within plot
variability and a small number of observations per plot, the mixed model
approach has substantially reduced power compared to the plot means

>From a scientific point of view, we actually don't mind making inferences at
the plot level as we are primarily concerned with landscape effects of the
treatment.

At this point I think that the plot means approach is the best choice, but I
want to make sure that I'm not missing anything.

Derek Sonderegger

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