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st: choice of ANOVA for an ecological experiment


From   Jacob Felson <felsonj@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: choice of ANOVA for an ecological experiment
Date   Sun, 30 Jan 2011 15:00:00 -0500

Hello,

I am wondering whether anyone might be able to advise me about the
best choice of ANOVA to analyze the results of an ecological
experiment.  In each of eight ponds, a certain number of various
species were put into enclosures that were randomly assigned to a set
of four predator conditions.  The four randomly assigned predator
conditions were: no predators, 8 predators, 16 predators, and 24
predators.  Each predator condition was assigned to 3 replicates.   So
the total number of enclosures was: 8 ponds x 4 predator conditions x
3 replicates = 96.  The outcome variables include the number of
individuals remaining, the weight of the individuals remaining, and
the size of the individuals remaining.

This experiment appears to follow a split-plot design. Is this
correct?  That is, the error of the pond effect is distinct from the
error of the predator condition effect.   The sum of squared error for
the pond would be equal to the sum of squares for the predator
condition.  The sum of squared error for the predator condition would
be equal to the residual sum of squares.

The predator condition variable is called density, and the outcome
variable is number of survivors.  If all of this is accurate, then I'm
guessing that a simple model might be:

anova survivors pond / density | pond /


Is this correct?  One further issue is that the ponds are fixed, not
random.  Unlike the textbook split-plot design, a whole-plot has not
been randomly assigned to ponds.  Instead, there are simply 8 ponds,
within each of which individuals were collected and placed in
enclosures with varying predator conditions.


I would very much appreciate help on this issue!


Sincerely,
Jacob Felson
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