st: RE: R: choice of ANOVA for an ecological experiment

["Lachenbruch, Peter" <Peter.Lachenbruch@oregonstate.edu>]

One reason might be that MANOVA is notoriously sensitive to non-normality.  The number of individuals remaining is likely not to be normal, weight might be, not sure about size - is it height or body volume or something else?  At any rate, one might compute a permutation test on T-squared values to get a valid test.

Tony

Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Carlo Lazzaro
Sent: Monday, January 31, 2011 12:17 AM
To: statalist@hsphsun2.harvard.edu
Cc: 'Jacob Felson'
Subject: st: R: choice of ANOVA for an ecological experiment

Jacob wrote:

"The outcome variables include the number of individuals remaining, the
weight of the individuals remaining, and the size of the individuals
remaining."

Just out of curiosity: why, with three outcomes, don't you consider a MANOVA
(see -  help manova - in Stata 9/2 SE)?

Kind Regards,
Carlo
-----Messaggio originale-----
Da: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Jacob Felson
Inviato: domenica 30 gennaio 2011 21.00
A: statalist@hsphsun2.harvard.edu
Oggetto: st: choice of ANOVA for an ecological experiment

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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