re: st: choice of ANOVA for an ecological experiment

["Airey, David C" <david.airey@vanderbilt.edu>]

.

A split plot for the simplest design might have sex as the between
subject factor and another factor repeatedly measured on each person as the
within subject factor. Here each person is a whole plot and the 
repeated measures are the split plots. Sex is often also treated 
as a whole plot fixed effect factor in this model. Subject is nested 
in sex, but crossed with treatment, leading to a mixed ANOVA.

anova outcome sex / subject|sex treatment sex#treatment /, repeated(treatment)

That is the Stata command for the simplest split plot design.

You could also find more on this syntax here:

<http://www.stata.com/support/faqs/stat/anova2.html#wsanova2>

and in the Stata manual for nested and mixed designs.

Your design sounds like a oneway ANOVA in each pond, if you use 
summary stats for each enclosure rather than measures on each 
prey animal (e.g., eaten/not eaten, weight, size). I guess the
enclosure is the experimental unit here, so using summary stats is 
OK. But you want an omnibus test across ponds.

This is kind of confusing, because pond is a fixed effect in your 
words, and you did not randomize fish to the ponds; you randomized 
density of predators to enclosures of fish native to each pond.

Certainly, fish are then nested in ponds, and at some level, you 
crossed fish with density of predation.

-Dave


> 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!



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