split-split-plot design and adonis

Kay,

Seems like a clever and reasonable approach, but I have a couple of
comments/questions.

First, it seems that with this approach, you cannot evaluate the sediment
x hydrology, the sediment x depth or the sediment x hydrology x depth
interactions. I'm not sure if Arnaud is interested in these interactions,
but one generally is in most split-plots.

Second, I tried your approach with my own data (which is just a split
plot). Perhaps I did it wrong, but the resulting anova seems wrong to me.
The residual df are too high, I think because the analysis is not taking
the strata variation and its df (in Arnaud's case, the site effect) out of
the error term.

Here's a suggestion. First, simplify Arnaud's design to a split plot
(removing the depth effect. In the species file, this will entail summing
abundances across depths for each site x hydrology combination.

Use a design predictor file as originally described by Arnaud (except
without the depth factor); I.e., site1, site2, ... site9, three sediment
types - sed1, sed2, sed3, and two hydrology types - dry, wet.

To analyze the split-plot effects, I would suggest the following

Adonis(community ~ sediment*hydrology + site, strata = site)

You should get an anova table that will give you the sediment main effect,
the hydrology main effect, the sediment*hydrology interaction, the site
effect (probably not of interest), and residual error. ***Note that the
sediment main effect is garbage here because it is tested with the
residual error term, which is not the correct error term and must be
disregarded; Your approach to getting it seems reasonable to me.*** The
hydrology effect and the hydrology*treatment interaction should be
correct, however, because both are tested with the residual (I.e.,
split-plot) error term.

For the split-split plot effects, you need to make a term equivalent to
the site x hydrology term (as described by Arnaud). That will be the
strata effect for the split-split plot (but not for the split-plot
effects). In this case, you'll use a species dataset in which the
abundances are not summed across depths for each site x hydro combination.
This is identical to the original species data file. In this case, I
suggest the following analysis:

Adonis(community ~ sediment*hydrology*depth + site_hydro, strata =
site_hydro).

Here, you disregard all results except those of depth and its interactions
with sediment and/or hydrology.

Another possible way to test the sediment main effect would be to create a
new species data file in which abundances are summed across all
hydrologies and depths for each site. The adonis statement is then simply:

Adonis(community ~ sediment)

I'd appreciate any feedback.

Thanks,
Steve

J. Stephen Brewer 
Professor 
Department of Biology
PO Box 1848
 University of Mississippi
University, Mississippi 38677-1848
 Brewer web page - http://home.olemiss.edu/~jbrewer/
FAX - 662-915-5144
Phone - 662-915-1077

split-split-plot design and adonis

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