In article <[EMAIL PROTECTED]>,
jersey <[EMAIL PROTECTED]> wrote:
> Background: I am an ecologist working with intertidal
> community structure data. My data is characterised by high
> non-normality and lack of equal variance between samples.
Be careful with this. Non-normal abundances distributions
and unequal variances among sites doesn't tell you much about
what is happening at the community level.
> am currently exploring various non-parametric multivariate
> techniques, such as non metric multidimensional scaling, and
> the suite of statistic tests applicable to such a technique.
> (For those of you not familiar with nMDS, it is an
> ordination technique that arranges points in space that are
> determined from a similarity matrix derived from say, the
> Bray-Curtis method. In actuality, nMDS uses the RANK
> similarity, and thus eliminates the need for many
> assumptions about the original data set.
Consider an metric index rather than the semimetric Bray-Curtis.
The apparent advantage of nonmetric multidimensional scaling
over metric scaling (i.e., Torgerson scaling or Gower PCoA)
often has a lot to do with the semimetric nature of the Bray-
Curtis similarity. A similar metric index will often yields
nearly identical non-metric and metric ordinations. See
Legendre & Legendre's Numerical Ecology (1st or 2nd ed)
for many metric indices.
>
> My data is comprised of the following: percent cover data
> about seaweeds in the intertidal. This is determined by
> laying a 8 square quadrats on the beach (at 6 different
> sites - 8 quads at each), then sampling for a percent cover
> value of each species present. So, I have 8 replicate
> samples at each of six sites.
>
> Anyways, my question is the following: Is it preferable to
> POOL the 8 samples, or to average the samples? What are the
> pros and cons of each scenario? I'm aware there is a loss of
> power if you pool the samples, but does that make a
> difference in this situation.
Discussion of power isn't really appropriate unless you've
proposed your statistical model. If you want a qualitative
look at the differences among the sites, plot the individual
replicates. Neither pool nor average. If you want to
test for differences among sites, consider using Excoffier's
AMOVA (designed for genetic distance indices, but an ecological
metric index <not Bray Curtis> would do fine.
Legendre & Anderson, Ecol. Monogr. 1999 provide a quantitative
method for testing for differences among sites with Bray Curtis
and redundancy analysis. You would neither pool nor average
to use this method.
With the individual replicates, you can create bootsrapped or
jackknifed averages and plot these to show how different the
groups are (see the back of Greenacre's Correspondence analysis
book for examples of this method).
--
Eugene D. Gallagher
ECOS, UMASS/Boston
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