🚀 go-pugleaf

In article <Pine.OSF.3.96.980518070912.21248B-100000@axe.humboldt.edu>,
Curt Seeliger writes:
|> Folks,  I'm currently at a loss.  I'm developing vegetation types using
|> standard hierarchic clustering techniques (Euclidian distance, Ward's
|> method).  I'm testing these groups using Multiple-Response Permutation
|> Procedures, which estimates the likelyhood of finding tighter clusters. 
|> MRPP results in p-values ranging from 0.0002 to 0.90 for clusters derived
|> in this manner, depending on how I transform the data matrix before
|> clustering. 
|> 
|> My problem is that groupings which are statistically significant do not
|> appear to be of any ecological meaning.  I'm fairly boggled by these
|> results, as I would assume that any sort of clustering method would always
|> produce groupings which are at least better than random (p < 0.50), but
|> this does not seem to be the case.

If you are using the same distance matrix for the cluster analysis
and the MRPP, and your data set is not tiny, then you should indeed
get wildly "significant" results. I would be surprised to see a
p-value over .0001. If you are using different distance matrices,
anything could happen. Perhaps weird things could also happen if
you used an extremely non-Euclidean distance matrix; for example,
something that had gross violations of the triangle inequality.

-- 

Warren S. Sarle       SAS Institute Inc.   The opinions expressed here
saswss@unx.sas.com    SAS Campus Drive     are mine and not necessarily
(919) 677-8000        Cary, NC 27513, USA  those of SAS Institute.

Thanks for the reply Warren.  I'm making hierarchical clusters based on
euclidian distances and linking using Ward's method, so I don't think I'm
warping my space.  I think my transformations of the raw matrix are also
reasonable.  On the otherhand, I'm unversed in the triangle inequality you
mentioned, so I can't comment on this. 

I did get a chance to run the question by a local statistician, who
thought that the zeros in my data (about 87% of which is zero) is causing
the test statistic to degrade i.e. takes on only a few values, so that
only extreme cases turn out to be significant.  An example of this she
gave was testing on a binomial distribution with only 4 points - in this
case only 1 outcome is 'significant'.  Unfortunately, she couldn't
recomend a better means of testing veg clusters, stating the well known
truth that clustering is an art, and generally not subjected to testing.

cur

On Tue, 19 May 1998, Warren Sarle wrote:

> 
> If you are using the same distance matrix for the cluster analysis
> and the MRPP, and your data set is not tiny, then you should indeed
> get wildly "significant" results. I would be surprised to see a
> p-value over .0001. If you are using different distance matrices,
> anything could happen. Perhaps weird things could also happen if
> you used an extremely non-Euclidean distance matrix; for example,
> something that had gross violations of the triangle inequality.
>