# Multivariate analyses

Richard Jensen rjensen at SAINTMARYS.EDU
Fri Jul 13 08:46:15 CDT 2001

```First, getting the results you like is not a suitable criterion for evaluating

Second, the arcsine transformation is used to extend the tails of the
distribution so that it approaches normality.  If that is your goal, then go
ahead and use it.

Third, if you want each proportion to contribute equivalently to relationships
in ordination (PCA) space, then standardize them to mean=0.0 and variance
=1.0.  And, use the correlation matrix, not the covariance matrix, for
extracting eignevalues (this will reduce the dominance of those characters that
have uniformly (perhaps disproportionately) large values across the data set.

Fourth, when using proportions (percentages), another problem arises:  there is
no longer independence among variables - if I have ten percentages, once I
enter the first 9, the last is not free to vary.  This dependence can create
problems in multivariate analyses.

Have fun!

Guido Flamini wrote:

> Dear Taxacomers,
>
> I have a problem with the multivariate statistical analyses of my data. I
> want to perform a PCA and a Cluster Analysis on chemical data (composition
> of the essential oils from different collecting places).
> Unfortunately each sample contain values ranging   between 0.01% to 96%.
> So, when I perform the calculations, nearly all the variance is explained
> by the first axis and I am not able to obtain the dispersion of the data on
> the other axis. I have tried to convert my data using the arcsin function,
> but the graphs are still ugly.
> Can you give me some suggestions?
> Is it correct to discard the 90% values from all the samples and reconduct
> to 100% the other percentages and then perform the analysis with these new
> data? (moreover, in this way I obtain the interpretation that I like!!).
>
> Thank you in advance,
>
> Guido
>
> *******************************************
> Dr. Guido Flamini
> Dipartimento di Chimica Bioorganica e Biofarmacia
> Via Bonanno 33, 56126 Pisa, Italia
> Tel: +3905044074; Fax: +3905043321
> e-mail: flamini at farm.unipi.it
> *******************************************

--
Richard J. Jensen              TEL: 219-284-4674
Department of Biology      FAX: 219-284-4716
Saint Mary's College         E-mail: rjensen at saintmarys.edu
Notre Dame, IN  46556     http://www.saintmarys.edu/~rjensen

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