From: Ravi Varadhan <rvaradhan_at_jhmi.edu>

Date: Thu, 31 May 2007 12:09:33 -0400

Date: Thu, 31 May 2007 12:09:33 -0400

Your data is "compositional data". The R package "compositions" might be useful. You might also want to consult the book by J. Aitchison: statistical analysis of compositional data.

Ravi.

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan_at_jhmi.edu

Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

-----Original Message-----

From: r-help-bounces_at_stat.math.ethz.ch

[mailto:r-help-bounces_at_stat.math.ethz.ch] On Behalf Of jiho
Sent: Thursday, May 31, 2007 11:37 AM

To: R-help

Subject: Re: [R] Comparing multiple distributions

Nobody answered my first request. I am sorry if I did not explain my problem clearly. English is not my native language and statistical english is even more difficult. I'll try to summarize my issue in more appropriate statistical terms:

Each of my observations is not a single number but a vector of 5 proportions (which add up to 1 for each observation). I want to compare the "shape" of those vectors between two treatments (i.e. how the quantities are distributed between the 5 values in treatment A with respect to treatment B).

I was pointed to Hotelling T-squared. Does it seem appropriate? Are there other possibilities (I read many discussions about hotelling vs. manova but I could not see how any of those related to my particular case)?

Thank you very much in advance for your insights. See below for my earlier, more detailed, e-mail.

On 2007-May-21 , at 19:26 , jiho wrote:

> I am studying the vertical distribution of plankton and want to

*> study its variations relatively to several factors (time of day,
**> species, water column structure etc.). So my data is special in
**> that, at each sampling site (each observation), I don't have *one*
**> number, I have *several* numbers (abundance of organisms in each
**> depth bin, I sample 5 depth bins) which describe a vertical
**> distribution.
**>
**> Then let say I want to compare speciesA with speciesB, I would end
**> up trying to compare a group of several distributions with another
**> group of several distributions (where a "distribution" is a vector
**> of 5 numbers: an abundance for each depth bin). Does anyone know
**> how I could do this (with R obviously ;) )?
**>
**> Currently I kind of get around the problem and:
**> - compute mean abundance per depth bin within each group and
**> compare the two mean distributions with a ks.test but this
**> obviously diminishes the power of the test (I only compare 5*2
**> "observations")
**> - restrict the information at each sampling site to the mean depth
**> weighted by the abundance of the species of interest. This way I
**> have one observation per station but I reduce the information to
**> the mean depths while the actual repartition is important also.
**>
**> I know this is probably not directly R related but I have already
**> searched around for solutions and solicited my local statistics
**> expert... to no avail. So I hope that the stats' experts on this
**> list will help me.
**>
**> Thank you very much in advance.
*

JiHO

--- http://jo.irisson.free.fr/ -- Ce message a iti virifii par MailScanner pour des virus ou des polluriels et rien de suspect n'a iti trouvi. CRI UPVD http://www.univ-perp.fr ______________________________________________ R-help_at_stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.Received on Thu 31 May 2007 - 16:22:35 GMT

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