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.


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