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
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
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
- 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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