[R] Testing significance in a design with unequal but proportional sample sizes

[Michael Rennie]

Hi, all

I have a rather un-ideal dataset that I am trying to work with, and would 
appreciate any advice you have on the matter.

I have 4 years worth of data taken at 3 depth-zones from which samples have 
been taken at random. I am looking at the abundance of organism A between depth 
zones and across years, and am interested in the possible interaction of 
organism A distributions shifting between depth zones over time. Unfortunately, 
the sample sizes (n) differ between depth zones, as follows:

             Year
             1   2   3   4
Depth Zone 1 15  15  15  15
           2 10  10  10  10
           3 5   5   5   5

As such, I have a 2-way anova with unequal but proportional subclass numbers.
Sokal and Rolf (3rd Ed., 1995) have a nifty method of working out sums of 
squares in this type of scenario (page 357, 358, box 11.6).  However, they 
don't tell you how to calculate the probabilities, but refer the reader on to 
Snedecor and Cochran (1967), which I am on my way to consult shortly.

I'm curious as to whether there is a more straightforward method of coding this 
into R, rather than having to more or less customize my own statistical test.  
I found some discussions in the archives revolving around type III sums of 
squares from 2001, but the lack of consensus around the discussion did little 
to assure me that I should try this approach.

Anyone with advice, code or suggestions, I'd love to hear any of it.

Cheers,

Mike

-- 
Michael Rennie
Ph.D. Candidate
University of Toronto at Mississauga
3359 Mississauga Rd. N.
Mississauga ON  L5L 1C6
Ph: 905-828-5452  Fax: 905-828-3792