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

[Tom Blackwell]

Michael  -

Since your email says that the data are "the abundance of organism A",
I am moved to ask whether the abundances are integer counts, sometimes
zero, and whether the "samples" are perhaps dips of a net, or the
contents of a filter after pumping a certain amount of water through it,
or something akin to 'quadrats' in forest sampling.

If the abundances are integer counts, then it would be natural to
analyze the data with a log-linear model using R's  glm()  rather
than with anova.  Snedecor and Cochran is an excellent book, but for
this purpose Venables and Ripley's MASS (Modern Applied Statistics
with S and S-plus) might be better.

-  tom blackwell  -  u michigan medical school  -  ann arbor  -

On Thu, 4 Mar 2004, Michael Rennie wrote:

> 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
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