On 30 Nov 1999, Richard M. Barton wrote:
> A biology student came to me with a data analysis situation that I
> wasn't sure how to deal with. Sound advice would be appreciated.
> Scenario:
> Ben has a number of 1 meter square plots where he placed
> one or more seeds:
> 50 plots with 1 seed
> 10 plots with 25 seeds
> 10 plots with 50 seeds
>
> He replicated that design with four species of seeds.
> He visited the plots every day for a week to count the number of
> seeds remaining.
And was this possible to do without disturbing the seeds?
They couldn't have been planted very deep, or else Ben was using
transparent soil, which rather sounds like a contradiction in terms.
But if the seeds were disturbed in the process of counting them, one
wonders what point, if any, remains to the experiment.
What (presumably natural) mechanisms would have removed seeds
from the plots, so that there would be fewer seeds to be found on
successive days? If more than one mechanism exist, (a) can one
distinguish between them and (b) would the distinction not be important?
> So the questions of interest are:
> a) Does density have an effect on seed survival?
> b) Does species have an effect on survival?
> c) What does the data look like over time?
These sound suspiciously like questions one thought one might be able to
ask in a statistical analysis, as surrogates for the questions one
really wanted to ask but couldn't figure out how to answer. So, what
were the _real_ questions?
> We considered modelling/analyzing the data in two ways (using SAS):
>
> 1) with seed as the unit of analysis, using Proc Lifetest to generate
> survival curves.
I'm unfamiliar with SAS and Lifetest, so cannot usefully comment;
nor is it clear why the non-independence you worry about below would
constitute an impediment.
> The problem: for medium and high density plots, seeds would not
> seem to be independent.
Do you intend to imply that for the low density plots the seeds _were_
independent? In what sense is independence (or non-) conditional on
density? If the seeds were acorns and the observations were made over a
period of ten years, one might well expect seedlings to be influenced by
nearby "sibling"-competitors. But over 1 week?
And, now I come to think of it, over so short a period, what does
constitute survival/non-survival? Wouldn't seem to be enough time for
non-survivors to be rotting enough to tell that they'd died...
> 2) with plot as the unit of analysis, using GLM to get a mixed model,
> where time is a repeated measure and density and species are
> between groups factors.
> Problem: low density (1 seed) plots have a dichotomous outcome,
> so much of the data is non-normal.
I don't see why this is a problem. (And if it IS a problem, I don't see
why it isn't even more of a problem (a fortiori) when you take seed as
the unit of analysis (approach 1 above); but as I said I'm unfamiliar
with the Lifetest procedure...)
Anyway: The hypothesis being tested deals with mean survival
numbers (or, equivalently, survival rates), not with the survival of any
particular seed. For all three levels of density, to make the outcomes
quantitatively comparable, you must be converting the raw number of seeds
observed to a survival rate. For the 1-seed plots, just as for the
others, you are observing a proportion, which is surely approximately
normally distributed.
But you have 50 such plots, where there are only 10 each of the
medium- and high-density plots; so treat them as 10 plots each of 5
seeds, only they're 5-square-meter plots instead of 1-sq-m plots.
So far as you've yet mentioned, your only measure of density is the three
different categorical levels. You might later like to present results in
terms of number of seeds per square meter, in seeking a quantitative
description of the qualitative results found in ANOVA, but you surely can
put that off until you _have_ some ANOVA results!
-- Don.
------------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
348 Hyde Hall, Plymouth State College, [EMAIL PROTECTED]
MSC #29, Plymouth, NH 03264 603-535-2597
184 Nashua Road, Bedford, NH 03110 603-471-7128
