On 19-Dec-03 Warren Schlechte wrote:
I would like some references for the following type design.
Consider an area, much of which will not be treated. However,
small sections will be treated, and if the treatment works, the
density of an organism will be lessened. The basic question is
What is the likelihood that the low-density areas would have
happened by chance, in the absence of the treatment? If this
likelihood is very small, then we could suggest the treatment
is the reason we have lower densities in these areas. Note,
there could be a gradient with edge effects.
How would one go about making a decision rule for testing whether
the treatment was effective?
My guess is that the non-treated areas will be quite patchy.
Our hope is that in the treated areas, if the organism isn't
completely eliminated, the density will be considerably less.
[...]
Warren Schlechte
HOH Fisheries Science Center
The issues you raise occur also in classical agricultural field
trials, and you might like to consider using classical field
experiment techniques.
For instance, you could select a set of what you call sections
as plots, and randomly allocate half the plots to treatment/control.
Then, if you are mainly interested in a hypothesis-test type of
inference (which your statement suggests is the case), the randomisation
distribution of treatment/control comparison would give you a valid
result. If you can select well-separated plots so that they do not
interfere with each other, this may be all you need.
If gradients are a serious concern, you could make your experiment
more sensitive by identifying strata to use as blocks, within
each of which you expect to find less variation due to this cause.
Then you randomise on plots chosen within each block, and again
make use of the appropriate randomisation distribution.
However, if you need to make a more quantitative inference,
such as producing estimates with confidence intervals (or even
merely doing a t or F test), then you may need to take account
of possible spatio/temporal correlations on order to estimate the
variances of your estimates, and this is not so easy. Again, there
is a good deal of literature about this in the domain of agricultural
experimentation.
Given where you are writing from, it seems you may be looking
at bodies of water. You do not say whether these are rivers/canals
(approximately linear structures), or lakes or seas (2, or even 3,
dimensional). This would affect the type of layout you would
choose.
In canals or lakes, the water may be relatively static, so the
treatment is more likely to remain within the plot, while in
rivers or seas, the presence of currents may disperse it.
The latter complication, as a serious issue, is rare in agricultural
experiments. However, it may perhaps mainly influence your choice of
procedure for measuring the concentration of the organism, though it
could also severely complicate your estimation of variability.
You do not say what the treatment is, by the way.
I hope these thoughts help a bit.
Best wishes,
Ted.
E-Mail: (Ted Harding) [EMAIL PROTECTED]
Fax-to-email: +44 (0)870 167 1972
Date: 20-Dec-03 Time: 16:33:43
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