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1357RE: AI-GEOSTATS: Hypothesis Testing in a Spatial Framework

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  • Ted Harding
    Dec 20, 2003
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      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.


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      E-Mail: (Ted Harding) <Ted.Harding@...>
      Fax-to-email: +44 (0)870 167 1972
      Date: 20-Dec-03 Time: 16:33:43
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