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AI-GEOSTATS: Hypothesis Testing in a Spatial Framework

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  • Warren Schlechte
    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
    Message 1 of 3 , Dec 19, 2003
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      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.

      Thanks,

      Also, any suggestions for sample sizes and sample distributions (regular,
      clustered in treatment and non-treatment areas) would be appreciated.



      Warren Schlechte
      HOH Fisheries Science Center
      HC 7 Box 62
      Ingram, TX 78025
      Phone 830.866.3356
      Fax 830.866.3549


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    • Isobel Clark
      Warren We have had some success with a sort of hypothesis test in this regard. I had a task some years back to prove that the first area mined in a deposit was
      Message 2 of 3 , Dec 20, 2003
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        Warren

        We have had some success with a sort of hypothesis
        test in this regard. I had a task some years back to
        prove that the first area mined in a deposit was not
        significantly lower than could be expected by chance
        selection.

        We used a combination between 'between block variance'
        and a sort of cutoff analysis. It helps if your
        samples have a simple distribution like Normal or
        lognormal. Basically, you work out the probability
        that a block of a certain size would have a value that
        low (in our case). It is, effectively, a simple
        application of volume/variance. Chapter 3 in my 'old'
        book which can be read (or downloaded) at
        http://uk.geocities.com/practica.htm

        Isobel

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      • Ted Harding
        ... The issues you raise occur also in classical agricultural field trials, and you might like to consider using classical field experiment techniques. For
        Message 3 of 3 , 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.


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

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