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RE: AI-GEOSTATS: Summary: Large sample size and normal distribution

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  • Ruben Roa Ureta
    ... is a common argument in simulation experiments, that because you can do an infinite number of replicate simulations, somehow the differences detected are
    Message 1 of 5 , Aug 11, 2003
      > Hi,
      >
      > I'm not sure i agree with the idea that a test can be too powerful. This
      is a common argument in simulation experiments, that because you can do an
      infinite number of replicate simulations, somehow the differences
      detected are not real. In fact, the differences are real. They may not
      be biologically (or geologically or whatever field you are in)
      significant, but they are still real. That is why it is better to decide
      first on the magnitude of difference that you consider significant.

      The null hypothesis is always false although it might be false by a very
      small quantity, that is the trivial fact that the very large sample size
      illustrates in the common test of significance. The conclusion to be drawn
      from this is not that we must set in advance the amount of difference that
      we would find significant (a rather restrictive strategy which will be
      violated very often because it is nonsensical), but rather that the only
      sensible strategy is to compare hypotheses one against another. This can
      be done on an evidential basis by evaluating the likelihood ratio, the
      likelihood of the data under one hypothesis divided by the likelihood of
      the data under another hypothesis. By constructing the whole likelihood
      function (in the case of a single parameter) any pair of hypotheses can be
      tested for the value of the likelihood ratio.

      > Now, in the case of deviation from normality, I suppose you wouldn't
      have much intuition about what is significant, but the relevant question
      is what is the effect of small deviations from normality on your test or
      conclusions of your analysis?

      Perhaps a better question is what the data say about a given hypothesis
      for the mean versus another value for the mean assuming the normal
      distribution is true? If the variance is unknown there is a simple
      solution only for the normal and a few other cases, by orthogonalization,
      and then the two parameters can be assessed separately. For comparing two
      different models, say normal versus lognormal, a likelihood based
      approach, the Akaike Information Criterion, is available although i am not
      sure that Akaike's approach is fully in agreement with the likelihood
      principle.

      Ruben

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