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1311Re: AI-GEOSTATS: Detecting spatial autocorrelation in highly non normal data

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  • Pierre Goovaerts
    Nov 20, 2003
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      Hello,

      I agree that in most situations testing for spatial correlation
      is not very informative since the null hypothesis of spatial
      independence is unrealistici and its rejection is trivial.
      This is why at Biomedware we are working on tests
      of hypothesis where the null hypothesis is a particular spatial pattern.
      Stochastic simulation allows one to generate many realizations of this
      spatial pattern that are then used to derive the distribution of the
      test statistics. More information can be found in the following
      publication: http://www-personal.engin.umich.edu/~goovaert/liebisch.pdf

      Cheers,

      Pierre Goovaerts
      <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

      Dr. Pierre Goovaerts
      President of PGeostat, LLC
      Chief Scientist with Biomedware Inc.
      710 Ridgemont Lane
      Ann Arbor, Michigan, 48103-1535, U.S.A.

      E-mail: goovaert@...
      Phone: (734) 668-9900
      Fax: (734) 668-7788
      http://alumni.engin.umich.edu/~goovaert/

      <><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

      On Thu, 20 Nov 2003, Volker Bahn wrote:

      > The problem is not unique to testing significance of spatial correlation.
      > Any traditional hypothesis test is non-sensical as you describe because we
      > ALWAYS know that the null hypothesis is wrong. The question of interest is
      > how wrong it is and whether the detected effect is of practical consequence.
      > However, a hypothesis test does not test practical relevance of an effect
      > but statistical power to detect it, which depends on sample size, inherent
      > variability and also on effect size. Given a large enough sample size, one
      > will always reject the null hypothesis. Why then do people still hold on to
      > hypothesis tests? Because it gives them a false sense of objectivity. No one
      > wants to admit that the judgement of whether an effect is of practical
      > consequence is a to a certain degree inherently subjective decision (as is
      > the level of alpha etc).
      >
      > Cheers
      >
      > Volker
      >
      >
      > ----- Original Message -----
      > From: "Edzer J. Pebesma" <e.pebesma@...>
      > To: <trevor.middel@...>
      > Cc: <ai-geostats@...>
      > Sent: Thursday, November 20, 2003 5:11
      > Subject: Re: AI-GEOSTATS: Detecting spatial autocorrelation in highly non
      > normal data
      >
      >
      > | Trevor,
      > |
      > | I always wonder what the value of testing significance of spatial
      > | correlation is, and never advise to do it. See, if data are spatial, it
      > | is extremely unlikely that they are spatially uncorrelated. Rejecting
      > | the test is usually only a matter of collecting sufficient evidence,
      > | and not at all an interesting finding, because the data were spatial.
      > |
      > | Probably a more real problem is: to what extent does the spatial
      > | correlation present (which may be very weak!) mess up an analysis
      > | that assumes independence of observations. If you choose for
      > | an analysis method that addresses spatial correlation, you're always
      > | on safe ground.
      > |
      > | If your data were collected using some form of random sampling,
      > | analysis based on independent observations is perfectly valid for
      > | estimating areal mean values. This does not imply that data are
      > | spatially uncorrelated, but just that they may be treated independent
      > | because of the sampling scheme.
      > | --
      > | Edzer
      > |
      > | trevor.middel@... wrote:
      > |
      > | >Hi Folks,
      > | >
      > | >I'm hoping someone can help steer me in the right direction.
      > | >
      > | >I have several sets of data acquired from acoustic surveys conducted on a
      > | >small lake trout lake. The data consist of sampling units aligned in
      > | >transects. Each sampling unit is 50 m in length. A mean lake trout
      > density
      > | >is associated with each sampling unit.
      > | >
      > | >I'm interested in examining whether any significant spatial
      > autocorrelation
      > | >in the exists in the observed distribution of lake trout. The data are
      > | >highly non-normal with 75-90% of the observations being zero. Log and Ln
      > | >transformations do not normalize the data.
      > | >
      > | >I've been doing some reading and it seems that most methods of
      > quantifying
      > | >spatial autocorrelation require some kind of normality in the data. Any
      > | >suggestions on how I might proceed with these data?
      > | >
      > | >Thanks in advance for all suggestions.
      > | >
      > | >Apologies for the simplicity of the question, but I'm just beginning my
      > | >foray into spatial statistics.
      > | >
      > | >Trevor Middel
      > | >
      > | >--
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      > |
      > |
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