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GEOSTATS: Mantel Test Software: Summary of replies

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  • Daniel Bebber
    Dear all, thank you for the large number of replies I received in response to my query on Mantel test software and testing the significance of autocorrelation.
    Message 1 of 1 , Sep 23, 1999
      Dear all,
      thank you for the large number of replies I received in response to my query
      on Mantel test software and testing the significance of autocorrelation.
      ______________________
      Background: I have data on seedling growth and light environment for ~1500
      seedlings which are spatially auto- (and cross-) correlated. I want to find
      out whether the semivariances I calculate could have been obtained in the
      absence of spatial autocorrelation, i.e. whether the spatial autocorrelation
      is statistically significant, and from there to determine how far spatial
      autocorrelation extends.
      One way of testing the significance of spatial dependence is the Mantel test
      (Mantel 1967). The Mantel statistic (z) can be tested for significance by
      carrying out a large number of randomisations of the data and seeing how
      often the experimental z falls above or below the randomised data z. Another
      way is an asymptotic t-approximation test if the number of observations is
      large. With such a large number of observations and permutations a computer
      program is the only way of testing z by randomisation.

      Mantel, N. 1967. The detection of disease clustering and a generalised
      regression approach. Cancer Res. 27:209-220
      ______________________
      Query: "does anyone know of free or very cheap software for Windows that
      does Mantel tests. As a last resort I can use the R-package with a Mac
      emulator.
      Alternatively, is there a method of calculating the statistical significance
      of semivariances?"
      ______________________
      Answers:

      Andrew Lister [ne100fia@...]suggested the paper "Kabrick J. M.,
      Clayton M. K. & McSweeney K. 1997. Spatial patterns of carbon texture on
      drumlins in northeastern Wisconsin. Soil Sci. Soc. Am. J. 61(2):541-548"
      which gives a method of calculating confidence intervals on semivariances
      and also a z-test for differences between semivariances which could be used
      to test the experimental semivariance against random (spatially independent)
      data. Their formula for confidence intervals was taken from "Cressie, N. A.
      C. 1991. Statistics for spatial data. John Wiley & Sons, New York". Andrew
      also suggested the homepage of Marcia Gumpertz who has a course on spatial
      statistics (http://www.stat.ncsu.edu/~gumpertz/).

      Russell Cole [r.cole@...] sent an IML program (by Brian McArdle) for
      SAS which conducts Mantel tests.

      Donald Myers [myers@...]noted "that the values at the different
      lags are
      somewhat dependent and one should be careful about treating or testing
      them separately. In particular the (theoretical) model must satisfy a
      positive definiteness condition. The ordinary correlation coefficient is
      only the value of the autocorrelation function at lag zero. Note that
      non-bounded variograms (such as the power model) do not relate to
      autocorrelation functions (since the variance is not finite)."

      Roger Friedman [rdf4@...]sent details of a program which runs a
      Mantel-Haenszel chi-squared test for equality of survival distributions- not
      the same test but useful anyway. (See Mantel, N. & Haenszel, W. 1959.
      Statistical analysis of the analysis of data from retrospective studies of
      disease. Journal of the National Cancer Institute 22:719-748).

      Jaak Truu [jtruu@...] sent details of the "ADE-4 package, there is module
      for Mantel Test. Only problem is data file compilation. Program is free and
      available via web: http://pbil.univ-lyon1.fr/ADE-4/ADE-4.html

      Justin Quirouette [Justin_Quirouette@...] sent the following links for
      Mantel test programs.
      http://www.sci.qut.edu.au/nrs/mantel.htm
      http://herb.bio.nau.edu/~miller/mantel.htm

      Peter Smouse [smouse@...]. "NTSYS has a Mantel program, as
      does the R-Package. Also, Manly uses Mantel tests all the time, and probably
      has a program. Jeff Long at NIAAA in
      Bethesda has a Multiple-Mantel Program that he might be willing to send you,
      gratis. I have a copy sitting on my desk, but it isn't mine to hand out. His
      E-mail address is:jcl@.... The permutational test is fairly
      straightforward."
      The R-package can be found at
      http://alize.ere.umontreal.ca/~casgrain/en/labo/R/ but only runs on Unix or
      Mac.

      Michele Scardi [mscardi@...] has written a Mantel test program which
      runs on Windows which he very kindly sent me. "a few years ago I wrote a
      very basic (literally, as it was written in
      Basic) Mantel test program and recently I ported it to Fortran in order
      to manage very large matrices. It was compiled using MS Fortran
      PowerStation (now Digital Visual Fortran), so it runs under WIn9x/NT as
      a console application (i.e. in a DOS window). However, the source code
      can be easily recompiled for other platforms. If you or other people in
      AI-Geostatistics need it, just drop me a line."

      ______________________

      Summary: Thanks once again for all replies. Naturally any help or software
      used in any publications I manage to put together will be acknowledged.

      _____________________________________
      Mr. Daniel P. Bebber
      Department of Plant Sciences
      University of Oxford
      South Parks Road
      Oxford OX1 3RB
      UK
      Tel. 01865 275000 Fax. 01865 275074

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