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
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
Alternatively, is there a method of calculating the statistical significance
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
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
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.
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
The R-package can be found at
but only runs on Unix or
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
Tel. 01865 275000 Fax. 01865 275074
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