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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