ruth@utstat.uucp (Ruth Croxford) (11/18/88)
Topic: Assessing significance of the association between two spatial processes
Speaker: Peter Clifford, Oxford University and McGill University
Date: 2:00 p.m., Friday, November 25, 1988
Place: Room 142, Ramsay Wright Zoological Labs, U of T
Abstract:
A fundamental question, frequently asked in statistical investigations, is
whether the apparent association between two variables is due to something other
than chance. In 1896, Pearson proposed the product-moment correlation
coefficient r as a measure of association. Subsequently, Student (1908)
obtained the sampling distribution of r under the null hypothesis of no
association, assuming the variables to be independent normal samples.
Correlation coefficients are now routinely calculated in all branches of
science as one of the first steps in an analysis. Our particular interest is in
situations in which the variables are observed at a variety of spatial
locations.
Right from the start, statisticians have cautioned against the uncritical
use of the correlation coefficient when the observed variables are from a
bivariate time series or a bivariate spatial process. In an early paper
Student (1914) investigates a method of "eliminating spurious correlation due
to position in time of space", and for time series, Bartlett (1935) has shown
that the asymptotic variance of the correlation coefficient is inflated when
the variables are each positively autocorrelated. Thus, under these circum-
stances, the use of standard critical values of r will lead to inflated type-I
error. Given the popularity of the correlation coefficient, it is important
that its significance should be assessed in a more conservative manner.
In this talk, a method of modifying the correlation coefficient by
introducing an "effective sample size" is discussed. The method is
illustrated by data on the association between disease and environment for
the "departements" of France.
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Coffee and tea will be served in the Delury Lounge (SS6006) at 1:30 p.m.