Scenario: the geographic distribution of standardized mortality rates across Glasgow.
Source: R. Haining, Spatial Data Analysis in the Social and
Behavioral Sciences, CUP, 1990; R. Haining, "Bivariate correlation
with spatial data," Geographical Analysis, 23 (1991): 210-227.
The geographic distribution of disease cases has been of interest to public
health officials ever since Dr. Snow mapped cholera cases in London in
1854. The general geographic processes in operation are contagion and/or
common locational exposure risks. These processes result in the clustering
of cases, and hence spatial autocorrelation in maps of individual and/or
geographically aggregated cases.
This case study tracks and maps selected standardized mortality rates in
Glasgow, base upon aggregates for eighty-seven community medicine areas
during 1980-82. These rates are related to contributory factors; for
example, cancer rates are correlated with low quality of life, which is
believed to induce stress. Proper measures of bivariate correlation between
these georeferenced variables are outlined, together with their accompanying
sampling distributions. The first involves prewhitening the two
georeferenced variables under study. The second involves calculating the
effective sample size that is affiliated with spatially autocorrelated
data. The demonstrations presented emphasize that the presence of spatial
correlation in map data undermines the standard statistical theory of
inference pertaining to bivariate correlation.
The objective of securing a good estimate of the population mean also is
treated by Haining (1990). As before, the discussion is cast in terms of
impacts of spatial autocorrelation on the sampling distribution of a sample
mean. The demonstrations here emphasize that spatial dependency implies a
loss of information in the estimation of a mean. Information loss arising
from positive spatial autocorrelation can lead to incorrectly failing to
reject a null hypothesis.
Principal concepts: effective sample size (1990, p. 318; 1991,
p. 213-214), pre-whitening (1991, p. 216), bivariate correlation (1990,
p.313-323; 1991, p. 217), sample mean (1990, pp. 161-166).
Questions:
- Why does spatial autocorrelation cause information loss when
calculating a sample mean?
- How can the phrase "effective sample size" be defined?
- What happens to the sampling distribution of a correlation coefficient
or a sample mean as positive spatial autocorrelation increases?
- Why should an epidemiologist be concerned about the presence of spatial
autocorrelation in disease rates?
- What are some implications for a multivariate analysis of georeferenced
disease rates that can be gleaned from univariate and bivariate findings
concerning the presence of spatial autocorrelation?
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