# The Contiguity Ratio and Statistical Mapping

The Contiguity Ratio and Statistical Mapping THE CONTIGUITY RATIO AND STATISTICAL MAPPING by R. C. GEARY Introduction and Summary The problem discussed in this paper is to determine whether statistics given for each "county" in a "country" are distributed at random or whether they form a pattern. The statistical instrument is the contiguity ratio c defined by formula (1.1) below, which is an obvious generalization of the Von Neumann (1941) ratio used in one-dimensional analysis, particularly time series. While the appli­ cations in the paper are confined to one- and two-dimensional problems, it is evident that the theory applies to any number of dimensions. If the figures for adjoining counties are generally closer than those for counties not adjoining, the ratio will clearly tend to be less than unity. The constants are such that when the statistics are distributed at random in the counties, the average value of the ratio is unity. The statistics will be regarded as contiguous if the actual ratio found is significantly less than unity, by reference to the standard error. The theory is discussed from the viewpoints of both randomization and classical normal theory. With the randomization approach, the observations themselves are the "universe" and no assumption need be made http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the Royal Statistical Society Series D: The Statistician Oxford University Press

# The Contiguity Ratio and Statistical Mapping

, Volume 5 (3): 27 – Dec 5, 2018
27 pages

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# References (9)

Publisher
Oxford University Press
ISSN
2515-7884
eISSN
1467-9884
DOI
10.2307/2986645
Publisher site
See Article on Publisher Site

### Abstract

THE CONTIGUITY RATIO AND STATISTICAL MAPPING by R. C. GEARY Introduction and Summary The problem discussed in this paper is to determine whether statistics given for each "county" in a "country" are distributed at random or whether they form a pattern. The statistical instrument is the contiguity ratio c defined by formula (1.1) below, which is an obvious generalization of the Von Neumann (1941) ratio used in one-dimensional analysis, particularly time series. While the appli­ cations in the paper are confined to one- and two-dimensional problems, it is evident that the theory applies to any number of dimensions. If the figures for adjoining counties are generally closer than those for counties not adjoining, the ratio will clearly tend to be less than unity. The constants are such that when the statistics are distributed at random in the counties, the average value of the ratio is unity. The statistics will be regarded as contiguous if the actual ratio found is significantly less than unity, by reference to the standard error. The theory is discussed from the viewpoints of both randomization and classical normal theory. With the randomization approach, the observations themselves are the "universe" and no assumption need be made

### Journal

Journal of the Royal Statistical Society Series D: The StatisticianOxford University Press

Published: Dec 5, 2018