Besag and Newell's Statistics
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Ho |
The number of cases in an area follows a Poisson distribution with a common rate. |
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Ha |
For some areas, the number of cases exceeds that predicted by a Poisson distribution with a common rate. |
Test statistics
This method assesses clustering at the local and global scale using two test statistics: l for the local scale and r for the global scale. Thus, use l to evaluate local scale clustering, and use r to examine global-scale clustering. This method is designed for case and population-at-risk count data aggregated into regions with small population sizes. Regions could be census tracts, zip codes, or towns.
The l statistic describes the extent of local clustering, the number of regions needed to aggregate at least k cases, with k defined by the user. If the cases are in a cluster, you can imagine there would be fewer regions to aggregate to find a set number of cases than if they were not clustered. The r statistic is simply the total number of clusters found in the local-scale analysis.
Notes
Waller and Turnbull (1993) show that the significance of l depends on the level of aggregation and the chosen value of k.