The Effects of Weight Choices on the Power of the Getis–Ord Statistic

When local spatial clustering exists, local statistics are most likely to be significant when their associated weights match the spatial form and extent of the actual clustering. This paper focuses upon the cost of misspecifying the weights of the Getis–Ord statistic. In particular, it is more difficult to reject false null hypotheses when the weights are poorly chosen. I also examine the likelihood of finding spatial clusters when a range of spatial scales is examined, and when the multiple testing that this entails is accounted for. If there is uncertainty regarding the scale of the process, there is little cost in examining a range that includes spatial scales that are larger than the true cluster. Gains in the power to detect significant clustering may be had if the examination of cluster sizes that are clearly too small may be omitted. A small number of Bonferroni-adjusted tests will often provide a slight decline in statistical power, relative to tests that search comprehensively over a range, but may have the benefit of providing a relatively better estimate of the location of change.