A revised understanding of the influence of the variance of spatial weights on the Getis-Ord statistic

Geospatial hotspot statistics measure concentration in space. One of the most popular such methods is the Getis-Ord statistic, a measure for revealing geographical structure in the tails of an attribute value distribution. The original 1995 paper introducing this measure includes an interpretation of how the variance of the spatial weights employed feeds into the local measures, but the corresponding mathematical expression can be shown to be erroneous. The current paper corrects this expression and discusses the implications of the revised term for the link between the Getis-Ord statistic and the local variances of the spatial weights.