Geary's C

Geary's C, introduced by Roy Geary in 1954, is a spatial autocorrelationSpatial AutocorrelationSpatial autocorrelation measures the degree to which values at nearby locations are similar (positive) or dissimilar ... statistic that evaluates the degree of spatial association in a dataset by comparing the values of neighboring observations directly through their squared differences. This contrasts with Moran's IMoran's IMoran's I is the most widely used global measure of spatial autocorrelation, quantifying the degree to which values a..., which uses deviations from the global mean, making Geary's C more sensitive to local differences between adjacent observations.

Geary's C is calculated as a ratio of the weighted sum of squared differences between neighboring values to the total variance of the dataset. The statistic ranges from 0 to approximately 2, with an expected value of 1 under spatial randomness. Values below 1 indicate positive spatial autocorrelationSpatial AutocorrelationSpatial autocorrelation measures the degree to which values at nearby locations are similar (positive) or dissimilar ... (similar values are clustered together), while values above 1 indicate negative spatial autocorrelation (dissimilar values are adjacent). The inversely related scale compared to Moran's IMoran's IMoran's I is the most widely used global measure of spatial autocorrelation, quantifying the degree to which values a... can be initially counterintuitive: low Geary's C corresponds to high Moran's I.

While both statistics measure spatial autocorrelationSpatial AutocorrelationSpatial autocorrelation measures the degree to which values at nearby locations are similar (positive) or dissimilar ..., they are sensitive to different aspects of the spatial pattern. Moran's IMoran's IMoran's I is the most widely used global measure of spatial autocorrelation, quantifying the degree to which values a... is a more global measure that is influenced by the overall cross-product of deviations from the mean. Geary's C, based on direct comparisons between neighbors, responds more to local spatial heterogeneity. In practice, both statistics are often computed together to provide a more complete picture of spatial structure. They will generally agree on the presence or absence of spatial autocorrelation but may differ in magnitude.

Geary's C is used alongside Moran's IMoran's IMoran's I is the most widely used global measure of spatial autocorrelation, quantifying the degree to which values a... in exploratory spatial data analysis across fields including epidemiology, ecology, economics, and criminology. Researchers apply it when they are particularly interested in the smoothness of local spatial transitions or when local-level autocorrelation is more relevant than global clustering patterns.