Geary's C — Spatial Contiguity Ratio

Both measure global spatial autocorrelation, but they use different formulas. Moran's I is based on cross-products of mean-deviated values and ranges roughly from -1 to +1, resembling a correlation coefficient. Geary's C uses squared differences between neighbor pairs and ranges from 0 to 2 with a null value of 1. Geary's C is more sensitive to local dissimilarity and less sensitive to global clustering than Moran's I. The two statistics often agree but can diverge when the spatial pattern involves fine-grained alternation.

The choice depends on the theoretical notion of neighborhood appropriate for your data. Queen contiguity (shared edge or vertex) and rook contiguity (shared edge only) are common for regular grids. For irregular polygons, queen contiguity or a k-nearest-neighbor matrix is typical. The key rule is to define neighbors before seeing the results and to check sensitivity by comparing outcomes under two or three reasonable specifications.

Not directly. Geary's C is designed for areal units where adjacency or proximity can be encoded in a weights matrix. For point data you should either aggregate the points to polygons and then apply Geary's C, or use a point-pattern statistic such as Ripley's K or kernel density estimation instead.

A value near 0 indicates strong positive spatial autocorrelation: neighboring units have very similar attribute values, much more so than random assignment would produce. Values near 1 indicate spatial randomness, and values approaching 2 indicate negative autocorrelation (a checkerboard pattern where neighbors tend to have dissimilar values).

A permutation test is generally preferred because it makes no distributional assumption about the attribute values and is reliable even with small maps (30–100 units). The normal approximation is acceptable for large maps (several hundred units or more) with approximately symmetric attribute distributions, but always report the chosen inference method so readers can evaluate it.