Global Spatial Structure¶

Question: Is there spatial autocorrelation across my entire study area?

Global statistics return a single summary value for the whole dataset, answering whether the overall pattern is more clustered or dispersed than expected under spatial randomness.

Choosing a method:

• Moran’s I — the standard choice for continuous variables. Compares each observation to its mean-centred value and its neighbours’ mean-centred values; positive \(I\) signals clustering, negative \(I\) signals dispersion.

• Geary’s C — also for continuous variables but based on squared differences between neighbours rather than cross-products. More sensitive to local contrasts; \(C < 1\) is positive autocorrelation, \(C > 1\) is negative.

• Getis-Ord G — tests for spatial concentration of raw (non-negative) values rather than deviations from the mean. Well-suited to counts, prices, and rates where the magnitude matters.

• Join Counts — designed for binary or categorical variables; counts how often similar or dissimilar categories share a boundary.

All methods support permutation-based inference, which avoids distributional assumptions and is recommended for small samples or skewed data.