Eyes find patterns everywhere; spatial statistics asks whether patterns are real. Built on the observation that near things tend to be related (spatial autocorrelation), the toolkit tests clustering globally (Moran’s I), locates statistically significant hot and cold spots (Getis-Ord Gi*, LISA), detects clusters in point events, and fits regression models that respect geography. It is how crime maps, disease maps and risk maps graduate from suggestive to defensible.
Autocorrelation: the foundational idea
Spatial autocorrelation measures whether similar values cluster (positive), disperse (negative) or scatter randomly. Global indices like Moran’s I summarise the whole map in one significance-tested number; their local versions decompose it, attaching a statistic to every district or cell.
Beyond description, autocorrelation is a warning: it violates the independence assumed by ordinary statistics, which is why spatial data demands spatial methods.
Hotspots and clusters, honestly
Getis-Ord Gi* answers the operational question — where are values significantly high or low, given neighbours? — producing the confidence-classed hotspot maps used in policing, epidemiology and retail. Local Moran’s I (LISA) adds outlier types: high surrounded by low, and vice versa.
Point-pattern tools (Ripley’s K, kernel density with significance, scan statistics) handle event data — crimes, cases, failures — separating genuine clusters from artefacts of population density, the classic trap that naive heat maps fall into.
Modelling with geography inside
Spatial regression brings structure into inference: spatial lag and error models absorb neighbourhood dependence; geographically weighted regression (GWR and successors) lets relationships vary across the map, revealing where drivers matter most.
Delivered well, these methods come with their assumptions and diagnostics attached — weight-matrix choices, multiple-testing corrections, sensitivity runs — because a hotspot map without significance is just cartographic rhetoric.