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Can tests for spatial autocorrelation be done in ArcGIS?
Yes, starting at ArcGIS 9.0, the Spatial Statistics Toolbox in ArcToolbox provides a number of tools to measure spatial autocorrelation, analyze spatial patterns (clustering or dispersion) and assess feature spatial distributions. Some of these tools are Spatial Autocorrelation (Global Moran's I), High/Low Clustering (Getis-Ord General G), Cluster and Outlier Analysis (Anselin Local Moran's I), Hot Spot Analysis (Getis-Ord Gi*), and Directional Distribution (Standard Deviational Ellipse).
Tools to measure spatial autocorrelation are not available in the Spatial Analyst extension for raster datasets.