About Anselin's Local Moran statistic

The local Moran test (Anselin 1995), detects local spatial autocorrelation. It can be used to identify local clusters (regions where adjacent areas have similar values) or spatial outliers (areas distinct from their neighbors).

The Local Moran statistic decomposes Moran's I (Moran 1950) into contributions for each location, Ii. The sum of Ii for all observations is proportional to Moran's I, an indicator of global pattern. Thus, there can be two interpretations of Local Moran statistics, as indicators of local spatial clusters and as a diagnostic for outliers in global spatial patterns.

SpaceStat implements two types of Local Moran statistics, univariate and bivariate. The univariate Local Moran tests for spatial autocorrelation in a single variable in one time period. The bivariate Local Moran can test for spatial pattern in two variables in one time period, or spatio-temporal autocorrelation in one variable over time.

The screenshot below shows the original data (upper left), and SpaceStat' map and scatter plot output for a univariate local Moran test on lung cancer rates.  See Local Moran Results for information on how to interpret this information.