How Cluster and Outlier Analysis: Anselin Local Moran's I (Spatial Statistics) works

Given a set of weighted features, the Cluster and Outlier Analysis tool identifies clusters of features with values similar in magnitude. The tool also identifies spatial outliers. To do this, the tool calculates a Local Moran's I value, a Z score, a p-value, and a code representing the cluster type for each feature. The Z score and p-value represent the statistical significance of the computed index value.


Local Moran's I Computations

View additional mathematics for Local Moran's I.

The p-values are numerical approximations of the area under the curve for a known distribution, limited by the test statistic. See What is a Z score? What is a p-value?.


A positive value for I indicates that the feature is surrounded by features with similar values. Such a feature is part of a cluster. A negative value for I indicates that the feature is surrounded by features with dissimilar values. Such a feature is an outlier. The Local Moran's index can only be interpreted within the context of the computed Z score or p-value (see What is a Z score? What is a p-value?).

The COType field distinguishes between a statistically significant (0.05 level) cluster of high values (HH), cluster of low values (LL), outlier in which a high value is surround primarily by low values (HL), and outlier in which a low value is surrounded primarily by high values (LH).

Potential applications

Applications can be found in economics, resource management, biogeography, political geography, and demographics.

Additional Resources:

Mitchell, Andy. The ESRI Guide to GIS Analysis, Volume 2. ESRI Press, 2005.

Anselin, Luc. "Local Indicators of Spatial Association – LISA," Geographical

Analysis, 27(2): 93–115, 1995.