How Spatial Autocorrelation: Moran's I (Spatial Statistics) works

This tool measures spatial autocorrelation (feature similarity) based on both feature locations and feature values simultaneously. Given a set of features and an associated attribute, it evaluates whether the pattern expressed is clustered, dispersed, or random. The tool calculates the Moran's I Index value and both a Z score and p-value evaluating the significance of that index. In general, a Moran's Index value near +1.0 indicates clustering while an index value near -1.0 indicates dispersion. However, without looking at statistical significance you have no basis for knowing if the observed pattern is just one of many, many possible versions of random.

In the case of the Spatial Autocorrelation tool, the null hypothesis states that "there is no spatial clustering of the values associated with the geographic features in the study area". When the p-value is small and the absolute value of the Z score is large enough that it falls outside of the desired confidence level, the null hypothsis can be rejected. If the index value is greater than 0, the set of features exhibits a clustered pattern. If the value is less than 0, the set of features exhibits a dispersed pattern.

Calculations


Mathematics used to compute Global Moran's I

View additional mathematics for Global Moran's I.

The p-value is a numerical approximation 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?.

Potential applications

Additional Resources:

The following books and journal articles have further information about this tool.

Goodchild, Michael F. Spatial Autocorrelation. Catmog 47, Geo Books. 1986.

Griffith, Daniel. Spatial Autocorrelation: A Primer. Resource Publications in Geography, Association of American geographers. 1987.

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