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

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

• Determine the feasibility of using a particular statistical method (for example, linear regression analysis and many other statistical techniques require independent observations).
• Perform spatial filtering prior to regression analysis to avoid violating assumptions of data independence.
• Help identify an appropriate neighborhood distance for a variety of spatial analysis methods.
• Determine the feasibility of using a particular statistical method. For example, linear regression analysis and many other statistical techniques require independent observations. Also useful for testing regression residuals.
• Help identify an appropriate neighborhood distance for a variety of spatial analysis methods. For example, find the distance where spatial autocorrelation is strongest.
• Measure broad trends in ethnic or racial segregation over time—is segregation increasing or decreasing.
• Summarize the diffusion of an idea, disease or trend over space and time—is the idea, disease, or trend remaining isolated and concentrated or spreading and becoming more diffuse.