Spatial Autocorrelation

[<– 4 Average Nearest Neighbor](http://giscollective.org/tutorials/gis-techniques/spatial-statistics/average-nearest-neighbor/)

Also known as Global Moran’s I. Spatial autocorrelation statistics measure and analyze the degree of dependency among observations in geographic space. Spatial autocorrelation statistics such as Moran’sIare global in the sense that they estimate the overall degree of spatial autocorrelation for a dataset. Spatial autocorrelation is more complex than one-dimensional autocorrelation because spatial correlation is multi-dimensional (i.e. 2 or 3 dimensions of space) and multi-directional.

Negative/positive values indicate negative/positive positive spatial autocorrelation. Values range from -1 (indicating perfect dispersion) to 1 (perfect correlation). A zero value indicates a random spatial pattern. For statistical hypothesis testing, Moran’s I values can be transformed to z-scores in which values greater than 1.96 or smaller than -1.96 indicate spatial autocorrelation that is significant at the 5% level.

How to do:

Step 1: Add US_Income feature class to a new ArcMap document.

Step 2: Select Spatial Autocorrelation tool (ArcToolbox > Spatial Statistics > Analyzing Patterns > Spatial Autocorrelation (Moran’s I))

Step 3: Fill in fields as specified below:

  • Input Field: B34_2008 is the average wage per county (make sure to check generate report)
  • Conceptualization of Spatial Relationships: see tool help for explanation of each conceptualization. For this exercise we will use the inverse distance conceptualization (i.e. Tobler’s First Law of Geography) where nearer features have a greater influence on the computation
  • Distance Method: either straight line (Euclidean) or at right angles (Manhattan). We’ll use Euclidean distance here
  • Standardization: standardize spatial weights if spatial distribution of features is biased. Leave as ‘None’
  • Distance Band: specifies a cutoff distance for Inverse Distance and Fixed Distance options. Leave blank

Step 4: Hit OK and run the tool. The tool will run and output a graphical summary as an HTML file. Note: the report that is produced below will not open after the tool completes running. To open the HTML file, navigate to the results window. (If the window is not open, you can open the window via Geoprocessing > Results.) Then double-click on HTML Report File.

As you can see, the global Moran’s I for the average wage is 0.924772, which indicates that there is a high positive spatial autocorrelation (highly clustered pattern). Given the z-score of 159.37, there is less than 1% likelihood that this clustered pattern could be the result of random choice.