[<– 3 | Hot Spot Analysis](http://giscollective.org/tutorials/gis-techniques/spatial-statistics/hot-spot-analysis/) |

The Average Nearest Neighbor tool measures the distance between each feature centroid and its nearest neighbor’s centroid location. It then averages all these nearest neighbor distances. If the average distance is less than the average for a hypothetical random distribution, the distribution of the features being analyzed is considered clustered. If the average distance is greater than a hypothetical random distribution, the features are considered dispersed. The average nearest neighbor ratio is calculated as the observed average distance divided by the expected average distance (with expected average distance being based on a hypothetical random distribution with the same number of features covering the same total area).

The Average Nearest Neighbor tool returns five values: Observed Mean Distance, Expected Mean Distance, Nearest Neighbor Index, z-score, and p-value.

How to do:

Goal: To determine if residential crimes in Lincoln are clustered or dispersed.

Step 1: Add Lincoln_resburglaries feature class from the SampleData File Geodatabase to a new ArcMap document.

Step 2: Select Average Nearest Neighbor toll (ArcToolbox > Spatial Statistics > Analyzing Patterns > Average Nearest Neighbor)

Step 3: Fill in the fields as specified:

- Make sure to check
**Generate Report** - Distance Method: either straight line (Euclidean) or right angles (Manhattan). _We’ll use Euclidean _distance

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 will not open after the tool completes running. To open the HTML file, navigate to the results window (if the window isn’t open, you can open the window via Geoprocessing > Results). Then double-click on the HTML Report File.

As you can see, the nearest neighbor ratio (0.498004) indicates that the residential burglaries are clustered. Given the z-score of -37.39, there is a less than 1% likelihood that this clustered pattern could be the result of random chance.

[5 | Spatial Autocorrelation (Global Moran’s I) –>](http://giscollective.org/tutorials/gis-techniques/spatial-statistics/spatial-autocorrelation/) |