Average Nearest Neighbor (Spatial Statistics)
Summary
Calculates a nearest neighbor index based on the average distance from each feature to its nearest neighboring feature. Results are accessible from the Results window.
Learn more about how Average Nearest Neighbor Distance works
Illustration
Usage

The Average Nearest Neighbor tool returns five values: Observed Mean Distance, Expected Mean Distance, Nearest Neighbor Index, zscore, and pvalue. These values are accessible from the Results window and are also passed as derived output values for potential use in models or scripts. Optionally, this tool will create an HTML file with a graphical summary of results. Doubleclicking on the HTML entry in the Results window will open the HTML file in the default Internet browser. Rightclicking on the Messages entry in the Results window and selecting View will display the results in a Message dialog box.
Note: If this tool is part of a custom model tool, the HTML link will only appear in the Results window if it is set as a model parameter prior to running the tool.
 For best display of HTML graphics, ensure your monitor is set for 96 DPI.

The zscore and pvalue results are measures of statistical significance which tell you whether or not to reject the null hypothesis. For the Average Nearest Neighbor statistic, the null hypothsis states that features are randomly distributed.

The Nearest Neighbor Index is expressed as the ratio of the Observed Mean Distance to the Expected Mean Distance. The expected distance is the average distance between neighbors in a hypothetical random distribution. If the index is less than 1, the pattern exhibits clustering; if the index is greater than 1, the trend is toward dispersion or competition.

The average nearest neighbor method is very sensitive to the Area value (small changes in the Area parameter value can result in considerable changes in the results). Consequently, the Average Nearest Neighbor tool is most effective for comparing different features in a fixed study area. Use the Calculate Area tool on the study area polygon as one way to get an Area value for the Area parameter. The picture below is a classic example of how identical feature distributions can be dispersed or clustered depending on the study area specified.

If an Area parameter value is not specified, then the area of the minimum enclosing rectangle around the input features is used. Unlike the extent, a minimum enclosing rectangle will not necessarily align with the x and yaxes.

There are special cases of input features that would result in invalid (zeroarea) minimum enclosing rectangles. In these cases, a small value derived from the input feature XY tolerance will be used to create the minimum enclosing rectangle. For example, if all features are coincident (i.e., all have the exact same X and Y coordinates), the area for a very small square polygon around the single location will be used in calculations. Another example would be if all features align perfectly (e.g., 3 points in a straight line); in this case the area of a rectangle polygon with a very small width around the features will be used in computations. It is always best to supply an Area value when using the Average Nearest Neighbor tool.

Although this tool will work with polygon or line data, it is most appropriate for event, incident, or other fixedpoint feature data. For line and polygon features, the true geometric centroid for each feature is used in computations. For multipoint, polyline, or polygons with multiple parts, the centroid is computed using the weighted mean center of all feature parts. The weighting for point features is 1, for line features is length, and for polygon features is area.

Calculations based on either Euclidean or Manhattan distance require projected data to accurately measure distances.

Map layers can be used to define the Input Feature Class. When using a layer with a selection, only the selected features are included in the analysis.
When using shapefiles, keep in mind that they cannot store null values. Tools or other procedures that create shapefiles from nonshapefile inputs may store or interpret null values as zero. This can lead to unexpected results. See also Geoprocessing considerations for shapefile output.
Syntax
Parameter  Explanation  Data Type 
Input_Feature_Class 
The feature class, typically a point feature class, for which the average nearest neighbor distance will be calculated.  Feature Layer 
Distance_Method 
Specifies how distances are calculated from each feature to neighboring features.
 String 
Generate_Report 
 Boolean 
Area (Optional) 
A numeric value representing the study area size. The default value is the area of the minimum enclosing rectangle that would encompass all features (or all selected features). Units should match those for the Output Coordinate System.  Double 
Code Sample
The following Python Window script demonstrates how to use the AverageNearestNeighbor tool.
import arcpy arcpy.env.workspace = r"C:\data" arcpy.AverageNearestNeighbor_stats("burglaries.shp", "EUCLIDEAN_DISTANCE", "NO_REPORT", "#")
The following standalone python script demonstrates how to use the AverageNearestNeighbor tool.
# Analyze crime data to determine if spatial patterns are statistically significant # Import system modules import arcpy # Local variables... workspace = "C:/data" crime_data = "burglaries.shp" try: # Set the current workspace (to avoid having to specify the full path to the feature classes each time) arcpy.env.workspace = workspace # Obtain Nearest Neighbor Ratio and zscore # Process: Average Nearest Neighbor... nn_output = arcpy.AverageNearestNeighbor_stats(crime_data, "EUCLIDEAN_DISTANCE", "NO_REPORT", "#") # Create list of Average Nearest Neighbor output values by splitting the result object nn_values = nn_output.split(";") print "The nearest neighbor index is: " + nn_values[0] print "The zscore of the nearest neighbor index is: " + nn_values[1] print "The pvalue of the nearest neighbor index is: " + nn_values[2] print "The expected mean distance is: " + nn_values[3] print "The observed mean distance is: " + nn_values[4] print "The path of the HTML report: " + nn_values[5] except: # If an error occurred when running the tool, print out the error message. print arcpy.GetMessages()
Environments
 Output Coordinate System
Feature geometry is projected to the Output Coordinate System prior to analysis. All mathematical computations are based on the Output Coordinate System spatial reference.