How Average Nearest Neighbor Distance (Spatial Statistics) works

The Average Nearest Neighbor Distance 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 are considered clustered. If the average distance is greater than a hypothetical random distribution, the features are considered dispersed. The index is expressed as the ratio of the observed distance divided by the expected distance (expected distance is based on a hypothetical random distribution with the same number of features covering the same total area).


If the index is less than 1, the pattern exhibits clustering. If the index is greater than 1, the trend is toward dispersion. It is imperative to remember that the Local Moran's I value can only be interpreted if the Z score is significant (What is a Z Score?). If the Z score is not significant, the Local Moran's I value means nothing because it is possible that it occured by random chance.

The equations used to calculate the Average Nearest Neighbor Distance Index and Z score are based on the assumption that the points being measured are free to locate anywhere within the study area (for example, there are no barriers, and all cases or features are located independently of one another). In addition, the index and Z score for this statistic are sensitive to changes in the study area or changes to the Area parameter. For all these reasons, comparing results from this statistic are most appropriate when the study area is fixed: comparing average nearest neighbor distances for different types of retail stores within a particular county or comparing a single type of retail for a fixed study area over time, for example.

Possible applications

Additional Resources:

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

Ebdon, David. Statistics in Geography. Blackwell, 1985.