Overlap test statistics

BoundarySeer offers four overlap statistics for crisp boundaries. While they were developed for difference boundaries, overlap statistics can be applied to areal boundaries, though overlap between two areal boundaries will be better quantified by areal overlap statistics that will come in the next version of BoundarySeer.

Overlap statistics are based on mean nearest neighbor distances (Jacquez 1995). For ease of reference, we will term one set of boundaries boundary G and the other Boundary H.

OS

the count of the number of Boundary Elements (BEs) that are included in both sets of boundaries

OG

the mean distance from BEs in G to the nearest BE in H

OH

the mean distance from BEs in H to the nearest BE in G

OGH

the mean distance from a BE in either boundary to the nearest BE in the other

Calculating overlap statistics

Following Jacquez (1995), BoundarySeer calculates overlap statistics using the following formulae:

overlapeqn.jpg

Where BG is the set of BEs for boundary G, and BH is the set for boundary H. D is a distance matrix of dimension NG by NH, whose elements, dij, are the geographic distances between location i in BG and location j in BH. The minimum distance from the ith BE in BG to any location in BH is min(d•j ); the equivalent minimum distance for elements of BH is min( di• ).

Next step:

See also: