A Scale‐Sensitive Test of Attraction and Repulsion Between Spatial Point Patterns

Abstract

There exist a variety of tests for attraction and repulsion effects between spatial point populations, most notably those involving either nearest‐neighbor or cell‐count statistics. Diggle and Cox (1981) showed that for the nearest‐neighbor approach, a powerful test could be constructed using Kendall's rank correlation coefficient. In the present paper, this approach is extended to cell‐count statistics in a manner paralleling the K‐function approach of Lotwick and Silverman (1982). The advantage of the present test is that, unlike nearest‐neighbors, one can identify the spatial scales at which repulsion or attraction are most significant. In addition, it avoids the torus‐wrapping restrictions implicit in the Monte Carlo testing procedure of Lotwick and Silverman. Examples are developed to show that this testing procedure can in fact identify both attraction and repulsion between the same pair of point populations at different scales of analysis.