New Tests of Spatial Segregation Based on Nearest Neighbor Contingency Tables

The spatial clustering of points from two or more classes (or species) has important implications in many fields and may cause the spatial patterns of segregation and association, which are two major types of spatial interaction between the classes. The null patterns we consider are random labeling (RL) and complete spatial randomness (CSR) of points from two or more classes, which is called CSR independence, henceforth. The segregation and association patterns can be studied using a nearest neighbor contingency table (NNCT) which is constructed using the frequencies of nearest neighbor (NN) types in a contingency table. Among NNCT-tests (i.e., tests based on NNCTs), Pielou’s test is equivalent to the usual (Pearson’s) test of independence for contingency tables, but is liberal under CSR independence or RL patterns. On the other hand, Dixon’s test of segregation has the desired significance level under the RL pattern. We propose three new multivariate clustering tests based on NNCTs using the appropriate sampling distribution of the cell counts in a NNCT and suggest a simple correction for Pielou’s test for data with rectangular support. We compare the finite sample performance of these new tests with Pielou’s and Dixon’s tests and Cuzick & Edward’s k-NN tests in terms of empirical size under the null cases and empirical power under various segregation and association alternatives and provide guidelines for using the tests in practice. We demonstrate that the newly proposed NNCT-tests perform relatively well compared to their competitors and illustrate the tests using three example data sets. Furthermore, we compare the NNCT-tests with the second-order methods such as Ripley’s L-function and pair correlation function using these examples.