  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. 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 Pielou's test is liberal the null pattern but Dixon's test has
the desired significance level under the RL pattern. We propose three new
multivariate clustering tests based on NNCTs. 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 using these examples.
