  Spatial interaction patterns such as segregation and association can be
tested using nearest neighbor contingency tables (NNCTs). We introduce new
cell-specific (or pairwise) and overall segregation tests and determine their
asymptotic distributions. In particular, we demonstrate that cell-specific
tests enjoy asymptotic normality, while overall tests have chi-square
distributions asymptotically. We also perform an extensive Monte Carlo
simulation study to compare the finite sample performance of the tests in terms
of empirical size and power. In addition to the cell-specific tests as post-hoc
tests for overall tests, we discuss one-class-versus-rest type of NNCT-tests
after an overall test yields significant interaction. We also introduce the
concepts of total, strong, and partial segregation/association to label levels
of these patterns. We compare these new tests with the existing NNCT-tests in
literature with simulations as well and illustrate the NNCT-tests on an
ecological data set.
