A comparison of five distance-based methods for spatial pattern analysis

The behaviour of five statistics (extensions of Pielou's, Clark and Evans', Pollard's, Johnson & Zimmer's, and Eberhardt's statistics, which are denoted as P-i, C-e, P-o, J(z) and E-b respectively) that involve the distance from a random point to its jth nearest neighbour were examined against several alternative patterns (lattice-based regular, inhomogeneous random. and Poisson cluster patterns) through Monte Carlo simulation to test their powers to detect patterns. The powers of all the five statistics increase as distance order j increases against inhomogeneous random pattern. They decrease for P-i and C-e and increase for P-o, J(z), and E-b against regular and Poisson cluster patterns, P-o, J(z), and E-b can reach high powers with the third or higher order distances in most cases. However, P-o is recommended because no extra information is needed. it can reach a high power with the second or third distance even though the sample size is not large in most cases. and the test can be performed with an approximate chi (2) distribution associated with it. When a regular pattern is expected, J(z) is recommended because it is more sensitive to lattice-based regular pattern than P-o and E-b, especially for the first distance. However, simulation tests should be used because the speed of convergence of J(z) to normal distribution is very slow.