An empirical comparison of edge effect correction methods applied to K-function analysis

This paper explores various edge correction methods for K-function analysis via Monte Carlo simulation. The correction methods discussed here are Ripley's circumference correction, a toroidal correction, and a guard area correction. First, simulation envelopes for a random point pattern are constructed for each edge correction method. Then statistical powers of these envelopes are analyzed in terms of the probability of detecting clustering and regularity in simulated clustering/regularity patterns. In addition to the K-function, K(h), determined for individual distances, h, an overall statistic k is also examined. A major finding of this paper is that the K-function method adjusted by either the Ripley or toroidal edge correction method is more powerful than what is not adjusted or adjusted by the guard area method. Another is that the overall statistic k outperforms the individual K(h) across almost the entire range of potential distances h.