Testing mutual independence between two discrete-valued spatial processes: a correction to pearson chi-squared

A common feature of data collected in environmental and earth sciences is that they typically exhibit spatial autocorrelation. Violating the assumption of independent observations can have dramatic effects on inferences derived from standard statistical methods. In this article, we examine the consequences of spatial autocorrelation on Pearson's chi-squared test of mutual independence between two categorical responses with a general number of classes. Correspondingly, we suggest a simple modification to the standard test statistic that allows for spatial autocorrelation. Our modified statistic is based on a first-order correction factor and thus provides only an approximate test. However, we show by Monte Carlo simulation that this approximation results in satisfactory inferences in several situations of practical interest. The usefulness of the method is displayed through an application to categorical data arising in the study of the relationship between the distribution pattern of plant species and woodland age in a forest in northern Belgium.