Assessing the significance of the correlation between two spatial processes

Modified tests of association based on the correlation coefficient or the covariance between two spatially autocorrelated processes are presented. These tests can be used both for lattice and nonlattice data. They are based on the evaluation of an effective sample size that takes into account the spatial structure. For positively autocorrelated processes, the effective sample size is reduced. A method for evaluating this reduction via an approximation of the variance of the correlation coefficient is developed. The performance of the tests is assessed by Monte Carlo simulations. The method is illustrated by examples from geographical epidemiology.