MODIFYING THE T-TEST FOR ASSESSING THE CORRELATION BETWEEN 2 SPATIAL PROCESSES

Clifford, Richardson, and Hemon (1989, Biometrics 45, 123-134) present ed modified tests of association between two spatially autocorrelated processes, for lattice and non-lattice data. These tests are built on the sample covariance and on the sample correlation coefficient; they require the estimation of an effective sample size that takes into acc ount the spatial structure of both processes. Clifford et al. develope d their method on the basis of an approximation of the variance of the sample correlation coefficient and assessed it by Monte Carlo simulat ions for lattice and non-lattice networks of moderate to large size. I n the present paper, the variance of the sample covariance is computed for a finite number of locations, under the multinormality assumption , and the mathematical derivation of the definition of effective sampl e size is given. The theoretically expected number of degrees of freed om for the modified t test with renewed modifications is compared with that computed on the basis of equation (2.9) of Clifford et al. (1989 ). The largest differences are observed for small numbers of locations and high autocorrelation, in particular when the latter is present wi th opposite sign in the two processes. Basic references that were miss ing in Clifford et al. (1989) are given and inherent ambiguities are d iscussed.