Clifford, Richardson, and Hemon (1989, Biometrics 45, 123-134) presented 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 account the spatial structure of both processes. Clifford et al. developed their method on the basis of an approximation of the variance of the sample correlation coefficient and assessed it by Monte Carlo simulations for lattice and non-lattice networks of moderate to large size. In 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 sample size is given. The theoretically expected number of degrees of freedom 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 with opposite sign in the two processes. Basic references that were missing in Clifford et al. (1989) are given and inherent ambiguities are discussed.