Approximate analysis of variance of spatially autocorrelated regional data

The classical method for analysis of variance of data divided in geographic regions is impaired if the data are spatially autocorrelated within regions, because the condition of independence of the observations is not met. Positive autocorrelation reduces within-group variability, thus artificially increasing the relative amount of among-group variance. Negative autocorrelation may produce the opposite effect. This difficulty can be viewed as a loss of an unknown number of degrees of freedom. Such problems can be found in population genetics, in ecology and in other branches of biology, as well as in economics, epidemiology, geography, geology, marketing, political science, and sociology. A computer-intensive method has been developed to overcome this problem in certain cases. It is based on the computation of pooled within-group sums of squares for sampled permutations of internally connected areas on a map. The paper presents the theory, the algorithms, and results obtained using this method. A computer program, written in PASCAL, is available.This work was supported by NSERC grant no. A7738 to Pierre Legendre and by grant BSR 8614384 from the National Science Foundation to Robert R. Sokal. This is contribution No. 366 of the Groupe d'Ecologie des Eaux Douces, Université de Montréal, and contribution No. 727 in Ecology and Evolution from the State University of New York at Stony Brook.