Assessing the Significance of a Spatial Correlogram

Simulations comparing the power of the Q-test to the power of several other techniques under several alternative hypotheses reveal the following. The decision rule involving inspection of only the lag-1 autocorrelation coefficient is insensitive to certain forms of spatial dependence, for example, dependence involving interactions that are strongest at high-order lags. A modified Kooijman's (1976) technique is roughly equal in power to the other methods investigated, but requires a simulation for each correlogram tested. Kooijman's original recommendation for estimating the variance of I/max/ can lead to negative variance estimates and should therefore not be used. The Sidak (1967) and Bonferroni methods, which are computationally very simple, are preferable to the Q-test when there are few distance classes and weak spatial pattern. As pattern intensity and number of distance classes increase, the Q-test becomes more powerful.

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