Spatial autocorrelation and statistical tests in ecology

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Abstract
The presence of positive spatial autocorrelation in ecological data causes parametric statistical tests to give more apparently significant results than the data justify, which is a serious problem for both statistical and ecological interpretation. In this paper, we review this problem and some of the statistical approaches that have been used to address it, concentrating on statistical methods rather than on sampling or experimental design. We then describe in more detail the technique of adjusting the “effective sample size” based on the autocorrelation structure of the data. Unfortunately, the effective sample size cannot be reliably estimated from the data, and therefore this approach may not be a general solution to the problem. An alternative approach is to determine a parametric model of the data and its spatial autocorrelation structure, and then to use a Monte Carlo approach to generate the distribution of the test statistic of interest using that model. We suggest that this latter approach should be used in situations in which no robust analytically derived solution is available.