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Published online by Cambridge University Press: 19 June 2025
The presence of autocorrelation in data violates the usual assumption of independence in the data for evaluating inferential statistics. We describe several models of autocorrelation in spatial data (both positive and negative). Given two serial variables, x and y, autocorrelation observed in y can be due to inherent autoregression in the variable itself, autoregression induced by its dependence on x, which has its own autocorrelation, or doubly autoregressive, with autocorrelation in both variables. This effect can be addressed by estimating the effective sample size (number of independent observations equivalent in information content to the n that are autocorrelated). We present the calculation of the effective sample size for many inferential statistics, including correlation, partial correlation, t-tests and ANOVA. The use of restricted randomization is explained as a method for testing when other approaches are not available. We also provide recommendations for sampling and experimental design in the presence of spatial autocorrelation.
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