Spatial autocorrelation and statistical tests: Some solutions

Spatial dependence or spatial autocorrelation often occurs in ecological data and can be a serious problem in analysis, affecting the significance rates of statistical tests, making them too liberal when the dependence is positive. Ecological phenomena often are patchy and give data with a wave structure, producing autocorrelation that cycles between positive and negative with increasing distance, further complicating the situation. This article describes the essentials of dealing with this problem as commonly encountered in analyzing ecological data for two variables. We investigated two related approaches to correcting statistical tests for data with spatial autocorrelation from one-dimensional sampling schemes like the transects used in plant ecology, the example of interest here. Both approaches estimate the “effective sample size” based on the observed autocorrelation structures of the variables. We examined tests of correlation and bivariate goodness-of-fit tests, as well as extensions beyond both of these test classes. The correction methods prove to be robust for a wide range of spatial autocorrelation structures in one-dimensional data and provide reliable corrections in most cases. They fail only when the data have strong and consistent waves that cause persistent cycles in the autocorrelation as a function of distance. By examining the spatial autocorrelation structure of the ecological data, we can predict the likelihood of successful correction for these bivariate tests.