Correcting for spatial autocorrelation in statistical tests: Ways to deal with low-replication field experiments

We develop a simple method to better analyze field experiments in the face of spatial autocorrelation, especially when there is little or no spatial replication of treatment blocks. Spatial autocorrelation is known to inflate alpha in statistical tests. Our method decomposes a correlation matrix for pre-treatment data (estimated using Moran's I for various lag distances) into eigenvalues and eigenvectors and uses them to generate uncorrelated estimates of post-treatment data values. These corrected, uncorrelated data may be subject to standard statistical tests such as ANOVA or regression. We evaluate the robustness of this method by simulating spatially and temporally correlated experimental data and comparing ANOVA results for corrected vs. uncorrected data. The simulation results show that our approach can ameliorate the inflation of alpha caused by spatial autocorrelation without adversely affecting non-correlated data, and can dramatically increase the power to detect treatment effects, especially when an experiment has low numbers of treatment blocks or has a completely pseudo-replicated design.