EFFECTS OF SPATIAL STRUCTURES ON THE RESULTS OF FIELD EXPERIMENTS

Abstract

Field experiments have been designed to account for spatial structures since the inception of randomized complete block designs by R. A. Fisher. In recent years, our understanding of spatial structures led to refinements in the design and analysis of field experiments in the face of spatial patterning. In the presence of spatial autocorrelation in the response variable, is it possible to optimize the experimental design to maximize the response to the experimental factors? The questions addressed in this paper are: (1) What is the effect of spatial autocorrelation on type I error of the tests of significance commonly used to analyze the results of field experiments? (2) How effectively can we control for the effect of spatial autocorrelation by the design of the experiment? (3) Which experimental designs lead to tests of significance that have greater power? (4) What is the influence of spatial autocorrelation on power of ANOVA tests of significance? This paper attempts to answer these questions through numerical simulations with known spatial autocorrelation. Response variable were simulated to represent the sum of separate effects: (1) an explanatory environmental variable (which could be used as a covariable in the analysis) with a deterministic structure plus spatial autocorrelation, (2) an effect of the experimental treatments, (3) spatial autocorrelation in the response (e.g., biological) variable, and (4) a random error. The program repeatedly generated and analyzed surfaces with given parameters (1000 replicates). The rejection rate of the null hypothesis of no effect of the treatment onto the response variable provided estimates of type I error and power. The simulations showed the following: (1) In the presence of spatial autocorrelation, or if repetitive deterministic structures are present in the variables influencing the response, experimental units should not be positioned at random. (2) ANOVA that takes blocking into account is an efficient way of correcting for deterministic structures or spatial autocorrelation. (3) For constant effort, experimental designs that have more, smaller blocks, broadly spread across the experimental area, lead to tests that have more power in the presence of spatial autocorrelation. (4) Short-ranged spatial autocorrelation affects the power of ANOVA tests more than large-ranged spatial autocorrelation.