Practical considerations for experimental designs of spatially autocorrelated data using computer intensive methods

Classical experimental design depends upon randomization of treatment applications. However, if data come from a spatially autocorrelated random process, it is possible to find specific designs that are much better. For example, it is possible to find universally optimum complete block designs that are optimal for a spatial process where the variables are independent among blocks but within blocks follow an autoregressive second order process. The problem with these designs is that they are only possible for certain combinations of plots, blocks, and treatments, and the optimality criteria is based on a particular set of contrasts. In this paper, I use methods based on simple genetic algorithms with simulating annealing to find good experimental designs for any combination of plots, blocks, treatments, and any set of contrasts. The computer intensive methods find optimal designs equivalent to universally optimum complete block design for certain sets of contrasts, and they find better designs for other sets of contrasts. The computer intensive methods are much better than randomized designs. I show a real example for a 2×3 factorial experiment where shade and water treatments were applied to examine their effects on caribou forage quality, where I also examine the robustness of the design. General guidelines are discussed on using computer intensive methods to find near-optimal designs.