Spatial Nature of Randomization and Its Effect on the Outcome of Field Experiments
- H. M. van Es and
- C. L. van Es
Many sites used for field trials exhibit a spatially-dependent variance structure in that nearby observations are autocorrelated. This may affect treatment comparisons made at unequal distances. This study investigated (i) the probabilistic nature of randomization with respect to spatial distances in randomized complete block (RCB) designs and (ii) the effect of spatially unbalanced designs on the outcome of field experiments. The mean distance of treatment comparison increases linearly with the number of treatments in the experiment. The lack of spatial balance also increases and is inversely related to the number of replications. This may result in increases in Type 11 errors for short-distance treatment contrasts and increases in Type I errors for long-distance contrasts. Evaluation of two experimental RCB designs involving four and nine treatments and four replications showed that the randomization process does not ensure spatial balance. Two simulated experiments, each using 50 randomizations based on the Mercer and Hall data showed no adverse effect from spatially unbalanced treatment comparisons if the underlying variance structure is random, but significant effects if spatial autocorrelation is present. Expected variances for long-distance comparisons (5.6% of all comparisons) were 51% higher than the error term resulting in tests of treatment differences at a = 0.05 to actually be conducted at the 0.09 error level. Alternative design and analysis methods that ensure spatially balanced treatment comparisons are discussed.
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