Validity of Spatial Analyses for Large Field Trials

A number of recent articles report that analyses which account for spatial variation in eld trials in terms of correlations between plot errors are more eecient than the classical randomized blocks analysis of variance. In most cases, these eeciency comparisons are in terms of model-based or 'predicted' estimates of precision. The validity of estimates of precision has not been generally demonstrated for these correlated errors (CE) analyses, however. We describe a simulation study to assess validity (as well as eeciency) of several CE and alternative xed eeects spatial analyses. We focus on situations typical of large eld trials with limited replication, and with realistic levels of both xed and random components of spatial variation. Results show that when spatial autocorrelation is present the CE analyses are robust with respect to validity, except when strong xed trend is underrtted in the analysis. Also, when spatial autocorrelation is present, eeciency of the CE analyses is substantially greater than that for the classical blocks analysis, xed eeects trend analysis, and row-column analysis, but is only slightly better than an uniterated Papadakis analysis. These results are illustrated using a corn yield data set which is also used to demonstrate a graphical technique for assessing adequacy of a CE model.