RECOVERY OF INTERBLOCK, INTERGRADIENT, AND INTERVARIETY INFORMATION IN INCOMPLETE BLOCK AND LATTICE RECTANGLE DESIGNED EXPERIMENTS

Spatial analysis and blocking analysis of experimental results are tre ated separately in the literature. Here we combine these analyses into a single analysis. The information arising from the random nature of different gradients within incomplete blocks is used to adjust treatme nt means. We extend Cox's (1958, Journal of the Royal Statistical Soci ety, Series B 20, 193-204) idea of differential gradients within colum ns of a Latin square to within blocks for incomplete block and row-col umn designed experiments and, in addition, treat them as random effect s. With this analysis, the restrictions on randomization due to blocki ng are taken into consideration whereas they are often ignored in spat ial analysis literature. Some comments on designing experiments and an alyzing experimental results to control heterogeneity are presented. A numerical example illustrates the computational procedure and indicat es effect of alternative analyses. The class of augmented experiment d esigns has been found useful for experiments involving comparisons of standard check treatments with a set of new and untried treatments, us ually with one replicate. Interreplicate, interblock, interrow, and/or intercolumn information is available to use in obtaining solutions fo r new treatment effects. Since the new treatment effects are often con sidered to be random effects, their distributional properties may be u sed to increase the efficiency of the experiment. We demonstrate the s tatistical procedures for recovering this information in block and row -column designs using mixed model procedures.