Optimal Allocation of Experimental Material.
Interim rept. Sep 72-Mar 73,
AEROSPACE RESEARCH LABS WRIGHT-PATTERSON AFB OHIO
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The problem considered is that of how to allocate optimally a fixed number of experimental units to a given number of treatments when there are covariates and the values of the covariates are known prior to the advent of the actual experiment. The underlying statistical model is assumed to be linear in all its parameters, and the criterion of optimality was, for the most part, taken to be D-optimality for inferences on the treatment means. An allocation of the experimental units is shown to be optimal according to this criterion if and only if it is D-optimal for inferences on all parameters. It is shown that the computations required to determine an optimal allocation can be simplified by taking advantage of known results on the determinants of partitioned matrices. D-optimal designs were computed for a simple example taken from the chemical industry, and it was found that, at least in some instances, their use would result in a considerable increase in efficiency over choosing an allocation by randomization. Modified author abstract
- Statistics and Probability