Nearly Optimal Allocation of Experimental Units Using Observed Covariate Values

Abstract

In many of the experimental situations to which the analysis-of-covariance model applies, the values of the covariates are known prior to the actual experiment so that they can be used in allocating the experimental units to the treatments. Due to the large number of possible allocations, the computation of an allocation that is D-optimal for inferences on the treatment means will generally not be practical. Good allocations can be constructed by a multistage procedure that allocates one or more units at each stage. These allocations can be made even better by applying an iterative algorithm that induces small changes in the design at each iteration. The techniques were applied to an example taken from the chemical industry and produced highly efficient allocations. Similar design techniques can be used in experimental situations where the experimental units become available and must be allocated in stages.

KEY WORDS:

• Experimental Design
• Analysis of Covariance
• D-optimal Designs