Analysis of a lattice square design and its use in bioassays.

Abstract

This dissertation deals with the analysis of an experimental design called the Lattice Square design and its use in estimating the relative potency of test preparations in parallel line bioassays. A Lattice Square is an incomplete two-way design and has the advantage of being able to eliminate two sources of variation simultaneously while keeping the block size from becoming too large. The row and column incidence matrices of the design have many interesting mathematical properties which are derived and described in this dissertation, which contribute to making the analysis more elegant. Under suitable conditions and assumptions, the estimates of treatment effects can be improved upon due to the use of recovery of inter-row and column information. The complete detail of the analysis of such designs are also derived in this dissertation and a numerical illustration of the use of this design in multiple bioassay is provided. Furthermore, this dissertation contains interesting and useful results and information about "BLUPs" (Best Linear Unbiased Predictors) of random row and column effects and "penalized least squares" equations and their advantages in the analysis of incomplete two-way designs.