10 A critique of some aspects of experimental design

Abstract

This chapter discusses several aspects of experimental design. An experiment is done using “experimental material.” The materials can be divided into divided into units. Usually, on each unit, one of the treatments is applied, and a variable is measured, which in some sense denotes the “effect” of the treatment applied to it “plus” (i.e., “confounded with”) the effect of its own “innate characteristics” (i.e., its “individual effect”). To help “average out” over such individual effects, the principle of “replication” (i.e., try each treatment on several units) was founded. Three criteria of goodness of a design include (1) variance-optimality, (2) sensitivity, and (3) revealing power. Variance-optimality seeks to determine a design that maximizes some functions of the information matrix of the estimates of the parameters. The chapter also discusses several other models used in experimental design. These models include search linear models, designs with one nuisance factor, row-column designs, and factorial experiments.