Block Designs

Abstract

The theory of linear estimation and linear hypotheses developed in the first two chapters will be applied to specific designs in this and later chapters. We start with a discussion on general block designs in this chapter which includes both complete and incomplete block designs. If an experimenter is able to get plots which are homogeneous with respect to the yield of interest, then the CRD model discussed in Examples 1.2.13 and 2.3.7 can be used. For example, if several teaching methods have to be compared for their efficacy, then one may choose students of a particular age group who have almost similar abilities as evident from almost identical scores in a test given to them. For sub-groups of such homogeneous students, the different teaching methods to be compared can be administered. If such homogeneous plots are not available for an experiment, but a number of groups of plots are available such that the plots within a group are homogeneous but plots across groups are not, then one can go for models associated with block designs, which is the subject matter of this chapter. In many situations, homogeneous plots are not available for experimenters and block designs are very useful models in such situations. After discussing linear estimation in general block designs, testing of standard omnibus hypotheses in general block designs is discussed. The theory of general block designs is then applied to the study of randomized block design, balanced incomplete block design, and partially balanced incomplete block design.

Statisticians, like artists, have the bad habit of falling in love with their models

—G.E.P. Box