Randomized Complete Block Designs

Abstract

This article discusses the general need for blocking when experimental units are not homogeneous. Complete, generalized, and incomplete block designs are discussed, together with issues of randomization, missing cells, and the usual assumption of “no interaction”. Two specific cases of the Randomized Complete Block Design are considered: the fixed case (treatments and blocks are both fixed) and the mixed case (treatments are fixed, blocks are random). For each case, the scalar linear models are defined in full-rank and non-full-rank versions, together with necessary assumptions. Point estimates and standard errors are given for main-effect means and cell means, and for variance components. The analysis of variance table is given, with expected mean squares, for testing hypotheses.