The Optimum Design of a Two-Factor Experiment Using Prior Information

Abstract

This paper is concerned with a two-factor analysis of variance situation, the factors being conveniently referred to as blocks and treatments. One of the treatments has the role of a control. Attention is focused on inference about the treatment parameters, the block parameters being regarded as nuisance parameters. With a general multivariate normal form for the distribution of errors and for the prior distribution on the block and treatment parameters, the posterior distribution of the treatment parameters is derived. With a quadratic loss function an algorithm is derived for the optimum allocation of treatments over a given sample with known blocking. In special cases the optimum allocation can be written down immediately and the algorithm need not be resorted to.