The Design and Analysis of Block Experiments

Summary This paper attempts to give a systematic derivation of the principal results of the analysis of block experiments using matrix notation. It also shows how the problem of design can be formulated in an analytical form and illustrates the type of mathematical problem that arises in such a formulation. The systematic approach to the analysis of experiments enables methods to be evolved for performing these analyses on automatic calculating machines and to facilitate this the paper discusses the analysis of spoilt experiments and the iterative solution of the equations arising in the recovery of inter-block information.