Existence and construction of randomization defining contrast subspaces for regular factorial designs

TL;DR

This paper introduces a unified geometric approach to construct regular factorial designs with randomization restrictions, enabling systematic design creation and analysis.

Contribution

It develops a systematic method using finite projective geometry to determine existence and construct such designs, unifying various existing designs under a common framework.

Findings

Finite projective geometry determines design existence.

Systematic construction approach developed.

Common factorial designs are special cases.

Abstract

Regular factorial designs with randomization restrictions are widely used in practice. This paper provides a unified approach to the construction of such designs using randomization defining contrast subspaces for the representation of randomization restrictions. We use finite projective geometry to determine the existence of designs with the required structure and develop a systematic approach for their construction. An attractive feature is that commonly used factorial designs with randomization restrictions are special cases of this general representation. Issues related to the use of these designs for particular factorial experiments are also addressed.