Construction of regular, single-replicate, two-factor designs

Abstract

Abstract The existence and construction of regular, single-replicate, two-factor designs with specified numbers of degrees of freedom confounded from each factorial space is investigated. Regularity is an important property since it ensures that the estimable contrasts belonging to the factorial spaces span the space of estimable contrasts in the design, and no information is wasted on estimating unimportant contrasts. The general existence problem is reduced to easily verifiable number theoretic conditions and a simple construction method is given. The problem of constructing regular designs which minimize the loss of information on the interaction is considered. It is shown that the minimization can be achieved within the class of single-replicate generalized cyclic designs. An algorithm is given for the more difficult problem of constructing designs which minimize the confounding of the main effects at the expense of the interaction.