Generalised deletion designs

In this paper asymmetrical single replicate factorial designs are constructed from symmetrical single replicate factorial designs using the deletion technique. The study is along the lines of Voss(1986), Chauhan(1989) and Gachii and Odhiambo(1997). We give results for the general order deletion designs of the form sn-m1(s – L)m1. . which are proper, for 1 < L < (s – 1) and m1 less than or equal to the number of generators of the preliminary single replicate generalized cyclic design. We generalize results by earlier authors. Results identifying the set of estimable factorial effects of the deletion designs based on the information available from the preliminary factorial design are given. Simple formulas for calculating the loss of information due to confounding with blocks are given. Efficiency with respect to the number of treatment combinations needed to estimate a given set of interactions of the preliminary factorial design is compared with that of the resulting deletion designs.