Two-Level Factorial and Fractional Factorial Designs in Blocks of Size Two

Abstract

It is sometimes necessary to perform two-level factorial designs in blocks of size two. We investigate what combinations of designs in different pairing arrangements permit estimation of all main effects and two-factor interactions. The confounding patterns of selected combination designs which combine several 2k designs in different pairings are presented for k = 2, 3, 4, and 5. We seek “best” combination designs which provide the most pure (within block) estimates of main effects and two-factor interactions under each confounding pattern given. Some “best” sequential combinations of 2k designs with various choices of initial arrangements are also given. The popular mirror-image pairing design is not the best initial arrangement, but is valuable for providing pure estimates of all the main effects. Extensions to 2k−p fractional factorial designs are illustrated. An example illustrates the use of a follow-up inter-block analysis.