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 2^k 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 2^k 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 2^k−p fractional factorial designs are illustrated. An example illustrates the use of a follow-up inter-block analysis.

• Blocking
• Factorial Designs
• Fractional Factorial Designs
• Sequential Designs

Additional information

Notes on contributors

Yuyun Jessie Yang

Dr. Yang lives in San Jose, CA. She is a Member of ASQ. Her email address is [email protected].

Norman R. Draper

Dr. Draper is an Emeritus Professor of Statistics. He is a Fellow of ASQ. His email address is [email protected].