Two-level Orthogonal and Saturated Designs for Estimating Main Effects and Certain Important Interactions

Abstract

In a two-level factorial experiment, we consider orthogonal designs that allow joint estimation of the grand mean, all main effects, and certain classes of two-level interactions, assuming that the remaining effects are all negligible. Based on a judicious allocation of the factorial effects of interest to the columns of a Hadamard matrix, we propose some general classes of orthogonal and saturated designs which include some existing orthogonal main-effect plans of asymmetric factorials as special cases.

Keywords:

• Factorial design
• Hadamard matrix
• Main-effect plan
• Orthogonal array

Mathematics Subject Classification:

• 62K10