Statistica Sinica 21 (2011), 1453-1471
doi:10.5705/ss.2008.289

A COSET PATTERN IDENTITY BETWEEN A $2^{n-p}$

DESIGN AND ITS COMPLEMENT

Peng Zeng$^1$, Hong Wan$^2$ and Yu Zhu$^2$

$^1$Auburn University and $^2$Purdue University

Abstract: The coset pattern matrix contains more detailed information about effect aliasing in a factorial design than the commonly used wordlength pattern. More flexible and elaborate design criteria can be proposed using the coset pattern matrix. In this article, we establish an identity that relates the coset pattern matrix of a design to that of its complement. As an application, the identity is used to characterize minimum $M$-aberration designs through their complements.

Key words and phrases: Complementary design, coset pattern matrix, fractional factorial design, minimum M-aberration, wordlength pattern.