Statistica Sinica 14(2004), 1069-1074

A NOTE ON REGULAR FRACTIONAL FACTORIAL

DESIGNS

Kenny Q. Ye

Albert Einstein College of Medicine

Abstract: This paper shows that any two-level factorial design that has no partial aliasing must be a $2^{k-p}$ design or replicates of a $2^{k-p}$ design. This is a special case of a more general result regarding $q$-level factorial designs, where $q$ is a prime power, under a certain parameterization of the factorial effects.

Key words and phrases: Indicator function, orthogonal array.