Projective properties of certain orthogonal arrays

A question of importance in factor screening is when a two-level orthogonal design for a multifactor experiment can be projected into lower dimension, typically P = 2 or 3. New results relate to the projectivity P of saturated designs in which n − 1 factors are tested in n runs. It is shown that: a design obtained by ‘doubling’ an n × n orthogonal array is always of projectivity P = 2; a two-level cyclic design is either a factorial array, and hence has P = 2, or it has P = 3; a two-level orthogonal design with 4m runs, m odd, has P = 3. In particular these results allow the designs derived by Plackett & Burman (1946) to be categorised in terms of these projective properties.