Effects confounded with blocks in factorial designs: a projective geometric approach with two blocks

Screening designs are useful for situations where a large number of factors (q) is examined but only few (k) of these are expected to be important. [Plackett and Burman 1946] designs and Hadamard matrices have traditionally been studied for this purpose. (Box, G.E.P., Tyssedal, J., 1996. Projective properties of certain orthogonal arrays. Biometrika 83, 950-955, Cheng, C.-S., 1995. Some projection properties of orthogonal arrays. Ann. Statist. 23, 1223-1233, Plackett, R.L., Burman, J.P., 1946. The design of optimum multifactorial experiments. Biometrika 33, 305-325). After the identification of the active factors, the design is projected into lower dimensions in order to entertain and estimate significant effects. The geometric approach of the problem suggests that additional runs need to be added in order to form a full or a fractional factorial design of suitable resolution for this purpose. Since additional runs are often performed in different experimental environments, it is not clear if blocking affects the analysis results.