Preserving projection properties when regular two-level designs are blocked

Abstract

The main finding is that by allowing blocks to be partially confounded with interactions, the projectivity was increased for all the designs which were tested, compared to the usual recommended blocking based on confounding of interactions. Using the suggested blocking thereby enables estimation of all effects for a higher number of active factors than when using blocking based on confounding. The drawback of allowing partial confounding between blocks and interactions is that it results in higher standard deviations for the estimates of the corresponding effects.