The nonorthogonal estimator

Classical fractional factorial designs yield biased estimates of a set of parameters when aliased parameters are nonzero. In the early 1960s Ehrenfeld and Zacks constructed Randomization Procedures I and II to remove this bias from estimation of a subset of parameters of a full factorial experiment. The subset of parameters to be estimated using either of these randomization procedures must have a certain group structure and the sample size must be a multiple of the group size. In this paper, we discuss the nonorthogonal estimator which removes these restrictions while producing unbiased estimates in the case of a two-level experiment. Examples are provided.