Selection between variance-optimal and bias-optimal designs when some two-factor interactions are important

Fractional factorial designs are useful for collecting data in many fields of studies because they allow us to study the effects of many factors on the response. As the primary interest of most experiments is for screening important factors, interactions are generally assumed to be negligible. When some two-factor interactions are important, variance-optimal designs and bias-optimal designs are available. In this study, we compare these two types of designs by using a mean squared error criterion that takes effect sparsity into consideration. We obtain a closed-form expression of this mean squared error criterion for the two types of designs. Under different levels of sparsity, results are obtained for designs of 10, 12, 14, 20, 26, 28 runs, which will help practitioners to choose between the two types of designs.