A Bayesian Perspective on the Analysis of Unreplicated Factorial Experiments Using Potential Outcomes

Unreplicated factorial designs have been widely used in scientific and industrial settings, when it is important to distinguish “active” or real factorial effects from “inactive” or noise factorial effects used to estimate residual or “error” terms. We propose a new approach to screen for active factorial effects from such experiments that uses the potential outcomes framework and is based on sequential posterior predictive model checks. One advantage of the proposed method is its ability to broaden the standard definition of active effects and to link their definition to the population of interest. Another important aspect of this approach is its conceptual connection to Fisherian randomization tests. Extensive simulation studies are conducted, which demonstrate the superiority of the proposed approach over existing ones in the situations considered.