The need of considering the interactions in the analysis of screening designs

Fractional factorial designs are widely used experimental plans for identifying important factors in screening studies where many factors are involved. Traditionally, Plackett–Burman (PB) and related designs are employed in such studies because of their cost efficiencies. The caveat with the use of PB designs is that interactions among factors are implicitly assumed to be non‐existent. However, there are many practical situations where some interactions are significant and ignoring them can result in wrong statistical inferences, including biased estimates, missing out on important factors, and detection of spurious factors. We reanalyze data for three chemical experiments using the Hamada and Wu's method and showed that we are able to identify significant interactions in each of these chemical experiments and improve the overall fit of the model. In addition, we analyze the data using a Bayesian approach that confirms our findings. In both approaches, graphical tools are employed along with easily available software for analysis.