Analyzing dispersion effects from replicated order-of-addition experiments

Dispersion effects may play a vital role, in addition to location effects, in exploring optimal addition orders of several materials in some chemical, industrial and pharmaceutical studies. Two replication-based statistical methods developed using frequentist and fiducial probability arguments are introduced in this paper to identify active dispersion effects from replicated order-of-addition experiments. Simulation results show that both approaches can maintain empirical sizes sufficiently close to the nominal level while their finite-sample performances are very similar. From a statistical perspective, the fiducial method can provide a unified probability framework to analyze dispersion effects as well as location effects. However, it is computationally more expensive than the frequentist method. Consequently, the frequentist method is recommended for real-world applications due to its low computational cost. A drug combination study is used to illustrate these two approaches. In addition, some eligible order-of-addition designs are collected in a catalogue for future work.