A more powerful test method for analyzing unreplicated factorial two-level experiments

Abstract

Most of existing methods for analyzing unreplicated two-level factorial designs need the assumption of effect sparsity and only perform well when the effectssparsity assumption holds. The effects-sparsity assumption is frequently true, but it is not always true. This paper proposes a new method that needs not the effects-sparsity assumption and has the potential for detecting up to m-1 active effects, in which m is the number of effects under study. The proposed method is illustrated by two unreplicated factorial designs appeared in the literature. An extensive Monte Carlo comparison study, based on 100,000 replications, is carried out to compare the proposed method with another four popular and powerful existing objective methods. The simulation study shows that the proposed method has more power than the remainder four compared methods in most of the conditions under study.

Keywords:

• Objective method
• Power
• Saturated design
• Simulation study
• Unreplicated factorial

Acknowledgements

This work was partially supported by the China Scholarship Council. We thank the editor and the anonymous reviewers for the constructive comments that improved this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s)

Additional information

Funding

This work was partially supported by the China Scholarship Council. We thank the editor and the anonymous reviewers for the constructive comments that improved this paper.