Analyzing unreplicated factorial experiments: A review with some new proposals

Recently, there have been many proposals for objectively analyzing unreplicated factorial experiments. We review these methods along with some earlier and perhaps lesser known ones. New methods are also proposed. The primary aim of this paper is to compare these methods and their variants via an extensive simulation study. Robustness of the various methods to non-normality is also considered. Many methods are comparable, but clearly some cannot be recommended. The results from the study also suggest some basic principles for evaluating new methods. Finally, we outline some issues that this study has raised and which might benefit from work in other areas such as multiple comparisons, outlier detection, ranking and selection, and robust statistics.