OUTLIERS AND THE USE OF THE RANK TRANSFORMATION TO DETECT ACTIVE EFFECTS IN UNREPLICATED 2^f EXPERIMENTS

Abstract

It is well known that outliers or faulty observations affect the analysis of unreplicated factorial experiments. This work proposes a method that combines the rank transformation of the observations, the Daniel plot and a formal statistical testing procedure to assess the significance of the effects. It is shown, by means of previous theoretical results cited in the literature, examples and a Monte Carlo study, that the approach is helpful in the presence of outlying observations. The simulation study includes an ample set of alternative procedures that have been published in the literature to detect significant effects in unreplicated experiments. The Monte Carlo study also, gives evidence that using the rank transformation as proposed, provides two advantages: keeps control of the experimentwise error rate and improves the relative power to detect active factors in the presence of outlying observations.

Keywords:

• Faulty observations
• Industrial experimentation
• Nonparametric analysis
• Rank transformation

ACKNOWLEDGMENTS

Much of this work was done while the first author was on sabbatical leave in the Department of Probability and Statistics at the Centro de Investigación en Matemáticas (CIMAT). This research was partially sponsored by Asociación Mexicana de la Cultura, A.C. The authors wish to thank two anonymous referees for their very helpful comments to improve the manuscript.