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A Simple Analysis of Unreplicated Factorials with Possible Abnormalities

Summary: Sometimes data analysis using the usual parametric techniques produces misleading results due to violations of the underlying assumptions, such as outliers or non-constant variances. In particular, this could happen in unreplicated factorial or fractional factorial experiments. To help in this situation alternative analyses have been proposed. For example Box and Meyer give a Bayesian analysis allowing for possibly faulty observations in unreplicated factorials and the well known Box-Cox transformation can be used when there is a change in dispersion. This paper presents an analysis based on the rank transformation that deals with the above problems. The analysis is simple to use and can be implemented with a general purpose statistical computer package. The procedure is illustrated with examples from the literature. A theoretical justification is outlined at the end of the paper.

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  • Topics: Design of Experiments
  • Keywords: Factorial designs,Transformation,Outliers
  • Author: Tores, Victor Aguirre
  • Journal: Journal of Quality Technology