Confounding of Location and Dispersion Effects in Unreplicated Fractional Factorials

Abstract

When studying both location and dispersion effects in unreplicated fractional factorial designs, a “standard” procedure is to identify location effects using ordinary least squares analysis, fit a model, and then identify dispersion effects by analyzing the residuals. In this paper, we show that if the model in the above procedure does not include all active location effects, then null dispersion effects may be mistakenly identified as active. We derive an exact relationship between location and dispersion effects, and we show that without information in addition to the unreplicated fractional factorial (such as replication) we can not determine whether a dispersion effect or two location effects are active.

• Confounding
• Dispersion
• Fractional Factorial Designs
• Scale Parameter

Additional information

Notes on contributors

Richard N. McGrath

Dr. McGrath is an Assistant Professor in the Department of Applied Statistics and Operations Research. He is a Member of ASQ. His email address is [email protected].

Dennis K. J. Lin

Dr. Lin is a Professor in the Department of Management Science and Information Systems and in the Department of Statistics. He is a Senior Member of ASQ.