Practical Inference from Industrial Split-Plot Designs

Abstract

In many industrial response surface experiments, some of the factors investigated are not reset independently. The resulting experimental design then is of the split-plot type, and the observations in the experiment are in many cases correlated. A proper analysis of the experimental data therefore is a mixed model analysis involving generalized least-squares estimation. Many people, however, analyze the data as if the experiment was completely randomized and estimate the model using ordinary least squares. The purposes of this article are to quantify the differences in conclusions reached from the two methods of analysis and to provide the reader with guidance for analyzing split-plot experiments in practice. The problem of determining the denominator degrees of freedom for significance tests in the mixed model analysis is discussed as well.

• Containment Method
• Generalized Least Squares
• Method of Kenward and Roger
• Ordinary Least Squares
• Residual Method
• Satterthwaite's Method

Additional information

Notes on contributors

Peter Goos

Dr. Peter Goos is a Professor in the Faculty of Applied Economics of the Universiteit Antwerpen. He is a member of ASQ. His email address is [email protected].

Ivan Langhans

Dr. Ivan Langhans is Senior Consultant at CQ Consultancy and a researcher at the Research Center for Operations Research & Business Statistics of the Katholieke Universiteit Leuven. His email address is [email protected].

Martina Vandebroek

Dr. Martina Vandebroek is a Professor at the Research Center for Operations Research & Business Statistics and at the University Center of Statistics, both at the Katholieke Universiteit Leuven. Her email address is [email protected].