Checking the Adequacy of Fit of Models from Split-Plot Designs

Abstract

One of the main features that distinguish split-plot experiments from other experiments is that they involve two types of experimental errors: the whole-plot (WP) error and the subplot (SP) error. Taking this into consideration is very important when computing measures of adequacy of fit for split-plot models. In this article, we propose the computation of two R², R²-adjusted, prediction error sums of squares (PRESS), and R²-prediction statistics to measure the adequacy of fit for the WP and the SP submodels in a split-plot design. This is complemented with the graphical analysis of the two types of errors to check for any violation of the underlying assumptions and the adequacy of fit of split-plot models. Using examples, we show how computing two measures of model adequacy of fit for each split-plot design model is appropriate and useful as they reveal whether the correct WP and SP effects have been included in the model and describe the predictive performance of each group of effects.

• Model Adequacy Checking
• PRESS
• Residual Analysis
• R²
• R²-Adjusted
• R²-Prediction
• Subplot Error
• Whole-Plot Error

Additional information

Notes on contributors

Ashraf A. Almimi

Dr. Almimi is a Postdoctoral Research Fellow at the National Aeronautics and Space Administration's Langley Research Center. He received his Ph.D. in Industrial Engineering from Arizona State University. He is a Member of ASQ. His email address is [email protected].

Murat Kulahci

Dr. Kulahci is an Associate Professor in the Department of Informatics and Mathematical Modeling at Technical University of Denmark. He is a Member of ASQ. His email address is [email protected].

Douglas C. Montgomery

Dr. Montgomery is Regents' Professor of Industrial Engineering and Statistics in the Department of Industrial, Systems and Operations Engineering at Arizona State University. He is a Fellow of ASQ. His email address is [email protected].