Powerful and robust dispersion contrasts for replicated orthogonal designs

Abstract

A popular approach for estimating location and dispersion effects in replicated designs under the common assumption of normal and independent errors is to use two linked generalized linear models (glms). This approach uses an asymptotic estimate for the variance of dispersion effect estimates and is very sensitive to the normality assumption. It is also possible to identify dispersion effects (after a logarithmic transformation) by using methods developed for identifying location effects in unreplicated designs. One such method is rather robust to the normality assumption but lacks power relative to the glm approach. We introduce a hybrid approach that strikes a balance between power and robustness when used for dispersion effect identification.

Keywords:

• Fractional factorial
• orthogonal array
• replication
• variance

Acknowledgements

We thank the editor and two reviewers for their insightful comments and suggestions that greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Richard N. McGrath

Richard N. (Herb) McGrath is a Professor of Applied Statistics and former Associate Dean in the College of Business at Bowling Green State University. His research interests lie in industrial statistics, i.e. design and analysis of experiments and statistical process control. He received a Ph.D. in Statistics and a B.S. in Industrial and Systems Engineering from The Pennsylvania State University and an M.S. in Statistics from Rutgers University.

Baffour Koduah

Baffour Koduah is a student of Statistics (PhD) at Bowling Green State University. He received his master's in Applied Statistics from Bowling Green State University and a BS from Kwame Nkrumah University of Science and Technology, Ghana.