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Inference for Unreplicated Factorial and Fractional Factorial Designs. William J Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1994 Inference for Unreplicated Factorial and Fractional Factorial Designs. William J. Kasperski Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Kasperski, William J., "Inference for Unreplicated Factorial and Fractional Factorial Designs." (1994). LSU Historical Dissertations and Theses. 5731. https://digitalcommons.lsu.edu/gradschool_disstheses/5731 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9502117 Inference for unreplicated factorial and fractional factorial designs Kasperski, William J., Ph.D. The Louisiana State University and Agricultural and Mechanical Col., 1994 UMI 300 N. ZeebRd. Ann Arbor, MI 48106 INFERENCE FOR UNREPLICATED FACTORIAL AND FRACTIONAL FACTORIAL DESIGNS A Dissertation Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The Interdepartmental Program in Business Administration by William J. Kasperski B.S., Northern Arizona University 1986 May 1994 ACKNOWLEDGMENTS I would like to express my appreciation to my major professor, Dr. Helmut Schneider, for his assistance, support, and guidance throughout this research. I look forward to continuing our research efforts in the future. I would also like to thank the members of my doctoral committee, Dr. Kwei Tang, Dr. Peter Kelle, Dr. Dan Rinks, Dr. Ye-Sho Chen, and Dr. Richard Kazmierczak. Their comments and suggestions helped make this a more thorough research study. Also, I would like to thank Dr. James Pruett for serving on my committee while he was at LSU. To Dr. Graydon Bell, thanks for getting me on the right track early in my academic career. Your straightforward comments were not fully appreciated for several years, until I realized that they were in my best interest. To Mrs. Forbes, your assistance in this work was an immense help. I would still be at this if it were not for you. Thanks for everything over the past several years. To Rob Rhoades, Ken Sosinski, Luciana Reis, Dr. Keith Johnson, Jeff Jonkman, and Phil Wadsworth, thanks for being there over the years and making things interesting. To my brother and sister, Frank and Mary Ann, thanks for your support over the years and for providing me with vacation possibilities across the U. S. and abroad. To my father, Franklin, thanks for making all of this possible. Your hard work and assistance has helped immeasurably over the years. Finally, I would like to dedicate this to the loving memory of my mother, Geraldine. TABLE OF CONTENTS Page ACKNOWLEDGMENTS ...................................................................................................ii LIST OF TABLES ............................................................................................................vii LIST OF FIGURES .......................................................................................................... ix ABSTRACT ................................................................................... x CHAPTER 1. INTRODUCTION........................................................................................ 1 1.1. Problem Statem ent ...........................................................................4 1.2. Contribution of the Research .......................................................... 5 1.3. Organization of the Research .......................................................... 6 2. FACTORIAL AND FRACTIONAL FACTORIAL DESIGNS .... 7 2.1. Factors, Effects, and Contrasts ....................................................... 7 2.2. Randomization ................................................................................... 9 2.3. Factorial Example ......................................................................... 11 2.4. Replication ....................................................................................... 12 2.5. Factorial Design Features.............................................................. 13 2.6. Two-Level Designs ......................................................................... 14 2.6.1. Redundancy in Factorial D esigns .................................... 15 2.7. Estimating Factor Effects in a Two-Level Design .................... 17 2.7.1. Table of + and - Coefficients ..........................................17 2.7.2. Symbolic Expressions ....................................................... 20 2.7.3. Yates’ Algorithm................................................................22 2.8. Fractional Factorial Designs .......................................................23 2.8.1. Obtaining the Fraction to A n a ly z e .................................25 2.8.2. Confounding ..................................................................... 26 2.8.3. Design Resolution .............................................................31 2.9. Plackett-Burman D e sig n s ..............................................................32 Page 3. COMPARISON OF PREVIOUS TECHNIQUES USED FOR DETERMINING ACTIVE EFFECTS IN AN UNREPLICATED FACTORIAL DESIGN................................................................. ____ 34 3.1. Factor Sparsity ................................................................. ____ 35 3.2. Daniel’s Normal Probability Plotting Procedure .... ____35 3.2.1. Description of Daniel’s Technique .................... ____ 36 3.2.2. Variations in Plotting Positions .......................... ____ 37 3.2.3. Advantages and Disadvantages of Daniel’s Procedure 39 3.3. Box and Meyer’s Bayesian Procedure .......................... ____ 39 3.3.1. Description of Box and Meyer’s Technique „ . , , 40 3.3.2. Estimation of Parameters in Box and Meyer’s Procedure .............................................................. .... 40 3.3.3. Advantages and Disadvantages of Box and Meyer’s P rocedure .............................................................. .41 3.4. Benski’s W’-test and Fourth-Spread Test Procedures . ____ 41 3.4.1. Description of Benski’s Technique .................... 42 3.4.2. Advantages and Disadvantages of Benski’s Procedure .............................................................. .44 3.5. Lenth’s Pseudo Standard Error Procedure .................... ____ 45 3.5.1. Description of Lenth’s Technique ....................... 45 3.5.2. Advantages and Disadvantages of Lenth’s Procedure .............................................................. ____ 47 3.6. A Published Example Comparing the Four Techniques ____ 48 4. SCHNEIDER, KASPERSKI, AND WEISSFELD’S PROCEDURE FOR DETERMINING ACTIVE EFFECTS IN AN UNREPLICATED FACTORIAL DESIGN............................................................. 51 4.1. Previous Related M aterial ..............................................................51 4.1.1. Quinlan’s Successive Pooling Procedure ......................52 4.1.2. Wilk, Gnanadesikan, and Freeny’s Variance Estimation P rocedure .......................................................................... 55 4.2. Description of Schneider, Kasperski, and Weissfeld’s Technique ................. 56 4.2.1. Determination of Critical t-values and Limits ............. 57 4.2.2. Advantages and Disadvantages of Schneider, Kasperski, Weissfeld’s Procedure .................................................... 60 4.3. Published Example of the Schneider, Kasperski, Weissfeld Procedure ......................................................................................60 iv Page 5. EMPIRICAL STUDY AND IN-DEPTH ANALYSIS ..........................63 5.1. Previous Comparison of the 4 Methods Using a Simulation S tu d y .............................................................................................
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