Design and Analysis of Experiments, Volume 3 E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Probability and Statistics
• Sprache: Englisch

Seitenzahl: 1040

Veröffentlichungsjahr: 2011

Beschreibung

Provides timely applications, modifications, and extensions of experimental designs for a variety of disciplines Design and Analysis of Experiments, Volume 3: Special Designs and Applications continues building upon the philosophical foundations of experimental design by providing important, modern applications of experimental design to the many fields that utilize them. The book also presents optimal and efficient designs for practice and covers key topics in current statistical research. Featuring contributions from leading researchers and academics, the book demonstrates how the presented concepts are used across various fields from genetics and medicinal and pharmaceutical research to manufacturing, engineering, and national security. Each chapter includes an introduction followed by the historical background as well as in-depth procedures that aid in the construction and analysis of the discussed designs. Topical coverage includes: * Genetic cross experiments, microarray experiments, and variety trials * Clinical trials, group-sequential designs, and adaptive designs * Fractional factorial and search, choice, and optimal designs for generalized linear models * Computer experiments with applications to homeland security * Robust parameter designs and split-plot type response surface designs * Analysis of directional data experiments Throughout the book, illustrative and numerical examples utilize SAS®, JMP®, and R software programs to demonstrate the discussed techniques. Related data sets and software applications are available on the book's related FTP site. Design and Analysis of Experiments, Volume 3 is an ideal textbook for graduate courses in experimental design and also serves as a practical, hands-on reference for statisticians and researchers across a wide array of subject areas, including biological sciences, engineering, medicine, and business.

Leseprobe

Table of Contents

Cover

Series page

Title page

Copyright page

Dedication

Preface

Contributors

CHAPTER 1 Genetic Crosses Experiments

1.1 INTRODUCTION

1.2 BASIC OBJECTIVES AND MODELS

1.3 DIALLEL MATING DESIGN OF TYPE I

1.4 DIALLEL CROSSES: TYPE II DESIGNS

1.5 PARTIAL DIALLEL CROSSES: NO BLOCKING OR COMPLETE BLOCKS

1.6 PARTIAL DIALLEL CROSSES IN INCOMPLETE BLOCKS

1.7 OPTIMALITY

1.8 ROBUSTNESS

1.9 THREE- OR HIGHER-WAY CROSSES

1.10 COMPUTATION

ACKNOWLEDGMENTS

CHAPTER 2 Design of Gene Expression Microarray Experiments

2.1 INTRODUCTION

2.2 GENE EXPRESSION MICROARRAY TECHNOLOGY

2.3 PREPROCESSING OF MICROARRAY FLUORESCENCE INTENSITIES

2.4 INTRODUCTION TO GENE EXPRESSION MICROARRAY EXPERIMENTAL DESIGN

2.5 TWO-TREATMENT EXPERIMENTS USING TWO-COLOR MICROARRAYS

2.6 TWO-COLOR MICROARRAY EXPERIMENTS INVOLVING MORE THAN TWO TREATMENTS

2.7 MULTIFACTOR TWO-COLOR MICROARRAY EXPERIMENTS

2.8 PHASE 2 DESIGNS FOR COMPLEX PHASE 1 DESIGNS

CHAPTER 3 Spatial Analysis of Agricultural Field Experiments

3.1 INTRODUCTION

3.2 METHODS TO ACCOUNT FOR SPATIAL VARIATION

3.3 A SPATIAL LINEAR MIXED MODEL

3.4 ANALYSIS OF EXAMPLES

CHAPTER 4 Optimal Designs for Generalized Linear Models

4.1 INTRODUCTION

4.2 NOTATION AND BASIC CONCEPTS

4.3 TOOLS FOR FINDING LOCALLY OPTIMAL DESIGNS

4.4 GLMs WITH TWO PARAMETERS

4.5 GLMs WITH MULTIPLE PARAMETERS

4.6 SUMMARY AND CONCLUDING COMMENTS

ACKNOWLEDGMENTS

CHAPTER 5 Design and Analysis of Randomized Clinical Trials

5.1 OVERVIEW

5.2 COMPONENTS OF A RANDOMIZED CLINICAL TRIAL

5.3 BIAS

5.4 STATISTICAL ANALYSIS OF RANDOMIZED CLINICAL TRIALS

5.5 FAILURE TIME STUDIES

5.6 OTHER TOPICS

CHAPTER 6 Monitoring Randomized Clinical Trials

6.1 INTRODUCTION

6.2 NORMALLY DISTRIBUTED OUTCOMES

6.3 BROWNIAN MOTION PROPERTIES

6.4 BRIEF HISTORICAL OVERVIEW OF GROUP SEQUENTIAL METHODS

6.5 DICHOTOMOUS OUTCOMES

6.6 TIME-TO-EVENT OUTCOMES

6.7 UNCONDITIONAL POWER

6.8 CONDITIONAL POWER

6.9 SPENDING FUNCTIONS

6.10 FLEXIBILITY AND PROPERTIES OF SPENDING FUNCTIONS

6.11 MODIFYING THE TRIAL’S SAMPLE SIZE BASED ON A NUISANCE PARAMETER

6.12 SAMPLE SIZE MODIFICATION BASED ON THE INTERIM TREATMENT EFFECT

6.13 CONCLUDING REMARKS

CHAPTER 7 Adaptive Randomization in Clinical Trials

7.1 INTRODUCTION

7.2 ADAPTIVE RANDOMIZATION PROCEDURES

7.3 LIKELIHOOD-BASED INFERENCE

7.4 RANDOMIZATION-BASED INFERENCE

7.5 CONCLUSIONS AND PRACTICAL CONSIDERATIONS

ACKNOWLEDGMENT

CHAPTER 8 Search Linear Model for Identification and Discrimination

8.1 INTRODUCTION

8.2 GENERAL LINEAR MODEL WITH FIXED EFFECTS

8.3 SEARCH LINEAR MODEL

8.4 APPLICATIONS

8.5 EFFECTS OF NOISE IN PERFORMANCE COMPARISON

CHAPTER 9 Minimum Aberration and Related Criteria for Fractional Factorial Designs

9.1 INTRODUCTION

9.2 PROJECTIONS OF FRACTIONAL FACTORIAL DESIGNS

9.3 ESTIMATION CAPACITY

9.4 CLEAR TWO-FACTOR INTERACTIONS

9.5 ESTIMATION INDEX

9.6 ESTIMATION INDEX, MINIMUM ABERRATION, AND MAXIMUM ESTIMATION CAPACITY

9.7 COMPLEMENTARY DESIGN THEORY FOR MINIMUM ABERRATION DESIGNS

9.8 NONREGULAR DESIGNS AND ORTHOGONAL ARRAYS

9.9 GENERALIZED MINIMUM ABERRATION

9.10 OPTIMAL FRACTIONAL FACTORIAL BLOCK DESIGNS

CHAPTER 10 Designs for Choice Experiments for the Multinomial Logit Model

10.1 INTRODUCTION

10.2 DEFINITIONS

10.3 THE MNL MODEL

10.4 DESIGN COMPARISONS

10.5 OPTIMAL DESIGNS FOR DCEs

10.6 USING COMBINATORIAL DESIGNS TO CONSTRUCT DCEs

10.7 BAYESIAN WORK

10.8 BEST–WORST EXPERIMENTS

10.9 MISCELLANEOUS TOPICS

CHAPTER 11 Computer Experiments

11.1 INTRODUCTION

11.2 SENSITIVITY/UNCERTAINTY ANALYSIS

11.3 GAUSSIAN STOCHASTIC PROCESS MODELS

11.4 INFERENCE

11.5 EXPERIMENTAL DESIGNS

11.6 MULTIVARIATE OUTPUT

11.7 MULTIPLE DATA SOURCES

11.8 CONCLUSION

CHAPTER 12 Designs for Large-Scale Simulation Experiments, with Applications to Defense and Homeland Security

12.1 INTRODUCTION

12.2 PHILOSOPHY: EVOLUTION OF COMPUTATIONAL EXPERIMENTS

12.3 APPLICATION: U.S. ARMY UNMANNED AERIAL VEHICLE (UAV) MIX STUDY

12.4 PARTING THOUGHTS

CHAPTER 13 Robust Parameter Designs

13.1 INTRODUCTION

13.2 TAGUCHI SIGNAL-TO-NOISE RATIO APPROACH

13.3 DUAL MODEL RESPONSE SURFACE METHODOLOGY

13.4 SINGLE MODEL RESPONSE SURFACE METHODS USING COMBINED ARRAYS

13.5 COMPUTER GENERATED COMBINED ARRAYS

13.6 RPD INVOLVING QUANTITATIVE AND QUALITATIVE FACTORS

13.7 CONCLUSIONS

CHAPTER 14 Split-Plot Response Surface Designs

14.1 INTRODUCTION

14.2 DIFFERENCES BETWEEN AGRICULTURAL AND INDUSTRIAL EXPERIMENTATION

14.3 OLS–GLS EQUIVALENT SECOND-ORDER SPLIT-PLOT DESIGNS AND ANALYSIS

14.4 EXACT TESTS FOR THE COEFFICIENTS

14.5 PROPER RESIDUALS FOR CHECKING ASSUMPTIONS

14.6 “OPTIMAL” SECOND-ORDER SPLIT-PLOT DESIGNS

CHAPTER 15 Design and Analysis of Experiments for Directional Data

15.1 SUMMARY

15.2 INTRODUCTION AND HISTORICAL BACKGROUND

15.3 ANOVA FOR CIRCULAR DATA

15.4 ANOVA FOR CYLINDRICAL DATA

15.5 ANOVA FOR SPHERICAL DATA

15.6 CONCLUSIONS

Name Index

Subject Index

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Library of Congress Cataloging-in-Publication Data:

Hinkelmann, Klaus, 1932–

 Design and analysis of experiments / Klaus Hinkelmann.

p. cm. – (Wiley series in probability and statistics)

 Includes index.

 Contents: v. III. Special designs and applications

 ISBN 978-0470-53068-9 (cloth)

 ISBN 978-1118-14764-1 (epub)

 ISBN 978-1118-14765-8 (mobi)

 ISBN 978-1118-14766-5 (epdf)

1. Experimental design. I. Title.

 QA279.K45 2008

 519.5'7–dc22

2007017347

In Memoriam

Oscar Kempthorne

Preface

Recently, the Department of Statistics at Virginia Tech offered a course on the history of statistics, and I was asked to present a lecture on the history of experimental design. There is no question that this history goes back many centuries, with one of the first recorded experiments being a controlled experiment on scurvy. It was carried out by the surgeon James Lind on board of HM Bark Salisbury in 1747. Twelve equally sick sailors were divided into pairs, and each pair was given a different treatment. Although this experiment showed already some indication of what we now consider to be the principles of experimental design, such as essentially uniform experimental units and replication of treatments, no statistical analysis was used or needed to come to the conclusion that the treatment consisting of two oranges and one lemon every day showed the best results for getting the men back to work. This may very well be the first recorded rudimentary form of what we now call a clinical trial.

The analogue to this experiment in an agricultural setting is the Broadbalk experiment set up by John Lawes in 1843 at Rothamsted, England. The experiment was set up to test the effects of various forms of inorganic fertilizer and farmyard manure on the yield of winter wheat. The experiment was not laid out according to modern principles of experimental design, but it is an elementary form of a factorial experiment, where one factor was changed at a time. Thus, even though not suited for statistical analysis, the Broadbalk experiment resulted in important numerical comparisons between certain forms of fertilizer and management treatments. Even today, it is considered to be one of the longest lasting and most successful agronomic experiments. It stimulated, of course, much of the groundbreaking work in experimental design done by R.A. Fisher, Frank Yates, and others in the 1920s and 1930s at Rothamsted Experiment Station.

From beginnings such as these, the importance of experimental design has spread throughout the worlds of scientific and industrial experimentation. It is difficult to imagine that today any scientific or industrial empirical research can be done successfully without using principles of experimental design and statistical analysis. In addition to Fisher and Yates, many people have contributed to the advances of experimental design, among them J. Neyman, R.C. Bose, C.R. Rao, W.G. Cochran, Gertrude Cox, D.J. Finney, O. Kempthorne, J. Kiefer, G.E.P. Box, D.R. Cox, and J.N. Srivastava. Much of their work we have described in Hinkelmann and Kempthorne’s Design and Analysis of Experiments, Volume 1: Introduction to Experimental Design, Second Edition (2008) and Volume 2: Advanced Experimental Design (2005). (In the chapters of this volume, these will be referred to as HK1 and HK2, respectively). This includes the most commonly used error-control and treatment designs for comparative experiments, with the analysis based on randomization theory and the general linear model.

The principles and notions exposited in HK1 and HK2 have, over the years, been expanded for and adapted to special situations and applications by many researchers. The stimulus has come very often from scientists and practitioners working in applied fields, such as genetics, medicine, marketing, manufacturing, industrial production, agriculture, forestry, pharmacy, engineering, defense, national security, and others. These areas may require special adaptations or implementations of existing designs and/or special methodologies for analyzing data from such experiments. The reason for writing this Volume 3: Special Designs and Applications is to acquaint readers with these types of problems. Each of the 15 chapters gives an introduction, often with a historical background, to the topic under consideration and then discusses solutions to the particular problems, with references to the most recent results.

We begin in Chapter 1 with the discussion of designs for genetic crosses, the topic that fostered my interest in experimental design. Incomplete block designs are not only used to generate appropriate mating designs for the evaluation of the combining abilities of inbred lines for the purpose of producing well performing hybrids, but they are also used to grow the offspring from the mating designs in environmental designs. Another topic of genetic interest is discussed in Chapter 2, where the design aspects of two-phase microarray experiments are considered. Whereas the usual error-control designs are used in the first phase for the purpose of obtaining tissue samples for measurement with microarrays, the second phase of measuring the mRNA content of the tissue imposes certain new and special conditions on the construction of designs. Special aspects of data analysis are discussed in Chapter 3 in the context of agricultural field experiments. Because the growing conditions over a large experimental site can be quite variable, in addition to planning the experiment carefully, it may be useful and necessary to model spatial heterogeneity using some form of mixed linear model when analyzing the data from such field trials. Such a model is quite different from and much more complicated than the linear model used in HK1 and HK2 for analyzing data for the commonly used error-control and treatment designs. Still other models, namely generalized linear models, are considered in Chapter 4 for experiments with, for example, binary or count responses. These types of responses may occur in noncomparative experiments, where the main objective is to study the relationship between treatment and response. This leads to questions about methods of constructing optimal designs for purposes of modeling such relations.

Entirely different considerations for designing and conducting an experiment arise in the context of clinical trials, the subject of Chapters 5, 6, and 7. The major difference from most other experiments is the fact that the experimental units are humans who have consented to be part of the trial. This imposes logistical constraints and ethical considerations within a regulatory framework. Careful monitoring of the subjects and the outcome of the trial are of paramount importance, which often leads to the use of sequential trials combined with adaptive randomization of subjects to treatments and ensuing interim analyses of the data. Thus, aspects of both design and analysis present special challenges, and they are discussed in these chapters.

Factorial experiments have long played an important role in scientific and industrial experimentation. A common feature and major concern is the fact that these experiments can become rather large and hence difficult to carry out. This has led to the introduction of fractional factorial experiments, and it has become important to find methods of constructing designs for this purpose. These methods are predicated on the assumption, and, indeed, existence of the sparsity of factor or factor combination effects. One way then to construct fractional factorial designs is to assume an approximate linear model for the data and then construct designs that will be able to estimate the effects contained in that model, as is done in Chapter 8. Another approach, as exposited in Chapter 9, is to provide various characterizations of fractional factorial designs and establish the estimating capabilities of such designs associated with certain properties. An interesting use of factorial and fractional factorial designs is described in Chapter 10 in the context of choice experiments, where people are asked to state a preference for, say, a particular type of service. The service is described by a number of attributes, each of which has a number of different alternatives. The attributes correspond to factors and the alternatives to the levels of those factors. The notion of fractional factorial designs is then used to construct and compare different designs for choice experiments, that is, designs consisting of different choice sets.

In the physical world, experiments are often limited by the number of factors that can be accommodated and by the degree of complexity involving the interaction among factors. These limitations can be overcome by empirical computer experiments through the simulation of complex systems and subsequent analysis of “data” in the form of a computer or simulation model. A general discussion and various alternatives of such an approach are described in Chapter 11. A special problem involving defense and homeland security is discussed in Chapter 12, where the study goal, the experimental setup, and regression and graphical analysis are provided in detail.

A different situation involving factorial designs arises in the context of robust parameter designs, where the factors are divided into control and noise factors. The basic problems, as discussed in Chapter 13, are concerned with understanding the influence of noise factors and with mitigating their impact on the response through judicious choice of the control factor settings. It is shown how this can be achieved by using either the dual model or single model response surface approach for modeling the mean response, as well as the variance of the response. Another problem arising often in practice when factorial designs are used in the context of response surface designs is addressed in Chapter 14. The distinction between hard-to-change and easy-to-change factors leads to special design considerations and to split-plot type designs, referred to as equivalent estimation designs. Special emphasis is being paid to OLS–GLS equivalent second-order response surface designs.

Chapter 15 is concerned with questions of analysis for a different type of responses or observations, namely directional data. The essential characteristics of circular, cylindrical, and spherical data are described as well as the distributions for such data, for example, the von Mises distribution. Even though familiar techniques are used for analyzing the data, the nature of the data and the different distributions lead to forms of test statistics different from the usual ones for linear models.

These chapters thus span a wide range of theory and application for the design and analysis of experiments. In conjunction with HK1 and HK2, the reader should get a very good impression of how much the field has developed in its scope and sophistication since the beginnings of James Lind and John Lawes, as many of the latest results are discussed in this volume. This suggests that this volume is not intended as a self-contained textbook, but should be seen rather as an extension of HK1 and HK2 (or books of a similar nature) with particular interest for teachers, graduate students, and researchers in the field of experimental design as a supplemental text and reference book. Some of the more applications-oriented chapters also should be accessible and useful to practitioners. To help with the understanding of the material, most chapters provide a number of illustrative, and, where appropriate, numerical examples, in the latter case using available software, such as SAS, JMP, R, and specially written software programs, which will be available as indicated in the particular chapter or at the FTP (ftp://ftp.wiley.com/public/sci_tech_med/special_designs) for this book, maintained by wiley.com.

This volume is the work of many excellent researchers in the field of experimental design, and I would like to express my gratitude and thanks to them for agreeing to contribute to this volume, for providing insightful and challenging chapters, and for cooperating with me on my wishes for revisions.

KLAUS HINKELMANN

Blacksburg, Virginia

February 2011

Contributors

Christine M. Anderson-Cook is a Research Scientist in the Statistical Sciences Group at Los Alamos National Laboratory, Los Alamos, New Mexico. Before this, she held a position as Associate Professor of Statistics at Virginia Polytechnic Institute and State University. She is a Fellow of the American Statistical Association and a Senior Member of the American Society for Quality. In 2009, she received the National Laboratory STAR Award. Dr. Anderson-Cook is the author/coauthor of more than 80 publications in statistical and applications journals and coauthor (with R.H. Myers and D.C. Montgomery) of Response Surface Methodology: Process and Product Optimization Using Designed Experiments, Third Edition. She is serving as the chair of the American Society for Quality Statistics Division, as associate editor for the Journal of Statistics Education, and on several editorial boards and as guest editor of statistics and quality engineering journals.

Leonie Burgess is a Visiting Fellow in the School of Mathematical Sciences at the University of Technology, Sydney, Australia. She is the author/coauthor of more than 20 papers on the design of experiments and co-author (with D.J. Street) of The Construction of Optimal Stated Choice Experiments: Theory and Practice. Dr. Burgess is a consultant on experimental design for academic researchers and industry clients.

Hegang H. Chen is an Associate Professor in the Division of Biostatistics and Bioinformatics at the University of Maryland School of Medicine, with prior service as Assistant Professor of Statistics at Virginia Polytechnic Institute and State University. Dr. Chen is the author/coauthor of more than 60 publications in professional journals. He is serving as associate editor of the International Journal of Statistics and Management Systems.

Ching-Shui Cheng is a Professor of Statistics at the University of California at Berkeley. He served previously as director of the Institute of Statistical Science at the Academia Sinica. Dr. Cheng is a Fellow of the Institute of Mathematical Statistics and of the American Statistical Association. He is the author/coauthor of more than 80 publications in statistical journals and serves as chair editor of Statistica Sinica and as associate editor for the Annals of Statistics, Biometrika, Technometrics, and Journal of Statistical Planning and Inference.

Brian R. Cullis is a Professor of Biometry in the Faculty of Informatics at the University of Wollongong, Australia. Dr. Cullis has more than 30 years experience in statistics with applications in the biological and agricultural sciences, with particular emphasis on experimental design, plant improvement, and genomics. His work has been widely adopted within the Australian grains industry and overseas. He is the author/coauthor of more than 150 articles in professional journals. He has served as coeditor of Biometrics.

Nancy L. Geller is the Director of the Office of Biostatistics Research at the National Heart, Lung, and Blood Institute in Bethesda, Maryland. She is a Fellow and the 2011 president of the American Statistical Association. Dr. Geller is the author/coauthor of more than 200 publications in professional journals and the editor of Advances in Clinical Trial Biostatistics (2005). She is a former president of the International Society for Clinical Biostatistics. Her editorial service includes associate editor of Biometrics and member of the Editorial Board of Clinical Trials.

Subir Ghosh is a Professor of Statistics at the University of California, Riverside, where he received the Academic Senate Distinguished Teaching Award and the Graduate Council Dissertation Advisor/Mentoring Award. Dr. Ghosh is a Fellow of the American Statistical Association, the American Association for the Advancement of Science, and an elected member of the International Statistical Institute. He is the author/coauthor of about 90 publications in professional journals and books. He served as executive editor of the Journal of Statistical Planning and Inference and as president of the International Indian Statistical Association.

Sudhir Gupta is a Professor of Statistics at Northern Illinois University, where he served as director of the Division of Statistics (2000–2004). He is a Fellow of the American Statistical Association. Dr. Gupta has authored/coauthored about 85 research papers and one Springer-Verlag research monograph. He is a member of the editorial boards of the Journal of Statistical Planning and Inference and Communications in Statistics and is a founding editor of the Journal of Statistics and Applications of the Forum for Interdisciplinary Mathematics. He has edited several issues of the Journal of Statistical Planning and Inference.

Eric S. Leifer is a Mathematical Statistician at the National Heart, Lung, and Blood Institute in Bethesda, Maryland. He is the author/coauthor of several publications in statistical journals and has performed editorial services for Biometrics, Biometrical Journal, Journal of Biopharmaceutical Statistics, Statistics in Medicine, and the Encyclopedia of Clinical Trials.

Thomas W. Lucas is an Associate Professor and Co-Director of the Simulation Experiments and Efficient Designs (SEED) Center for Data Farming in the Operations Research Department at the Naval Postgraduate School, Monterey, California. He is the author/coauthor of about 20 publications in professional journals.

Max D. Morris is a Professor of Statistics and Professor of Industrial and Manufacturing Systems Engineering at Iowa State University. He was previously scientific staff member at Oak Ridge National Laboratory, Oak Ridge, Tennessee. Dr. Morris is a Fellow of the American Statistical Association and a recipient of the Jack Youden Prize (2001), the Jerome Sacks Award for Cross-Disciplinary Research (2002), and the Frank Wilcoxon Prize (2010). He is the author/coauthor of about 65 publications in statistical and other professional journals and the author of Design of Experiments: An Introduction Based on Linear Models (2010). He has served as associate editor and editor of Technometrics and as associate editor for the Journal of Statistical Computation and Simulation and the Journal of Quality Technology.

Christopher J. Nannini, Lieutenant Colonel, U.S. Army, is a Military Instructor in the Department of Operations Research at the Naval Postgraduate School, Monterey, California, where he is also a PhD student in the Modeling, Virtual Environment and Simulations (MOVES) Program. He has worked on a simulation tool used for the allocation of unmanned aerial vehicles (UAVs) to mission areas. He is an Army Chemical Officer and Operations Research Systems Analyst.

Dan Nettleton is a Professor of Statistics and holds the Laurence H. Baker Endowed Chair in Biological Statistics at Iowa State University. He is a Fellow of the American Statistical Association. Dr. Nettleton is the author/coauthor of about 100 publications in statistical and biological journals. He served as president of the Iowa Chapter of the American Statistical Association and serves as associate editor of the Journal of the American Statistical Association, Journal of Agricultural, Biological, and Environmental Statistics, and Biometrics.

Sango B. Otieno is an Associate Professor of Statistics at Grand Valley State University, Michigan, where he also serves as director of the Statistical Consulting Center. He is author/coauthor of numerous publications in professional journals.

Rajender Parsad is the Head of the Division of Design of Experiments at the Indian Agricultural Statistics Research Institute, New Delhi, India. He had a previous appointment as a National Fellow at the International Center for Agricultural Research, India. Among his honors and awards are: recipient of the Young Scientist Award for Social Sciences from the Indian National Academy of Agricultural Sciences, recipient of the P.V. Sukhatme Gold Medal award, elected member of the International Statistical Institute, and Fellow of the National Academy of Agricultural Sciences. Dr. Parsad is the author/coauthor of more than 100 publications in professional journals and coauthor of two IASRI monographs. He is the joint secretary of the Indian Society of Agricultural Statistics and serves on the Executive Council, Forum for Interdisciplinary Mathematics. He is the coordinating editor of the Journal of the Indian Society of Agricultural Statistics.

Timothy J. Robinson is an Associate Professor of Statistics at the University of Wyoming. He is the author/coauthor of about 40 articles in professional journals and is coauthor (with R.H. Myers, D.C. Montgomery, and G.G. Vining) of Generalized Linear Models with Applications in Engineering and the Sciences, Second Edition (2010). Dr. Robinson has served as program chair for the Quality and Productivity Section of the American Statistical Association and serves as student grant chair for the Statistics Section of the American Society for Quality. His editorial service includes associate review editor for the Journal of the American Statistical Association and associate editor for Quality Engineering. He has served as statistical consultant for industry and government.

William F. Rosenberger is a Professor and Chairman of the Department of Statistics, George Mason University, Fairfax, Virginia. He is a Fellow of the American Statistical Association and of the Institute of Mathematical Statistics. Dr. Rosenberger is the author/coauthor of about 70 articles in professional journals and the coauthor (with J.L. Lachin) of Randomization in Clinical Trials: Theory and Practice (2002) and (with F. Hu) of The Theory of Response-Adaptive Randomization in Clinical Trials. He is the editor of two IMS monographs and serves as associate editor for several journals.

Paul J. Sanchez is a faculty member in the Operations Research Department at the Naval Postgraduate School, Monterey, California. His research focuses on the intersection between computer modeling and statistics. Dr. Sanchez has been an active member of the simulation community for more than 25 years and has served as referee, session chair, and proceedings editor for the Winter Simulation Conference.

Susan M. Sanchez is a Professor of the Department of Operations Research and Graduate School of Business and Public Policy, and Co-Director of the Simulation Experiments and Efficient Designs (SEED) Center for Data Farming, Naval Postgraduate School, Monterey, California. Her previous appointment was at the University of Missouri-St. Louis. Dr. Sanchez was a NRC Senior Postdoctoral Research Fellow, received the Kelleher U.S. Army TRADOC Analysis Center-Monterey Director’s Award for Research Excellence, and Outstanding Service Recognition from the INFORMS Simulation Society. She has published approximately 75 articles/chapters in professional journals/books. Her service to the profession includes: chair, Winter Simulation Conference Board of Directors; president, INFORMS College on Simulation; president, Forum on Women in OR/MS; and member, NATO Modeling and Simulation Group. She served as simulation area editor for INFORMS Journal on Computing, associate and deputy editor for Naval Research Logistics, and associate editor for Operations Research.

Murari Singh is a Senior Biometrician at the International Center for Agricultural Research in the Dry Areas (ICARDA) in Aleppo, Syria since 1989, with a limited term appointment in the Department of Mathematics and Statistics at Concordia University, Montreal, Canada from 2008 to 2010. From 1982 to 1989, he was statistician at the International Crops Research Institute for the Semi-Arid Tropics (ICRISAT) in Patancheru, India. Dr. Singh is a Fellow of the Royal Statistical Society, a Fellow of the Indian Society of Genetics and Plant Breeding, and an elected member of the International Statistical Institute. He is the author/coauthor of about 130 publications in statistical and subject matter journals and has served as associate editor and guest editor for the Journal of the Indian Society of Agricultural Statistics.

Alison B. Smith is a Senior Research Scientist at the Wagga Wagga Agricultural Research Institute, New South Wales Department of Industry and Investment, Australia. Dr. Smith has served more than 25 years as a consultant biometrician with emphasis on statistical methods for improving the efficiency of plant breeding and evaluation programs. She is the author/coauthor of 45 publications in professional journals.

Deborah J. Street is a Professor of Statistics in the School of Mathematical Sciences at the University of Technology, Sydney, Australia. She is a foundation Fellow of the Institute of Combinatorics and Its Applications. Dr. Street is the author/co-author of more 60 publications in statistical and mathematical journals and has co-authored (with A.P. Street) Combinatorics of Experimental Design and (with L. Burgess) The Construction of Optimal Stated Choice Experiments: Theory and Practice. She serves on the editorial board of Ars Conjectandi and has served on the editorial boards of the Australasian Journal of Combinatorics, Biometrics, Journal of Combinatorial Designs, and Utilitas Mathematica.

Joanne K. Stringer is a Senior Biometrician with BSES Limited in Queensland, Australia. Dr. Stringer has more than 25 years experience in the design, analysis and interpretation of data for the Australian Sugar Industry, with particular emphasis on new statistical approaches for the Australian sugarcane plant improvement program. She is the author/coauthor of 30 publications in professional journals.

John Stufken is a Professor and the Head of the Department of Statistics, University of Georgia. Previous appointments have been as program director for Statistics, Division of Mathematical Sciences of the National Sciences Foundation, Washington, DC, and professor of Statistics at Iowa State University. Dr. Stufken is a Fellow of the Institute of Mathematical Statistics, a Fellow of the American Statistical Association, and an elected member of the International Statistical Institute. He is a 2011 Rothschild Distinguished Visiting Fellow, Isaac Newton Institute for Mathematical Sciences, Cambridge, United Kingdom. He is the author/coauthor of about 70 articles in statistical and other professional journals and is coauthor (with A.S. Hedayat and N.J.A. Sloane) of Orthogonal Arrays: Theory and Applications. His editorial service includes editor of The American Statistician, associate editor of Journal of the American Statistical Association, Statistical Methodology, Journal of Statistical Theory and Practice, Journal of Statistical Planning and Inference, and Communications in Statistics.

G. Geoffrey Vining is a Professor of Statistics at Virginia Polytechnic Institute and State University, where he also served as department head (1999–2006). He is a Fellow of the American Statistical Association and of the American Society for Quality. Dr. Vining is the author/co-author of more than 50 publications in professional journals and the recipient of the 1990 Brumbaugh Award for the paper that has made the greatest contribution to the development of industrial applications of quality control, as well as the 2011 recipient of the Shewart Medal. He is the author of Statistical Methods for Engineers and coauthor (with D.C. Montgomery and E. A. Peck) of Introduction to Linear Regression Analysis and (with R.H. Myers and D.C. Montgomery) of Generalized Linear Models. He served as editor of the Journal of Quality Technology and as vice chair of the Publications Management Board of the American Society of Quality.

Hong Wan is an Assistant Professor in the School of Industrial Engineering at Purdue University, Indiana. She is the author/coauthor of about 15 publications in professional journals. Dr. Wan served as the 2009 Winter Simulation Conference Advanced Tutorial Track Coordinator. She is an associate editor of the ACM Transactions on Modeling and Computer Simulation and has served as referee for several operations research and computing journals. She is a member of the Institute of Operations Research and the Management Sciences.

Janet Wittes is the Founder and President of Statistics Collaborative, Inc., Washington, D.C. She was previously chief of the Biostatistics Research Branch, National Heart, Lung, and Blood Institute, Bethesda, Maryland. Dr. Wittes is a Fellow of the American Statistical Association, the American Association for the Advancement of Science, and the Society of Clinical Trials. In 2006, she received the Janet L. Norwood Award for Outstanding Achievement by a Woman in the Statistical Sciences. She is the author/coauthor of approximately 200 articles in professional journals. She is the coauthor (with M.A. Proschan and K.K.G. Lan) of Statistical Monitoring of Clinical Trials: A Unified Approach, (with A. Turk and J. Turk) of Ecology, Pollution, Environment, and (with A. Turk, J. Turk, and R. Wittes) of Environmental Science. She is former president of The Biometric Society, ENAR, and the Society for Clinical Trials. Her editorial service includes editor-in-chief of Controlled Clinical Trials (1994–1998) and member of the Editorial Board of Clinical Trials and Trials.

Min Yang is an Associate Professor of Statistics at the University of Missouri. He is the recipient of a National Science Foundation CAREER Award. Dr. Yang is the author/coauthor of 15 articles in statistical journals.

Zi-Fan Yu is a Consultant, Statistics Collaborative, Inc., Washington, DC. Dr. Yu is the author/coauthor of 10 publications in professional journals.

Lanju Zhang is a Senior Principal Statistician in the Biostatistics Department of MedImmune LLC. He is the author/coauthor of more than 20 papers in statistical and other professional journals and books. He has performed editorial service for Biometrics, Biometrika, International Journal of Biostatistics, Journal of Statistical Planning and Inference, Metrika, Journal of Biopharmaceutical Statistics, and Biometrical Journal.

CHAPTER 1

Genetic Crosses Experiments

Murari Singh, Sudhir Gupta, and Rajender Parsad

1.1 INTRODUCTION

A major objective of biometrical genetics is to explore the nature of gene action in determining quantitative traits. This also includes determination of the number of major genetic factors or genes responsible for the traits. The history of genetic experiments can be traced back to Mendel’s famous experiments on peas, the results of which he published in 1864. His work remained obscure until it was rediscovered independently by three scientists Hugo de Vries, Carl Correns, and Erich von Tschermak-Seysenegg, and published in 1900 (Monaghan and Corcos 1986, 1987); see http://www.eucarpia.org/secretariate/honorary/tschermak.html. Further genetic experimentation quickly followed these discoveries, and the subject of experimental genetics was thus founded.

This chapter deals with the type of genetic experiments that help assess variability in observed quantitative traits arising from genetic factors, environmental factors, and their interactions. To generate information on the variability, genetic entities, such as individual plants, animals, lines, clones, strains, and populations, are involved. Experimental design plays a twofold role in these experiments: a design to form genetic crosses and a design to evaluate the crosses in chosen environments. These two designs are called the mating design M and the environment design E, respectively. Some of the key resources in this area include standard texts and expository papers by Kempthorne (1956), Mather and Jinks (1982), Hayman (1954a, 1954b), Hinkelmann (1975), Singh and Chaudhary (1979), Falconer and MacKay (1996), Kearsey and Pooni (1996), and Lynch and Walsh (1998). There is also a wealth of research published in scholarly journals and special issues of symposia on the topic. Obviously it is not practically feasible to cover all the important themes and methodologies of genetical experiments here. This chapter, therefore, makes a subjective selection of the topics with the aim of providing a moderate account of the concepts necessary for achieving some of the major objectives of genetical experiments, and designs and analyses thereof.

Section 1.2 discusses some more specific objectives, basic generations raised for estimation of parameters and covariances between relatives. Various types of M and E designs are discussed in later sections. Specifically, M designs for diallel experiments of type I and type II are discussed in Sections 1.3 and 1.4, respectively. These designs are generally complete crosses evaluated in experimental material without any blocking system or with complete blocks. Designs based on partial diallel crosses and their analyses are presented in Section 1.5 for complete blocks and in Section 1.6 for incomplete blocks. Sections 1.7 and 1.8 are devoted to incomplete block designs with desirable properties, such as optimality and robustness. A number of variance and covariance parameters cannot be estimated from diallel crosses in the presence of epistatic effect. For this purpose, three- and higher way crosses are required. A short review of and designs involving three- or higher-way crosses and their analyses are given in Section 1.9. A real data set has been used to illustrate the analyses. Some references where one could obtain SAS codes for carrying out the analysis are given in Section 1.10, while codes in R language are provided on the John Wiley website (URL: ).