Design and Analysis of Experiments, Volume 3

Special Designs and Applications

Klaus Hinkelmann

• Publisher: Wiley
• Year: 2011
• Print ISBN: 9780470530689
• eBook ISBN: 9781118147641
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

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 M and E designs involving three- or higher-way crosses and their analyses ...

Table of contents

• Cover
• Series page
• Title page
• Copyright page
• Dedication
• Preface
• Contributors
• CHAPTER 1 Genetic Crosses Experiments
• CHAPTER 2 Design of Gene Expression Microarray Experiments
• CHAPTER 3 Spatial Analysis of Agricultural Field Experiments
• CHAPTER 4 Optimal Designs for Generalized Linear Models
• CHAPTER 5 Design and Analysis of Randomized Clinical Trials
• CHAPTER 6 Monitoring Randomized Clinical Trials
• CHAPTER 7 Adaptive Randomization in Clinical Trials
• CHAPTER 8 Search Linear Model for Identification and Discrimination
• CHAPTER 9 Minimum Aberration and Related Criteria for Fractional Factorial Designs
• CHAPTER 10 Designs for Choice Experiments for the Multinomial Logit Model
• CHAPTER 11 Computer Experiments
• CHAPTER 12 Designs for Large-Scale Simulation Experiments, with Applications to Defense and Homeland Security
• CHAPTER 13 Robust Parameter Designs
• CHAPTER 14 Split-Plot Response Surface Designs
• CHAPTER 15 Design and Analysis of Experiments for Directional Data
• Name Index
• Subject Index
• WILEY SERIES IN PROBABILITY AND STATISTICS