Advanced Analysis of Variance

Chihiro Hirotsu

• Publisher: Wiley
• Year: 2017
• Print ISBN: 9781119303336
• eBook ISBN: 9781119303350
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Introducing a revolutionary new model for the statistical analysis of experimental data

In this important book, internationally acclaimed statistician, Chihiro Hirotsu, goes beyond classical analysis of variance (ANOVA) model to offer a unified theory and advanced techniques for the statistical analysis of experimental data. Dr. Hirotsu introduces the groundbreaking concept of advanced analysis of variance (AANOVA) and explains how the AANOVA approach exceeds the limitations of ANOVA methods to allow for global reasoning utilizing special methods of simultaneous inference leading to individual conclusions.

Focusing on normal, binomial, and categorical data, Dr. Hirotsu explores ANOVA theory and practice and reviews current developments in the field. He then introduces three new advanced approaches, namely: testing for equivalence and non-inferiority; simultaneous testing for directional (monotonic or restricted) alternatives and change-point hypotheses; and analyses emerging from categorical data. Using real-world examples, he shows how these three recognizable families of problems have important applications in most practical activities involving experimental data in an array of research areas, including bioequivalence, clinical trials, industrial experiments, pharmaco-statistics, and quality control, to name just a few.

• Written in an expository style which will encourage readers to explore applications for AANOVA techniques in their own research

• Focuses on dealing with real data, providing real-world examples drawn from the fields of statistical quality control, clinical trials, and drug testing

• Describes advanced methods developed and refined by the author over the course of his long career as research engineer and statistician

• Introduces advanced technologies for AANOVA data analysis that build upon the basic ANOVA principles and practices

Introducing a breakthrough approach to statistical analysis which overcomes the limitations of the ANOVA model, Advanced Analysis of Variance is an indispensable resource for researchers and practitioners working in fields within which the statistical analysis of experimental data is a crucial research component.

Chihiro Hirotsu is a Senior Researcher at the Collaborative Research Center, Meisei University, and Professor Emeritus at the University of Tokyo. He is a fellow of the American Statistical Association, an elected member of the International Statistical Institute, and he has been awarded the Japan Statistical Society Prize (2005) and the Ouchi Prize (2006). His work has been published in Biometrika, Biometrics, and Computational Statistics & Data Analysis, among other premier research journals.

Table of contents

• Cover
• Title Page
• Table of Contents
• Preface
• Notation and Abbreviations
• 1 Introduction to Design and Analysis of Experiments
• 2 Basic Estimation Theory
• 3 Basic Test Theory
• 4 Multiple Decision Processes and an Accompanying Confidence Region
• 5 Two‐Sample Problem
• 6 One‐Way Layout, Normal Model
• 7 One‐Way Layout, Binomial Populations
• 8 Poisson Process
• 9 Block Experiments
• 10 Two‐Way Layout, Normal Model
• 11 Analysis of Two‐Way Categorical Data
• 12 Mixed and Random Effects Model
• 13 Profile Analysis of Repeated Measurements
• 14 Analysis of Three‐Way Categorical Data
• 15 Design and Analysis of Experiments by Orthogonal Arrays
• Appendix
• Index
• End User License Agreement