Advanced Analysis of VarianceISBN: 9781119303336
416 pages
August 2017

Description
Introducing a revolutionary new model for the statistical analysis of experimental data
In this important book, internationally acclaimed statistician, Chihiro Hirotsu, goes beyond evolutionary biologist Ronald Fisher’s 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 noninferiority; simultaneous testing for directional (monotonic or restricted) alternatives and changepoint hypotheses; and analyses emerging from categorical data. Using realworld 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, pharmacostatistics, 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 realworld 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.
Table of Contents
Contents
Preface
Notation and abbreviations
Chapter 1: introduction to design and analysis of experiments
1.1 Why simultaneous experiments?
1.2 Interaction effects
1.3 Choice of factors and their levels
1.4 Classification of factors
1.5 Fixed or random effects model?
1.6 Fisher’s three principles of experiments versus noise factor
1.7 Generalized interaction
1.8 Immanent problems in the analysis of interaction effects
1.9 Classification of factors in the analysis of interaction effects
1.10 Pseudo interaction effects (Simpson’s paradox) in categorical data
1.11 Upper bias by statistical optimization
1.12 Stage of experiments —exploratory, explanatory or confirmatory? —
References
Chapter 2: Estimation Theory
2.1 Best linear unbiased estimator (BLUE)
2.2 General minimum variance unbiased estimator
2.3 Efficiency of unbiased estimator
2.4 Linear model
2.5 Least squares (LS) method
2.6 Maximum likelihood estimator (MLE)
2.7 Sufficient statistics
References
Chapter 3: Basic Test Theory
3.1 Normal mean @
3.2 Normal variance
3.3 Confidence interval
3.4 Test theory in the linear model
3.5 Likelihood ratio test and efficient score test
References
Chapter 4: Multiple decision processes and accompanying confidence region
4.1 Introduction
4.2 Determining the sign of a normal mean
—Unification of one and twosided tests—
4.3 An improved confidence region
Reference
Chapter 5: TwoSample Problem
5.1 Normal theory
5.2 Nonparametric tests
5.3 Unifying approach to noninferiority, equivalence and superiority tests
References
Chapter 6: OneWay Layout, Normal Model
6.1 Analysis of variance (ANOVA, overall F test)
6.2 Testing the equality of variances
6.3 Linear score test (nonparametric test)
6.4 Multiple comparisons
6.5 Directional tests
References
Chapter 7: OnwWay Layout, Binomial Populations
7.1 Introduction
7.2 Multiple comparisons
7.3 Directional tests
References
Chapter 8: Poisson Process
8.1 Max acc. t1 for the monotone and step changepoint hypotheses
8.2 Max acc. t2 for the convex and slope changepoint hypotheses
Reference
Chapter 9: Block Experiments
9.1 Complete randomized blocks
9.2 Balanced incomplete blocks
9.3 Nonparametric method in block experiments
References
Chapter 10: TwoWay Layout, Normal Model
10.1 Introduction
10.2 Overall analysis of variance (ANOVA) of twoway data
10.3 Rowwise multiple comparisons
10.4 Directional inference
10.5 Easy method for unbalanced data
References
Chapter 11: Analysis of TwoWay Categorical Data
11.1 Introduction
11.2 Overall goodnessoffit chisquare
11.3 Rowwise multiple comparisons
11.4 Directional inference in the case of natural ordering only in columns
11.5 Analysis of ordered rows and columns
References
Chapter 12: Mixed and Random Effects Model
12.1 Oneway random effects model
12.2 Twoway random effects model
12.3 Twoway mixed effect model
12.4 General linear mixed effects model
References
Chapter 13: Profile Analysis of Repeated Measurements
13.1 Comparing treatments based on up or downward profiles
13.2 Profile analysis of 24hours measurements of blood pressure
References
Chapter 14: Analysis of ThreeWay Categorical Data
14.1Analysis of threeway response data
14.2 Oneway experiment with twoway categorical responses
14.3 Twoway experiment with oneway categorical responses
References
Chapter 15: Design and Analysis of Experiments by Orthogonal Arrays
15.1 Experiments by an orthogonal array
15.2 Ordered categorical responses in a highly fractional experiment
15.3 Optimality of an orthogonal array
References
Appendix
Index
Author Information
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.