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Advanced Analysis of Variance

ISBN: 978-1-119-30333-6
416 pages
August 2017
Advanced Analysis of Variance (1119303338) cover image

Description

 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.

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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 two-sided tests—

4.3 An improved confidence region

Reference

Chapter 5: Two-Sample Problem

5.1 Normal theory

5.2 Non-parametric tests

5.3 Unifying approach to non-inferiority, equivalence and superiority tests

References

Chapter 6: One-Way Layout, Normal Model

6.1 Analysis of variance (ANOVA, overall F test)

6.2 Testing the equality of variances

6.3 Linear score test (non-parametric test)

6.4 Multiple comparisons

6.5 Directional tests

References

Chapter 7: Onw-Way 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 change-point hypotheses

8.2 Max acc. t2 for the convex and slope change-point hypotheses

Reference

Chapter 9: Block Experiments

9.1 Complete randomized blocks

9.2 Balanced incomplete blocks

9.3 Non-parametric method in block experiments

References

Chapter 10: Two-Way Layout, Normal Model

10.1 Introduction

10.2 Overall analysis of variance (ANOVA) of two-way data

10.3 Row-wise multiple comparisons

10.4 Directional inference

10.5 Easy method for unbalanced data

References

Chapter 11: Analysis of Two-Way Categorical Data

11.1 Introduction

11.2 Overall goodness-of-fit chi-square

11.3 Row-wise 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 One-way random effects model

12.2 Two-way random effects model

12.3 Two-way 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 24-hours measurements of blood pressure

References

Chapter 14: Analysis of Three-Way Categorical Data

14.1Analysis of three-way response data

14.2 One-way experiment with two-way categorical responses

14.3 Two-way experiment with one-way 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

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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.

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