Description
Book SynopsisIntroducing 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 ca
Table of ContentsPreface xi
Notation and Abbreviations xvii
1 Introduction to Design and Analysis of Experiments 1
1.1 Why Simultaneous Experiments? 1
1.2 Interaction Effects 2
1.3 Choice of Factors and Their Levels 4
1.4 Classification of Factors 5
1.5 Fixed or Random Effects Model? 5
1.6 Fisher’s Three Principles of Experiments vs. Noise Factor 6
1.7 Generalized Interaction 7
1.8 Immanent Problems in the Analysis of Interaction Effects 7
1.9 Classification of Factors in the Analysis of Interaction Effects 8
1.10 Pseudo Interaction Effects (Simpson’s Paradox) in Categorical Data 8
1.11 Upper Bias by Statistical Optimization 9
1.12 Stage of Experiments: Exploratory, Explanatory or Confirmatory? 10
2 Basic Estimation Theory 11
2.1 Best Linear Unbiased Estimator 11
2.2 General Minimum Variance Unbiased Estimator 12
2.3 Efficiency of Unbiased Estimator 14
2.4 Linear Model 18
2.5 Least Squares Method 19
2.6 Maximum Likelihood Estimator 31
2.7 Sufficient Statistics 34
3 Basic Test Theory 41
3.1 Normal Mean 41
3.2 Normal Variance 53
3.3 Confidence Interval 56
3.4 Test Theory in the Linear Model 58
3.5 Likelihood Ratio Test and Efficient Score Test 62
4 Multiple Decision Processes and an Accompanying Confidence Region 71
4.1 Introduction 71
4.2 Determining the Sign of a Normal Mean – Unification of One- and Two-Sided Tests 71
4.3 An Improved Confidence Region 73
5 Two-Sample Problem 75
5.1 Normal Theory 75
5.2 Non-parametric Tests 84
5.3 Unifying Approach to Non-inferiority, Equivalence and Superiority Tests 92
6 One-Way Layout, Normal Model 113
6.1 Analysis of Variance (Overall F-Test) 113
6.2 Testing the Equality of Variances 115
6.3 Linear Score Test (Non-parametric Test) 118
6.4 Multiple Comparisons 121
6.5 Directional Tests 128
7 One-Way Layout, Binomial Populations 165
7.1 Introduction 165
7.2 Multiple Comparisons 166
7.3 Directional Tests 167
8 Poisson Process 193
8.1 Max acc. t1 for the Monotone and Step Change-Point Hypotheses 193
8.2 Max acc. t2 for the Convex and Slope Change-Point Hypotheses 197
9 Block Experiments 201
9.1 Complete Randomized Blocks 201
9.2 Balanced Incomplete Blocks 205
9.3 Non-parametric Method in Block Experiments 211
10 Two-Way Layout, Normal Model 237
10.1 Introduction 237
10.2 Overall ANOVA of Two-Way Data 238
10.3 Row-wise Multiple Comparisons 244
10.4 Directional Inference 256
10.5 Easy Method for Unbalanced Data 260
11 Analysis of Two-Way Categorical Data 273
11.1 Introduction 273
11.2 Overall Goodness-of-Fit Chi-Square 275
11.3 Row-wise Multiple Comparisons 276
11.4 Directional Inference in the Case of Natural Ordering Only in Columns 281
11.5 Analysis of Ordered Rows and Columns 291
12 Mixed and Random Effects Model 299
12.1 One-Way Random Effects Model 299
12.2 Two-Way Random Effects Model 306
12.3 Two-Way Mixed Effects Model 314
12.4 General Linear Mixed Effects Model 322
13 Profile Analysis of Repeated Measurements 329
13.1 Comparing Treatments Based on Upward or Downward Profiles 329
13.2 Profile Analysis of 24-Hour Measurements of Blood Pressure 338
14 Analysis of Three-Way Categorical Data 347
14.1 Analysis of Three-Way Response Data 348
14.2 One-Way Experiment with Two-Way Categorical Responses 361
14.3 Two-Way Experiment with One-Way Categorical Responses 375
15 Design and Analysis of Experiments by Orthogonal Arrays 383
15.1 Experiments by Orthogonal Array 383
15.2 Ordered Categorical Responses in a Highly Fractional Experiment 393
15.3 Optimality of an Orthogonal Array 397
References 399
Appendix 401
Index 407
