Advanced Analysis of Variance

 
 
Standards Information Network (Verlag)
  • erschienen am 19. Juli 2017
  • |
  • 432 Seiten
 
E-Book | PDF mit Adobe-DRM | Systemvoraussetzungen
978-1-119-30334-3 (ISBN)
 
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.
1. Auflage
  • Englisch
  • New York
  • |
  • USA
John Wiley & Sons Inc
  • Für Beruf und Forschung
  • 7,35 MB
978-1-119-30334-3 (9781119303343)
weitere Ausgaben werden ermittelt
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.
1 - Title Page [Seite 5]
2 - Copyright Page [Seite 6]
3 - Contents [Seite 7]
4 - Preface [Seite 13]
5 - Notation and Abbreviations [Seite 19]
6 - Chapter 1 Introduction to Design and Analysis of Experiments [Seite 23]
6.1 - 1.1 Why Simultaneous Experiments? [Seite 23]
6.2 - 1.2 Interaction Effects [Seite 24]
6.3 - 1.3 Choice of Factors and Their Levels [Seite 26]
6.4 - 1.4 Classification of Factors [Seite 27]
6.5 - 1.5 Fixed or Random Effects Model? [Seite 27]
6.6 - 1.6 Fisher´s Three Principles of Experiments vs. Noise Factor [Seite 28]
6.7 - 1.7 Generalized Interaction [Seite 29]
6.8 - 1.8 Immanent Problems in the Analysis of Interaction Effects [Seite 29]
6.9 - 1.9 Classification of Factors in the Analysis of Interaction Effects [Seite 30]
6.10 - 1.10 Pseudo Interaction Effects (Simpson´s Paradox) in Categorical Data [Seite 30]
6.11 - 1.11 Upper Bias by Statistical Optimization [Seite 31]
6.12 - 1.12 Stage of Experiments: Exploratory, Explanatory or Confirmatory? [Seite 32]
6.13 - References [Seite 32]
7 - Chapter 2 Basic Estimation Theory [Seite 33]
7.1 - 2.1 Best Linear Unbiased Estimator [Seite 33]
7.2 - 2.2 General Minimum Variance Unbiased Estimator [Seite 34]
7.3 - 2.3 Efficiency of Unbiased Estimator [Seite 36]
7.4 - 2.4 Linear Model [Seite 40]
7.5 - 2.5 Least Squares Method [Seite 41]
7.5.1 - 2.5.1 LS method and BLUE [Seite 41]
7.5.2 - 2.5.2 Estimation space and error space [Seite 44]
7.5.3 - 2.5.3 Linear constraints on parameters for solving the normal equation [Seite 46]
7.5.4 - 2.5.4 Generalized inverse of a matrix [Seite 50]
7.5.5 - 2.5.5 Distribution theory of the LS estimator [Seite 51]
7.6 - 2.6 Maximum Likelihood Estimator [Seite 53]
7.7 - 2.7 Sufficient Statistics [Seite 56]
7.8 - References [Seite 61]
8 - Chapter 3 Basic Test Theory [Seite 63]
8.1 - 3.1 Normal Mean [Seite 63]
8.1.1 - 3.1.1 Setting a null hypothesis and a rejection region [Seite 63]
8.1.2 - 3.1.2 Power function [Seite 67]
8.1.3 - 3.1.3 Sample size determination [Seite 69]
8.1.4 - 3.1.4 Nuisance parameter [Seite 70]
8.1.5 - 3.1.5 Non-parametric test for median [Seite 71]
8.2 - 3.2 Normal Variance [Seite 75]
8.2.1 - 3.2.1 Setting a null hypothesis and a rejection region [Seite 75]
8.2.2 - 3.2.2 Power function [Seite 77]
8.3 - 3.3 Confidence Interval [Seite 78]
8.3.1 - 3.3.1 Normal mean [Seite 78]
8.3.2 - 3.3.2 Normal variance [Seite 79]
8.4 - 3.4 Test Theory in the Linear Model [Seite 80]
8.4.1 - 3.4.1 Construction of F-test [Seite 80]
8.4.2 - 3.4.2 Optimality of F-test [Seite 83]
8.5 - 3.5 Likelihood Ratio Test and Efficient Score Test [Seite 84]
8.5.1 - 3.5.1 Likelihood ratio test [Seite 84]
8.5.2 - 3.5.2 Test based on the efficient score [Seite 85]
8.5.3 - 3.5.3 Composite hypothesis [Seite 86]
8.6 - References [Seite 90]
9 - Chapter 4 Multiple Decision Processes and an Accompanying Confidence Region [Seite 93]
9.1 - 4.1 Introduction [Seite 93]
9.2 - 4.2 Determining the Sign of a Normal Mean - Unification of One- and Two-Sided Tests [Seite 93]
9.3 - 4.3 An Improved Confidence Region [Seite 95]
9.4 - Reference [Seite 96]
10 - Chapter 5 Two-Sample Problem [Seite 97]
10.1 - 5.1 Normal Theory [Seite 97]
10.1.1 - 5.1.1 Comparison of normal means assuming equal variances [Seite 97]
10.1.2 - 5.1.2 Remark on the unequal variances [Seite 100]
10.1.3 - 5.1.3 Paired sample [Seite 101]
10.1.4 - 5.1.4 Comparison of normal variances [Seite 103]
10.2 - 5.2 Non-parametric Tests [Seite 106]
10.2.1 - 5.2.1 Permutation test [Seite 106]
10.2.2 - 5.2.2 Rank sum test [Seite 108]
10.2.3 - 5.2.3 Methods for ordered categorical data [Seite 110]
10.3 - 5.3 Unifying Approach to Non-inferiority, Equivalence and Superiority Tests [Seite 114]
10.3.1 - 5.3.1 Introduction [Seite 114]
10.3.2 - 5.3.2 Unifying approach via multiple decision processes [Seite 115]
10.3.3 - 5.3.3 Extension to the binomial distribution model [Seite 120]
10.3.4 - 5.3.4 Extension to the stratified data analysis [Seite 122]
10.3.5 - 5.3.5 Meaning of non-inferiority test and a rationale of switching to superiority test [Seite 126]
10.3.6 - 5.3.6 Bio-equivalence [Seite 129]
10.3.7 - 5.3.7 Concluding remarks [Seite 131]
10.4 - References [Seite 132]
11 - Chapter 6 One-Way Layout, Normal Model [Seite 135]
11.1 - 6.1 Analysis of Variance (Overall F-Test) [Seite 135]
11.2 - 6.2 Testing the Equality of Variances [Seite 137]
11.2.1 - 6.2.1 Likelihood ratio test (Bartlett´s test) [Seite 137]
11.2.2 - 6.2.2 Hartley´s test [Seite 138]
11.2.3 - 6.2.3 Cochran´s test [Seite 138]
11.3 - 6.3 Linear Score Test (Non-parametric Test) [Seite 140]
11.4 - 6.4 Multiple Comparisons [Seite 143]
11.4.1 - 6.4.1Introduction [Seite 143]
11.4.2 - 6.4.2 Multiple comparison procedures for some given structures of sub-hypotheses [Seite 144]
11.4.3 - 6.4.3 General approach without any particular structure of sub-hypotheses [Seite 147]
11.4.4 - 6.4.4 Closed test procedure [Seite 150]
11.5 - 6.5 Directional Tests [Seite 150]
11.5.1 - 6.5.1 Introduction [Seite 150]
11.5.2 - 6.5.2 General theory for unifying approach to shape and change-point hypotheses [Seite 152]
11.5.3 - 6.5.3 Monotone and step change-point hypotheses [Seite 158]
11.5.4 - 6.5.4 Convexity and slope change-point hypotheses [Seite 174]
11.5.5 - 6.5.5 Sigmoid and inflection point hypotheses [Seite 180]
11.5.6 - 6.5.6 Discussion [Seite 183]
11.6 - References [Seite 183]
12 - Chapter 7 One-Way Layout, Binomial Populations [Seite 187]
12.1 - 7.1 Introduction [Seite 187]
12.2 - 7.2 Multiple Comparisons [Seite 188]
12.3 - 7.3 Directional Tests [Seite 189]
12.3.1 - 7.3.1 Monotone and step change-point hypotheses [Seite 189]
12.3.2 - 7.3.2 Maximal contrast test for convexity and slope change-point hypotheses [Seite 193]
12.3.3 - 7.3.3 Cumulative chi-squared test for convexity hypothesis [Seite 203]
12.3.4 - 7.3.4 Power comparisons [Seite 207]
12.3.5 - 7.3.5 Maximal contrast test for sigmoid and inflection point hypotheses [Seite 209]
12.4 - References [Seite 212]
13 - Chapter 8 Poisson Process [Seite 215]
13.1 - 8.1 Max acc. t1 for the Monotone and Step Change-Point Hypotheses [Seite 215]
13.1.1 - 8.1.1 Max acc. t1 statistic in the Poisson sequence [Seite 215]
13.1.2 - 8.1.2 Distribution function of max acc. t1 under the null model [Seite 216]
13.1.3 - 8.1.3 Max acc. t1 under step change-point model [Seite 217]
13.2 - 8.2 Max acc. t2 for the Convex and Slope Change-Point Hypotheses [Seite 219]
13.2.1 - 8.2.1 Max acc. t2 statistic in the Poisson sequence [Seite 219]
13.2.2 - 8.2.2 Max acc. t2 under slope change-point model [Seite 220]
13.3 - References [Seite 221]
14 - Chapter 9 Block Experiments [Seite 223]
14.1 - 9.1 Complete Randomized Blocks [Seite 223]
14.2 - 9.2 Balanced Incomplete Blocks [Seite 227]
14.3 - 9.3 Non-parametric Method in Block Experiments [Seite 233]
14.3.1 - 9.3.1 Complete randomized blocks [Seite 233]
14.3.2 - 9.3.2 Incomplete randomized blocks with block size two [Seite 248]
14.4 - References [Seite 256]
15 - Chapter 10 Two-Way Layout, Normal Model [Seite 259]
15.1 - 10.1 Introduction [Seite 259]
15.2 - 10.2 Overall ANOVA of Two-Way Data [Seite 260]
15.3 - 10.3 Row-wise Multiple Comparisons [Seite 266]
15.3.1 - 10.3.1 Introduction [Seite 266]
15.3.2 - 10.3.2 Interaction elements [Seite 269]
15.3.3 - 10.3.3 Simultaneous test procedure for obtaining a block interaction model [Seite 270]
15.3.4 - 10.3.4 Constructing a block interaction model [Seite 272]
15.3.5 - 10.3.5 Applications [Seite 276]
15.3.6 - 10.3.6 Discussion on testing the interaction effects under no replicated observation [Seite 277]
15.4 - 10.4 Directional Inference [Seite 278]
15.4.1 - 10.4.1 Ordered rows or columns [Seite 279]
15.4.2 - 10.4.2 Ordered rows and columns [Seite 281]
15.5 - 10.5 Easy Method for Unbalanced Data [Seite 282]
15.5.1 - 10.5.1 Introduction [Seite 282]
15.5.2 - 10.5.2 Sum of squares based on cell means [Seite 282]
15.5.3 - 10.5.3 Testing the null hypothesis of interaction [Seite 283]
15.5.4 - 10.5.4 Testing the null hypothesis of main effects under H?? [Seite 285]
15.5.5 - 10.5.5 Accuracy of approximation by easy method [Seite 286]
15.5.6 - 10.5.6 Simulation [Seite 286]
15.5.7 - 10.5.7 Comparison with the LS method on real data [Seite 286]
15.5.8 - 10.5.8 Estimation of the mean ?ij [Seite 291]
15.6 - References [Seite 292]
16 - Chapter 11 Analysis of Two-Way Categorical Data [Seite 295]
16.1 - 11.1 Introduction [Seite 295]
16.2 - 11.2 Overall Goodness-of-Fit Chi-Square [Seite 297]
16.3 - 11.3 Row-wise Multiple Comparisons [Seite 298]
16.3.1 - 11.3.1 Chi-squared distances among rows [Seite 298]
16.3.2 - 11.3.2 Reference distribution for simultaneous inference in clustering rows [Seite 300]
16.3.3 - 11.3.3 Clustering algorithm and a stopping rule [Seite 300]
16.4 - 11.4 Directional Inference in the Case of Natural Ordering Only in Columns [Seite 303]
16.4.1 - 11.4.1 Overall analysis [Seite 303]
16.4.2 - 11.4.2 Row-wise multiple comparisons [Seite 305]
16.4.3 - 11.4.3 Multiple comparisons of ordered columns [Seite 306]
16.4.4 - 11.4.4 Re-analysis of Table taking natural ordering into consideration [Seite 310]
16.5 - 11.5 Analysis of Ordered Rows and Columns [Seite 313]
16.5.1 - 11.5.1 Overall analysis [Seite 313]
16.5.2 - 11.5.2 Comparing rows [Seite 314]
16.6 - References [Seite 318]
17 - Chapter 12 Mixed and Random Effects Model [Seite 321]
17.1 - 12.1 One-Way Random Effects Model [Seite 321]
17.1.1 - 12.1.1 Model and parameters [Seite 321]
17.1.2 - 12.1.2 Standard form for test and estimation [Seite 322]
17.1.3 - 12.1.3 Problems of negative estimators of variance components [Seite 324]
17.1.4 - 12.1.4 Testing homogeneity of treatment effects [Seite 325]
17.1.5 - 12.1.5 Between and within variance ratio (SN ratio) [Seite 325]
17.2 - 12.2 Two-Way Random Effects Model [Seite 328]
17.2.1 - 12.2.1 Model and parameters [Seite 328]
17.2.2 - 12.2.2 Standard form for test and estimation [Seite 329]
17.2.3 - 12.2.3 Testing homogeneity of treatment effects [Seite 330]
17.2.4 - 12.2.4 Easy method for unbalanced two-way random effects model [Seite 331]
17.3 - 12.3 Two-Way Mixed Effects Model [Seite 336]
17.3.1 - 12.3.1 Model and parameters [Seite 336]
17.3.2 - 12.3.2 Standard form for test and estimation [Seite 338]
17.3.3 - 12.3.3 Null hypothesis H?? of interaction and the test statistic [Seite 338]
17.3.4 - 12.3.4 Testing main effects under the null hypothesis H?? [Seite 340]
17.3.5 - 12.3.5 Testing main effects H? when the null hypothesis H?? fails [Seite 340]
17.3.6 - 12.3.6 Exact test of H? when the null hypothesis H?? fails [Seite 341]
17.4 - 12.4 General Linear Mixed Effects Model [Seite 344]
17.4.1 - 12.4.1 Gaussian linear mixed effects model [Seite 344]
17.4.2 - 12.4.2 Estimation of parameters [Seite 346]
17.4.3 - 12.4.3 Estimation of random effects (BLUP) [Seite 348]
17.5 - References [Seite 349]
18 - Chapter 13 Profile Analysis of Repeated Measurements [Seite 351]
18.1 - 13.1 Comparing Treatments Based on Upward or Downward Profiles [Seite 351]
18.1.1 - 13.1.1 Introduction [Seite 351]
18.1.2 - 13.1.2 Popular approaches [Seite 352]
18.1.3 - 13.1.3 Statistical model and approach [Seite 354]
18.2 - 13.2 Profile Analysis of 24-Hour Measurements of Blood Pressure [Seite 360]
18.2.1 - 13.2.1 Introduction [Seite 360]
18.2.2 - 13.2.2 Data set and classical approach [Seite 362]
18.2.3 - 13.2.3 Statistical model and new approach [Seite 362]
18.3 - References [Seite 367]
19 - Chapter 14 Analysis of Three-Way Categorical Data [Seite 369]
19.1 - 14.1 Analysis of Three-Way Response Data [Seite 370]
19.1.1 - 14.1.1 General theory [Seite 370]
19.1.2 - 14.1.2 Cumulative chi-squared statistics for the ordered categorical responses [Seite 380]
19.2 - 14.2 One-Way Experiment with Two-Way Categorical Responses [Seite 383]
19.2.1 - 14.2.1 General theory [Seite 383]
19.2.2 - 14.2.2 Applications [Seite 386]
19.3 - 14.3 Two-Way Experiment with One-Way Categorical Responses [Seite 397]
19.3.1 - 14.3.1 General theory [Seite 397]
19.3.2 - 14.3.2 Applications [Seite 399]
19.4 - References [Seite 404]
20 - Chapter 15 Design and Analysis of Experiments by Orthogonal Arrays [Seite 405]
20.1 - 15.1 Experiments by Orthogonal Array [Seite 405]
20.1.1 - 15.1.1 Orthogonal array [Seite 405]
20.1.2 - 15.1.2 Planning experiments by interaction diagram [Seite 409]
20.1.3 - 15.1.3 Analysis of experiments from an orthogonal array [Seite 411]
20.2 - 15.2 Ordered Categorical Responses in a Highly Fractional Experiment [Seite 415]
20.3 - 15.3 Optimality of an Orthogonal Array [Seite 419]
20.4 - References [Seite 421]
21 - Appendix [Seite 423]
22 - Index [Seite 429]
23 - EULA [Seite 435]

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