Statistical analysis of designed experiments:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
2002
|
| Edition: | 2. ed. |
| Series: | Springer texts in statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 500 S. |
| ISBN: | 0387987894 |
Staff View
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| 245 | 1 | 0 | |a Statistical analysis of designed experiments |c Helge Toutenburg |
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Record in the Search Index
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| adam_text | Contents
Preface v
1 Introduction 1
1.1 Data, Variables, and Random Processes 1
1.2 Basic Principles of Experimental Design 3
1.3 Scaling of Variables 5
1.4 Measuring and Scaling in Statistical Medicine 7
1.5 Experimental Design in Biotechnology 8
1.6 Relative Importance of Effects—The Pareto Principle . . 9
1.7 An Alternative Chart 10
1.8 A One Way Factorial Experiment by Example 15
1.9 Exercises and Questions 19
2 Comparison of Two Samples 21
2.1 Introduction 21
2.2 Paired t Test and Matched Pair Design 22
2.3 Comparison of Means in Independent Groups 25
2.3.1 Two Sample t Test 25
2.3.2 Testing Ho : a = r| = a2 25
2.3.3 Comparison of Means in the Case of Un¬
equal Variances 26
2.3.4 Transformations of Data to Assure
Homogeneity of Variances 27
2.3.5 Necessary Sample Size and Power of the Test . . 27
x Contents
2.3.6 Comparison of Means without Prior Test¬
ing Ho : a = a Cochran Cox Test for
Independent Groups 27
2.4 Wilcoxon s Sign Rank Test in the Matched Pair
Design 29
2.5 Rank Test for Homogeneity of Wilcoxon, Mann and
Whitney 33
2.6 Comparison of Two Groups with Categorical Response . 38
2.6.1 McNemar s Test and Matched Pair Design ... 38
2.6.2 Fisher s Exact Test for Two Independent
Groups 39
2.7 Exercises and Questions 41
3 The Linear Regression Model 45
3.1 Descriptive Linear Regression 45
3.2 The Principle of Ordinary Least Squares 47
3.3 Geometric Properties of Ordinary Least Squares
Estimation 50
3.4 Best Linear Unbiased Estimation 51
3.4.1 Linear Estimators 52
3.4.2 Mean Square Error 53
3.4.3 Best Linear Unbiased Estimation 55
3.4.4 Estimation of a2 57
3.5 Multicollinearity 60
3.5.1 Extreme Multicollinearity and Estimability ... 60
3.5.2 Estimation within Extreme Multicollinearity . . 61
3.5.3 Weak Multicollinearity 63
3.6 Classical Regression under Normal Errors 67
3.7 Testing Linear Hypotheses 69
3.8 Analysis of Variance and Goodness of Fit 73
3.8.1 Bivariate Regression 73
3.8.2 Multiple Regression 79
3.9 The General Linear Regression Model 83
3.9.1 Introduction 83
3.9.2 Misspecification of the Covariance Matrix .... 85
3.10 Diagnostic Tools 86
3.10.1 Introduction 86
3.10.2 Prediction Matrix 86
3.10.3 Effect of a Single Observation on the Esti¬
mation of Parameters 91
3.10.4 Diagnostic Plots for Testing the Model
Assumptions 96
3.10.5 Measures Based on the Confidence Ellipsoid ... 97
3.10.6 Partial Regression Plots 102
3.10.7 Regression Diagnostics by Animating Graphics . 104
Contents xi
3.11 Exercises and Questions 110
4 Single—Factor Experiments with Fixed
and Random Effects 111
4.1 Models I and II in the Analysis of Variance Ill
4.2 One Way Classification for the Multiple Compari¬
son of Means 112
4.2.1 Representation as a Restrictive Model 115
4.2.2 Decomposition of the Error Sum of Squares . . . 117
4.2.3 Estimation of a2 by M5Error 120
4.3 Comparison of Single Means 123
4.3.1 Linear Contrasts 123
4.3.2 Contrasts of the Total Response Values in
the Balanced Case 126
4.4 Multiple Comparisons 132
4.4.1 Introduction 132
4.4.2 Experimentwise Comparisons 132
4.4.3 Select Pairwise Comparisons 135
4.5 Regression Analysis of Variance 142
4.6 One Factorial Models with Random Effects 145
4.7 Rank Analysis of Variance in the
Completely Randomized Design 149
4.7.1 Kruskal Wallis Test 149
4.7.2 Multiple Comparisons 152
4.8 Exercises and Questions 154
5 More Restrictive Designs 157
5.1 Randomized Block Design 157
5.2 Latin Squares 165
5.2.1 Analysis of Variance 167
5.3 Rank Variance Analysis in the Randomized Block
Design 172
5.3.1 Friedman Test 172
5.3.2 Multiple Comparisons 175
5.4 Exercises and Questions 176
6 Multifactor Experiments 179
6.1 Elementary Definitions and Principles 179
6.2 Two Factor Experiments (Fixed Effects) 183
6.3 Two Factor Experiments in Effect Coding 188
6.4 Two Factorial Experiment with Block Effects 196
6.5 Two Factorial Model with Fixed Effects—Confidence
Intervals and Elementary Tests 199
6.6 Two Factorial Model with Random or Mixed Effects . . 203
6.6.1 Model with Random Effects 203
xii Contents
6.6.2 Mixed Model 207
6.7 Three Factorial Designs 211
6.8 Split Plot Design 215
6.9 2k Factorial Design 219
6.9.1 The 22 Design 219
6.9.2 The 23 Design 222
6.10 Exercises and Questions 225
7 Models for Categorical Response Variables 231
7.1 Generalized Linear Models 231
7.1.1 Extension of the Regression Model 231
7.1.2 Structure of the Generalized Linear Model. . . . 233
7.1.3 Score Function and Information Matrix 236
7.1.4 Maximum Likelihood Estimation 237
7.1.5 Testing of Hypotheses and Goodness of Fit . . . 240
7.1.6 Overdispersion 241
7.1.7 Quasi Loglikelihood 243
7.2 Contingency Tables 245
7.2.1 Overview 245
7.2.2 Ways of Comparing Proportions 246
7.2.3 Sampling in Two Way Contingency Tables . . . 249
7.2.4 Likelihood Function and Maximum Likeli¬
hood Estimates 250
7.2.5 Testing the Goodness of Fit 252
7.3 Generalized Linear Model for Binary Response 254
7.3.1 Logit Models and Logistic Regression 254
7.3.2 Testing the Model 257
7.3.3 Distribution Function as a Link Function .... 258
7.4 Logit Models for Categorical Data 258
7.5 Goodness of Fit—Likelihood Ratio Test 260
7.6 Loglinear Models for Categorical Variables 261
7.6.1 Two Way Contingency Tables 261
7.6.2 Three Way Contingency Tables 264
7.7 The Special Case of Binary Response 267
7.8 Coding of Categorical Explanatory Variables 270
7.8.1 Dummy and Effect Coding 270
7.8.2 Coding of Response Models 273
7.8.3 Coding of Models for the Hazard Rate 274
7.9 Extensions to Dependent Binary Variables 277
7.9.1 Overview 277
7.9.2 Modeling Approaches for Correlated Response . 279
7.9.3 Quasi Likelihood Approach for Correlated
Binary Response 280
7.9.4 The Generalized Estimating Equation Method
by Liang and Zeger 281
Contents xiii
7.9.5 Properties of the Generalized Estimating
Equation Estimate @g 283
7.9.6 Efficiency of the Generalized Estimating
Equation and Independence Estimating Equa¬
tion Methods 284
7.9.7 Choice of the Quasi Correlation Matrix Ri(a) . 285
7.9.8 Bivariate Binary Correlated Response Variables . 285
7.9.9 The Generalized Estimating Equation Method . 286
7.9.10 The Independence Estimating Equation Method 288
7.9.11 An Example from the Field of Dentistry 288
7.9.12 Full Likelihood Approach for Marginal Models . 293
7.10 Exercises and Questions 294
8 Repeated Measures Model 295
8.1 The Fundamental Model for One Population 295
8.2 The Repeated Measures Model for Two Populations . . . 298
8.3 Univariate and Multivariate Analysis 301
8.3.1 The Univariate One Sample Case 301
8.3.2 The Multivariate One Sample Case 301
8.4 The Univariate Two Sample Case 306
8.5 The Multivariate Two Sample Case 307
8.6 Testing of Ho : £* = T,y 308
8.7 Univariate Analysis of Variance in the Repeated
Measures Model 309
8.7.1 Testing of Hypotheses in the Case of Com¬
pound Symmetry 309
8.7.2 Testing of Hypotheses in the Case of Sphericity . 311
8.7.3 The Problem of Nonsphericity 315
8.7.4 Application of Univariate Modified Ap¬
proaches in the Case of Nonsphericity 316
8.7.5 Multiple Tests 317
8.7.6 Examples 318
8.8 Multivariate Rank Tests in the Repeated Measures Model 324
8.9 Categorical Regression for the Repeated Binary
Response Data 329
8.9.1 Logit Models for the Repeated Binary Re¬
sponse for the Comparison of Therapies 329
8.9.2 First Order Markov Chain Models 330
8.9.3 Multinomial Sampling and Loglinear Mod¬
els for a Global Comparison of Therapies .... 332
8.10 Exercises and Questions 339
9 Cross Over Design 341
9.1 Introduction 341
9.2 Linear Model and Notations 342
xiv Contents
9.3 2x2 Cross Over (Classical Approach) 343
9.3.1 Analysis Using i Tests 344
9.3.2 Analysis of Variance 348
9.3.3 Residual Analysis and Plotting the Data 352
9.3.4 Alternative Parametrizations in 2 x 2 Cross
Over 356
9.3.5 Cross Over Analysis Using Rank Tests 368
9.4 2x2 Cross Over and Categorical (Binary) Response . . 368
9.4.1 Introduction 368
9.4.2 Loglinear and Logit Models 372
9.5 Exercises and Questions 384
10 Statistical Analysis of Incomplete Data 385
10.1 Introduction 385
10.2 Missing Data in the Response 390
10.2.1 Least Squares Analysis for Complete Data .... 390
10.2.2 Least Squares Analysis for Filled Up Data ... 391
10.2.3 Analysis of Covariance—Bartlett s Method ... 392
10.3 Missing Values in the X Matrix 393
10.3.1 Missing Values and Loss of Efficiency 394
10.3.2 Standard Methods for Incomplete X Matrices . 397
10.4 Adjusting for Missing Data in 2 x 2 Cross Over Designs 400
10.4.1 Notation 400
10.4.2 Maximum Likelihood Estimator (Rao, 1956) . . 402
10.4.3 Test Procedures 403
10.5 Missing Categorical Data 407
10.5.1 Introduction 407
10.5.2 Maximum Likelihood Estimation in the
Complete Data Case 408
10.5.3 Ad Hoc Methods 409
10.5.4 Model Based Methods 410
10.6 Exercises and Questions 412
A Matrix Algebra 415
A.I Introduction 415
A.2 Trace of a Matrix 418
A.3 Determinant of a Matrix 418
A.4 Inverse of a Matrix 420
A.5 Orthogonal Matrices 421
A.6 Rank of a Matrix 422
A.7 Range and Null Space 422
A.8 Eigenvalues and Eigenvectors 423
A.9 Decomposition of Matrices 425
A. 10 Definite Matrices and Quadratic Forms 427
A.ll Idempotent Matrices 433
Contents xv
A.12 Generalized Inverse 434
A.13 Projections 442
A. 14 Functions of Normally Distributed Variables 443
A. 15 Differentiation of Scalar Functions of Matrices 446
A. 16 Miscellaneous Results, Stochastic Convergence 449
B Theoretical Proofs 453
B.I The Linear Regression Model 453
B.2 Single Factor Experiments with Fixed and Random Effects 475
C Distributions and Tables 479
References 487
Index 497
|
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| indexdate | 2024-07-09T19:02:05Z |
| institution | BVB |
| isbn | 0387987894 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009841888 |
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| spelling | Toutenburg, Helge 1943-2009 Verfasser (DE-588)107164310 aut Statistical analysis of designed experiments Helge Toutenburg 2. ed. New York u.a. Springer 2002 XV, 500 S. txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Experimenteel ontwerp gtt Plan d'expérience Statistische analyse gtt Experimental design Versuchsplanung (DE-588)4078859-3 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Experimentauswertung (DE-588)4153362-8 gnd rswk-swf Statistik (DE-588)4056995-0 s Experimentauswertung (DE-588)4153362-8 s DE-604 Versuchsplanung (DE-588)4078859-3 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009841888&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Toutenburg, Helge 1943-2009 Statistical analysis of designed experiments Experimenteel ontwerp gtt Plan d'expérience Statistische analyse gtt Experimental design Versuchsplanung (DE-588)4078859-3 gnd Statistik (DE-588)4056995-0 gnd Experimentauswertung (DE-588)4153362-8 gnd |
| subject_GND | (DE-588)4078859-3 (DE-588)4056995-0 (DE-588)4153362-8 |
| title | Statistical analysis of designed experiments |
| title_auth | Statistical analysis of designed experiments |
| title_exact_search | Statistical analysis of designed experiments |
| title_full | Statistical analysis of designed experiments Helge Toutenburg |
| title_fullStr | Statistical analysis of designed experiments Helge Toutenburg |
| title_full_unstemmed | Statistical analysis of designed experiments Helge Toutenburg |
| title_short | Statistical analysis of designed experiments |
| title_sort | statistical analysis of designed experiments |
| topic | Experimenteel ontwerp gtt Plan d'expérience Statistische analyse gtt Experimental design Versuchsplanung (DE-588)4078859-3 gnd Statistik (DE-588)4056995-0 gnd Experimentauswertung (DE-588)4153362-8 gnd |
| topic_facet | Experimenteel ontwerp Plan d'expérience Statistische analyse Experimental design Versuchsplanung Statistik Experimentauswertung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009841888&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT toutenburghelge statisticalanalysisofdesignedexperiments |