Statistical analysis of designed experiments:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
[2009]
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| Edition: | Third [revised and updated] edition |
| Series: | Springer texts in statistics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Preface to the third edition: " This book is the third revised and updated English edition of the German textbook "Versuchsplanung und Modellwahl" by Helge Toutenburg ..." |
| Physical Description: | XVIII, 615 Seiten Diagramme 24 cm |
| ISBN: | 9781441911476 |
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| 020 | |a 9781441911476 |c GB. : ca. EUR 79.29 (freier Pr.), ca. sfr 115.00 (freier Pr.) |9 978-1-4419-1147-6 | ||
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| 100 | 1 | |a Toutenburg, Helge |d 1943-2009 |e Verfasser |0 (DE-588)107164310 |4 aut | |
| 240 | 1 | 0 | |0 (DE-604)BV009555805 |a Versuchsplanung und Modellwahl (1994) |
| 245 | 1 | 0 | |a Statistical analysis of designed experiments |c Helge Toutenburg ; Shalabh |
| 250 | |a Third [revised and updated] edition | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c [2009] | |
| 264 | 4 | |c © 2009 | |
| 300 | |a XVIII, 615 Seiten |b Diagramme |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer texts in statistics | |
| 500 | |a Preface to the third edition: " This book is the third revised and updated English edition of the German textbook "Versuchsplanung und Modellwahl" by Helge Toutenburg ..." | ||
| 650 | 4 | |a Experimental design | |
| 650 | 0 | 7 | |a Experimentauswertung |0 (DE-588)4153362-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Versuchsplanung |0 (DE-588)4078859-3 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text |
Contents
Preface
to the Third Edition
v
Preface
vii
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 i-Test and Matched-Pair Design
. 22
2.3
Comparison of Means in Independent Groups
. 25
2.3.1
Two-Sample i-Test
. 25
2.3.2
Testing Ho
:
σ\ = σ| = σ1
. 25
2.3.3
Comparison of Means in the Case of
Unequal Variances
. 26
xii Contents
2.3.4 Transformations
of Data to Assure Homo¬
geneity of Variances
. 27
2.3.5
Necessary Sample Size and Power of the Test
. . 27
2.3.6
Comparison of Means without Prior Testing
Ho
:
σ\ = σ\\
Cochran-Cox Test for
Independent Groups
. 27
2.4
Wilcoxon's Sign-Rank Test in the Matched-Pair Design
28
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
. 40
2.7
Exercises and Questions
. 42
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
σ2
. 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
Břvariate
Regression
. 73
3.8.2
Multiple Regression
. 79
3.9
The General Linear Regression Model
. 84
3.9.1
Introduction
. 84
3.9.2
Misspecification of the Covariance Matrix
. 85
3.10
Diagnostic Tools
. 87
3.10.1
Introduction
. 87
3.10.2
Prediction Matrix
. 87
3.10.3
Effect of a Single Observation on the
Estimation of Parameters
. 91
3.10.4
Diagnostic Plots for Testing the Model
Assumptions
. 96
3.10.5
Measures Based on the Confidence Ellipsoid
. 97
Contents xiii
3.10.6
Partial
Regression
Plots
. 102
3.10.7 Regression
Diagnostics by Animating Graphics
. 105
3.11
Exercises and Questions
. 110
4
Single—Factor Experiments with Fixed and Random
Effects
113
4.1
Models I and II in the Analysis of Variance
. 113
4.2
One-Way Classification for the Multiple Compari¬
son of Means
. 115
4.2.1
Representation as a Restrictive Model
. 117
4.2.2
Decomposition of the Error Sum of Squares
. 119
4.2.3
Estimation of
σ2
by
MS®rror
. 123
4.3
Comparison of Single Means
. 126
4.3.1
Linear Contrasts
. 126
4.3.2
Contrasts of the Total Response Values in
the Balanced Case
. 129
4.4
Multiple Comparisons
. 134
4.4.1
Introduction
. 134
4.4.2
Experimentwise Comparisons
. 135
4.4.3
Select Pairwise Comparisons
. 137
4.5
Regression Analysis of Variance
. 144
4.6
One-Factorial Models with Random Effects
. 147
4.7
Rank Analysis of Variance in the Completely Ran¬
domized Design
. 151
4.7.1
Kruskal-Wallis Test
. 151
4.7.2
Multiple Comparisons
. 154
4.8
Exercises and Questions
. 156
5
More Restrictive Designs
159
5.1
Randomized Block Design
. 159
5.2
Latin Squares
. 168
5.2.1
Analysis of Variance
. 169
5.3
Rank Variance Analysis in the Randomized Block Design
175
5.3.1
Friedman Test
. 175
5.3.2
Multiple Comparisons
. 177
5.4
Exercises and Questions
. 179
6
Incomplete Block Designs
181
6.1
Introduction
. 181
6.2
General Theory of Incomplete Block Designs
. 183
6.3
Intrablock Analysis of Incomplete Block Design
. 185
6.3.1
Model and Normal Equations
. 185
6.3.2
Covariance Matrices of Adjusted Treatment
and Block Totals
. 188
xiv Contents
6.3.3
Decomposition of Sum of Squares and
Analysis of Variance
. 189
6.4
Interblock Analysis of Incomplete Block Design
. 193
6.4.1
Model and Normal Equations
. 195
6.4.2
Use of Intrablock and Interblock Estimates
. . . 197
6.5
Balanced Incomplete Block Design
. 201
6.5.1
Interpretation of Conditions of BIBD
. 202
6.5.2
Intrablock Analysis of BIBD
. 204
6.5.3
Interblock Analysis and Recovery of
Interblock Information in BIBD
. 211
6.6
Partially Balanced Incomplete Block Designs
. 219
6.6.1
Partially Balanced Association Schemes
. 220
6.6.2
General Theory of PBIBD
. 229
6.6.3
Conditions for PBIBD
. 230
6.6.4
Interpretations of Conditions of BIBD
. 230
6.6.5
Intrablock Analysis of PBIBD With Two
Associates
. 231
6.7
Exercises and Questions
. 241
7
Multifactor Experiments
245
7.1
Elementary Definitions and Principles
. 245
7.2
Two-Factor Experiments (Fixed Effects)
. 249
7.3
Two-Factor Experiments in Effect Coding
. 254
7.4
Two-Factorial Experiment with Block Effects
. 263
7.5
Two-Factorial Model with Fixed Effects
—
Confidence
Intervals and Elementary Tests
. 266
7.6
Two-Factorial Model with Random or Mixed Effects
. . 270
7.6.1
Model with Random Effects
. 270
7.6.2
Mixed Model
. 274
7.7
Three-Factorial Designs
. 278
7.8
Split-Plot Design
. 283
7.9
2k Factorial Design
. 287
7.9.1
The 22 Design
. 288
7.9.2
The 23 Design
. 290
7.10
Confounding
. 294
7.11
Analysis of Variance in Case of Confounded Effects
. . . 303
7.12
Partial Confounding
. 304
7.13
Fractional Replications
. 316
7.14
Exercises and Questions
. 322
8
Models for Categorical Response Variables
329
8.1
Generalized Linear Models
. 329
8.1.1
Extension of the Regression Model
. 329
8.1.2
Structure of the Generalized Linear Model
. . 331
8.1.3
Score Function and Information Matrix
. 334
Contents xv
8.1.4 Maximum
Likelihood Estimation
. 335
8.1.5
Testing of Hypotheses and Goodness of Fit
. 338
8.1.6
Overdispersion
. 339
8.1.7
Quasi Loglikelihood
. 341
8.2
Contingency Tables
. 343
8.2.1
Overview
. 343
8.2.2
Ways of Comparing Proportions
. 344
8.2.3
Sampling in Two-Way Contingency Tables
. . . 347
8.2.4
Likelihood Function and Maximum
Likelihood Estimates
. 348
8.2.5
Testing the Goodness of Fit
. 350
8.3
Generalized Linear Model for Binary Response
. 353
8.3.1
Logit Models and Logistic Regression
. 353
8.3.2
Testing the Model
. 355
8.3.3
Distribution Function as a Link Function
. 356
8.4
Logit Models for Categorical Data
. 357
8.5
Goodness of Fit—Likelihood Ratio Test
. 358
8.6 Loglinear
Models for Categorical Variables
. 359
8.6.1
Two-Way Contingency Tables
. 359
8.6.2
Three-Way Contingency Tables
. 362
8.7
The Special Case of Binary Response
. 365
8.8
Coding of Categorical Explanatory Variables
. 368
8.8.1
Dummy and Effect Coding
. 368
8.8.2
Coding of Response Models
. 372
8.8.3
Coding of Models for the Hazard Rate
. 372
8.9
Extensions to Dependent Binary Variables
. 375
8.9.1
Overview
. 376
8.9.2
Modeling Approaches for Correlated Response
. 377
8.9.3
Quasi-Likelihood Approach for Correlated
Binary Response
. 378
8.9.4
The Generalized Estimating Equation Method
by Liang and Zeger
. 379
8.9.5
Properties of the Generalized Estimating
Equation Estimate
ßa. 381
8.9.6
Efficiency of the Generalized Estimating
Equation and Independence Estimating
Equation Methods
. 383
8.9.7
Choice of the Quasi-Correlation Matrix
Щ(а)
. 383
8.9.8
Bivariate Binary Correlated Response Variables
. 384
8.9.9
The Generalized Estimating Equation Method
. 385
8.9.10
The Independence Estimating Equation Method
386
8.9.11
An Example from the Field of Dentistry
. 387
8.9.12
Full Likelihood Approach for Marginal Models
. 392
8.10
Exercises and Questions
. 392
xvi Contents
9
Repeated Measures Model
395
9.1
The Fundamental Model for One Population
. 395
9.2
The Repeated Measures Model for Two Populations
. . . 398
9.3
Univariate and Multivariate Analysis
. 401
9.3.1
The Univariate One-Sample Case
. 401
9.3.2
The Multivariate One-Sample Case
. 401
9.4
The Univariate Two-Sample Case
. 406
9.5
The Multivariate Two-Sample Case
. 407
9.6
Testing of Ho
:
Σχ = Συ.
407
9.7
Univariate Analysis of Variance in the Repeated
Measures Model
. 409
9.7.1
Testing of Hypotheses in the Case of
Compound Symmetry
. 409
9.7.2
Testing of Hypotheses in the Case of
Sphericity
. 411
9.7.3
The Problem of Nonsphericity
. 415
9.7.4
Application of Univariate Modified
Approaches in the Case of Nonsphericity
. 416
9.7.5
Multiple Tests
. 417
9.7.6
Examples
. 418
9.8
Multivariate Rank Tests in the Repeated Measures Model
424
9.9
Categorical Regression for the Repeated Binary
Response Data
. 429
9.9.1
Logit Models for the Repeated Binary
Response for the Comparison of Therapies
. 429
9.9.2
First-Order Markov Chain Models
. 430
9.9.3
Multinomial Sampling and Loglinear
Models for a Global Comparison of Therapies
. . 432
9.10
Exercises and Questions
. 439
10
Cross—Over Design
441
10.1
Introduction
. 441
10.2
Linear Model and Notations
. 442
10.3 2x2
Cross-Over (Classical Approach)
. 443
10.3.1
Analysis Using
i-Tests
. 444
10.3.2
Analysis of Variance
. 449
10.3.3
Residual Analysis and Plotting the Data
. 453
10.3.4
Alternative Parametrizations in
2
χ
2
Cross-
Over
. 457
10.3.5
Cross-Over Analysis Using Rank Tests
. 468
10.4 2x2
Cross-Over and Categorical (Binary) Response
. . 468
10.4.1
Introduction
. 468
10.4.2
Loglinear and Logit Models
. 473
10.5
Exercises and Questions
. 485
Contents xvii
11
Statistical Analysis of Incomplete Data
487
11.1
Introduction
. 487
11.2
Missing Data in the Response
. 492
11.2.1
Least Squares Analysis for Complete Data
. 492
11.2.2
Least Squares Analysis for Filled-Up Data
. 493
11.2.3
Analysis of Covariance
—
Bartlett's Method
. . . 494
11.3
Missing Values in the
.Х
-Matrix.
495
11.3.1
Missing Values and Loss of Efficiency
. 497
11.3.2
Standard Methods for Incomplete
Х
-Matrices .
499
11.4
Adjusting for Missing Data in
2
χ
2
Cross-Over Designs
502
11.4.1
Notation
. 502
11.4.2
Maximum Likelihood Estimator (Rao,
1956) . . 504
11.4.3
Test Procedures
. 505
11.5
Missing Categorical Data
. 510
11.5.1
Introduction
. 510
11.5.2
Maximum Likelihood Estimation in the
Complete Data Case
. 511
11.5.3
Ad
-Нос
Methods
. 511
11.5.4
Model-Based Methods
. 512
11.6
Exercises and Questions
. 515
A Matrix Algebra
517
A.I Introduction
. 517
A.2 Trace of a Matrix
. 520
A.3 Determinant of a Matrix
. 520
A.4 Inverse of a Matrix
. 522
A.5 Orthogonal Matrices
. 523
A.6 Rank of a Matrix
. 524
A.7 Range and Null Space
. 524
A.
8
Eigenvalues and Eigenvectors
. 525
A.
9
Decomposition of Matrices
. 527
АЛО
Definite Matrices and Quadratic Forms
. 530
A.
11
Idempotent Matrices
. 536
A.12 Generalized Inverse
. 537
A.13 Projections
. 545
A.
14
Functions of Normally Distributed Variables
. 546
A.
15
Differentiation of Scalar Functions of Matrices
. 549
A.
16
Miscellaneous Results, Stochastic Convergence
. 552
В
Theoretical Proofs
555
B.I The Linear Regression Model
. 555
B.2 Single-Factor Experiments with Fixed and Random
Effects
. 578
B.3 Incomplete Block Designs
. 581
xviii Contents
С
Distributions and Tables
591
References
599
Index
611 |
| any_adam_object | 1 |
| author | Toutenburg, Helge 1943-2009 Shalabh |
| author_GND | (DE-588)107164310 (DE-588)171638417 |
| author_facet | Toutenburg, Helge 1943-2009 Shalabh |
| author_role | aut aut |
| author_sort | Toutenburg, Helge 1943-2009 |
| author_variant | h t ht s |
| building | Verbundindex |
| bvnumber | BV035786089 |
| callnumber-first | Q - Science |
| callnumber-label | QA279 |
| callnumber-raw | QA279 |
| callnumber-search | QA279 |
| callnumber-sort | QA 3279 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | CM 4000 SK 840 |
| classification_tum | MAT 620f |
| ctrlnum | (OCoLC)436030791 (DE-599)DNB995510164 |
| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Psychologie Mathematik |
| edition | Third [revised and updated] edition |
| format | Book |
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| id | DE-604.BV035786089 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-25T00:19:42Z |
| institution | BVB |
| isbn | 9781441911476 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018645510 |
| oclc_num | 436030791 |
| open_access_boolean | |
| owner | DE-M49 DE-BY-TUM DE-355 DE-BY-UBR DE-11 DE-19 DE-BY-UBM DE-188 DE-83 |
| owner_facet | DE-M49 DE-BY-TUM DE-355 DE-BY-UBR DE-11 DE-19 DE-BY-UBM DE-188 DE-83 |
| physical | XVIII, 615 Seiten Diagramme 24 cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer texts in statistics |
| spelling | Toutenburg, Helge 1943-2009 Verfasser (DE-588)107164310 aut (DE-604)BV009555805 Versuchsplanung und Modellwahl (1994) Statistical analysis of designed experiments Helge Toutenburg ; Shalabh Third [revised and updated] edition New York [u.a.] Springer [2009] © 2009 XVIII, 615 Seiten Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Springer texts in statistics Preface to the third edition: " This book is the third revised and updated English edition of the German textbook "Versuchsplanung und Modellwahl" by Helge Toutenburg ..." Experimental design Experimentauswertung (DE-588)4153362-8 gnd rswk-swf Versuchsplanung (DE-588)4078859-3 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s Experimentauswertung (DE-588)4153362-8 s DE-604 Versuchsplanung (DE-588)4078859-3 s b DE-604 Shalabh Verfasser (DE-588)171638417 aut Erscheint auch als Online-Ausgabe 978-1-4419-1148-3 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018645510&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Toutenburg, Helge 1943-2009 Shalabh Statistical analysis of designed experiments Experimental design Experimentauswertung (DE-588)4153362-8 gnd Versuchsplanung (DE-588)4078859-3 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4153362-8 (DE-588)4078859-3 (DE-588)4056995-0 |
| title | Statistical analysis of designed experiments |
| title_GND | (DE-604)BV009555805 |
| title_alt | Versuchsplanung und Modellwahl (1994) |
| title_auth | Statistical analysis of designed experiments |
| title_exact_search | Statistical analysis of designed experiments |
| title_full | Statistical analysis of designed experiments Helge Toutenburg ; Shalabh |
| title_fullStr | Statistical analysis of designed experiments Helge Toutenburg ; Shalabh |
| title_full_unstemmed | Statistical analysis of designed experiments Helge Toutenburg ; Shalabh |
| title_short | Statistical analysis of designed experiments |
| title_sort | statistical analysis of designed experiments |
| topic | Experimental design Experimentauswertung (DE-588)4153362-8 gnd Versuchsplanung (DE-588)4078859-3 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Experimental design Experimentauswertung Versuchsplanung Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018645510&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT toutenburghelge versuchsplanungundmodellwahl1994 AT shalabh versuchsplanungundmodellwahl1994 AT toutenburghelge statisticalanalysisofdesignedexperiments AT shalabh statisticalanalysisofdesignedexperiments |