Gespeichert in:
| Titel: | Statistical analysis of designed experiments |
|---|---|
| Von: |
Helge Toutenburg ; Shalabh
|
| Person: |
Toutenburg, Helge
1943-2009 Verfasser aut Shalabh |
| Hauptverfassende: | , |
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New York [u.a.]
Springer
[2009]
|
| Ausgabe: | Third [revised and updated] edition |
| Schriftenreihe: | Springer texts in statistics
|
| Schlagworte: | |
| Online-Zugang: | 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 |
| Beschreibung: | 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 ..." |
| Beschreibung: | XVIII, 615 Seiten Diagramme 24 cm |
| ISBN: | 9781441911476 |
Internformat
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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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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-018645510 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 1002 MAT 620f 2010 A 2195(3) |
|---|---|
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| DE-BY-TUM_location | 10 |
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| DE-BY-UBR_call_number | 71/CM 4000 T736(3) |
| DE-BY-UBR_katkey | 4540042 |
| DE-BY-UBR_location | UB Lesesaal Philosophicum 2: Psychologie |
| DE-BY-UBR_media_number | 069037217225 |
| _version_ | 1835091044830543872 |
| 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 | 2024-12-20T14:00:09Z |
| 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 |
| 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 |
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