Statistical analysis of designed experiments: theory and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, N.J.
Wiley
2009
|
| Schriftenreihe: | Wiley series in probability and statistics
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XXIV, 679 S. graph. Darst. |
| ISBN: | 9780471750437 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV035173734 | ||
| 003 | DE-604 | ||
| 005 | 20090825 | ||
| 007 | t | ||
| 008 | 081121s2009 xxud||| |||| 00||| eng d | ||
| 010 | |a 2008009432 | ||
| 020 | |a 9780471750437 |c cloth |9 978-0-471-75043-7 | ||
| 035 | |a (OCoLC)212627345 | ||
| 035 | |a (DE-599)BVBBV035173734 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-703 |a DE-11 |a DE-578 | ||
| 050 | 0 | |a QA279 | |
| 082 | 0 | |a 519.5/7 | |
| 084 | |a SK 840 |0 (DE-625)143261: |2 rvk | ||
| 100 | 1 | |a Tamhane, Ajit C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Statistical analysis of designed experiments |b theory and applications |c Ajit C. Tamhane |
| 264 | 1 | |a Hoboken, N.J. |b Wiley |c 2009 | |
| 300 | |a XXIV, 679 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and statistics | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Experimental design | |
| 650 | 0 | 7 | |a Versuchsplanung |0 (DE-588)4078859-3 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4123623-3 |a Lehrbuch |2 gnd-content | |
| 689 | 0 | 0 | |a Versuchsplanung |0 (DE-588)4078859-3 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0829/2008009432-d.html |3 Publisher description | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0829/2008009432-t.html |3 Table of contents only | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016980625&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016980625 | ||
Datensatz im Suchindex
| _version_ | 1804138343111327744 |
|---|---|
| adam_text | Contents
Preface
xv
Abbreviations
xxi
1
Introduction
1
1.1
Observational Studies and Experiments
/ 1
1.2
Brief Historical Remarks
/ 4
1.3
Basic Terminology and Concepts of Experimentation
/ 5
1.4
Basic Principles of Experimentation
/ 9
1.4.1
How to Minimize Biases and Variability?
/ 9
1.4.2
Sequential Experimentation
/ 14
1.5
Chapter Summary
/ 15
Exercises
/ 16
2
Review of Elementary Statistics
20
2.1
Experiments for a Single Treatment
/ 20
2.1.1
Summary Statistics and Graphical Plots
/ 21
2.1.2
Confidence Intervals and Hypothesis Tests
/ 25
2.1.3
Power and Sample Size Calculation
/ 27
2.2
Experiments for Comparing Two Treatments
/ 28
2.2.1
Independent Samples Design
/ 29
2.2.2
Matched Pairs Design
/ 38
2.3
Linear Regression
/ 41
2.3.1
Simple Linear Regression
/ 42
2.3.2
Multiple Linear Regression
/ 50
2.4
Chapter Summary
/ 62
Exercises
/ 62
vii
VIU
CONTENTS
3 Single
Factor
Experiments:
Completely Randomized Designs
70
3.1
Summary Statistics and Graphical Displays
/71
3.2
Model
/ 73
3.3
Statistical Analysis
/ 75
3.3.1
Estimation
/ 75
3.3.2
Analysis of Variance
/ 76
3.3.3
Confidence Intervals and Hypothesis Tests
/ 78
3.4
Model Diagnostics
/ 79
3.4.1
Checking Homoscedasticity
/ 80
3.4.2
Checking Normality
/ 81
3.4.3
Checking Independence
/ 81
3.4.4
Checking Outliers
/ 81
3.5
Data Transformations
/ 85
3.6
Power of F-Test and Sample Size Determination
/ 87
3.7
Quantitative Treatment Factors
/ 90
3.8
One-Way Analysis of Covariance
/ 96
3.8.1
Randomized Block Design versus Analysis of
Covariance
/ 96
3.8.2
Model
/ 96
3.8.3
Statistical Analysis
/ 98
3.9
Chapter Notes
/ 106
3.9.1
Randomization Distribution of F-Statistic
/106
3.9.2
F-Test for Heteroscedastic Treatment
Variances
/ 108
3.9.3
Derivations of Formulas for Orthogonal
Polynomials
/110
3.9.4
Derivation of LS Estimators for One-Way Analysis
of Covariance
/ 112
3.10
Chapter Summary
/113
Exercises
/ 114
4
Single-Factor Experiments: Multiple Comparison and Selection
Procedures
126
4.1
Basic Concepts of Multiple Comparisons
/ 127
4.1.1
Family
/ 127
4.1.2
Family wise Error Rate
/ 128
4.1.3
Bonferroni Method
/ 129
4.1.4
Union-Intersection Method
/ 130
4.1.5
Closure Method
/131
CONTENTS
ІХ
4.2 Pairwise
Comparisons
/132
4.2.1
Least Significant Difference and Bonferroni
Procedures
/133
4.2.2
Tukey Procedure for Pairwise Comparisons
/134
4.2.3
Step-Down Procedures for Pairwise Comparisons
/136
4.3
Comparisons with a Control
/139
4.3.1
Dunnett Procedure for Comparisons with a
Control
/ 139
4.3.2
Step-Down Procedures for Comparisons with a
Control
/ 142
4.4
General Contrasts
/ 144
4.4.1
Tukey Procedure for Orthogonal Contrasts
/ 145
4.4.2
Scheffé
Procedure for All Contrasts
/ 146
4.5
Ranking and Selection Procedures
/ 148
4.5.1
Indifference-Zone Formulation
/148
4.5.2
Subset Selection Formulation
/ 154
4.5.3
Multiple Comparisons with the Best
/155
4.5.4
Connection between Multiple Comparisons with
Best and Selection of Best Treatment
/ 157
4.6
Chapter Summary
/ 158
Exercises
/159
5
Randomized Block Designs and Extensions
168
5.1
Randomized Block Designs
/ 169
5.1.1
Model
/ 169
5.1.2
Statistical Analysis
/ 171
5.1.3
Randomized Block Designs with Replicates
/177
5.2
Balanced Incomplete Block Designs
/180
5.2.1
Statistical Analysis
/182
5.2.2
Interblock Analysis
/ 185
5.3
Youden Square Designs
/ 188
5.3.1
Statistical Analysis
/ 189
5.4
Latin Square Designs
/ 192
5.4.1
Choosing a Latin Square
/ 192
5.4.2
Model
/ 195
5.4.3
Statistical Analysis
/ 195
5.4.4
Crossover Designs
/ 198
5.4.5
Graeco-Latin Square Designs
/ 202
5.5
Chapter Notes
/ 205
CONTENTS
5.5.1
Restriction
Error Model for Randomized Block
Designs
/ 205
5.5.2
Derivations of Formulas for BIB Design
/ 206
5.6
Chapter Summary
/211
Exercises
/212
General Factorial Experiments
224
6.1
Factorial versus One-Factor-at-a-Time Experiments
/ 225
6.2
Balanced Two-Way Layouts
/ 227
6.2.1
Summary Statistics and Graphical Plots
/ 227
6.2.2
Model
/ 230
6.2.3
Statistical Analysis
/ 231
6.2.4
Model Diagnostics
/ 235
6.2.5
Tukey s Test for Interaction for Singly Replicated
Two-Way Layouts
/ 236
6.3
Unbalanced Two-Way Layouts
/ 240
6.3.1
Statistical Analysis
/ 240
6.4
Chapter Notes
/ 245
6.4.1
Derivation of LS Estimators of Parameters for
Balanced Two-Way Layouts
/ 245
6.4.2
Derivation of ANOVA Sums of Squares and
F-Tests for Balanced Two-Way Layouts
/ 246
6.4.3
Three- and Higher Way Layouts
/ 248
6.5
Chapter Summary
/ 250
Exercises
/ 250
Two-Level Factorial Experiments
256
7.1
Estimation of Main Effects and Interactions
/ 257
7.1.1
22 Designs
/ 257
7.1.2
23 Designs
/ 261
7.1.3
V Designs
/ 266
7.2
Statistical Analysis
/ 267
7.2.1
Confidence Intervals and Hypothesis Tests
/ 267
7.2.2
Analysis of Variance
/ 268
7.2.3
Model Fitting and Diagnostics
/ 270
7.3
Single-Replicate Case
/ 272
7.3.1
Normal and Half-Normal Plots of Estimated
Effects
/ 272
7.3.2
Lenth Method
/ 278
CONTENTS
ХІ
7.3.3
Augmenting a 2P Design with Observations at the
Center Point
/ 279
7.4
2P Factorial Designs in Incomplete Blocks: Confounding of
Effects
/ 282
7.4.1
Construction of Designs
/ 282
7.4.2
Statistical Analysis
/ 286
7.5
Chapter Notes
/ 287
7.5.1
Yates
Algorithm
/ 287
7.5.2
Partial Confounding
/ 288
7.6
Chapter Summary
/ 289
Exercises
/ 290
8
Two-Level Fractional Factorial Experiments
300
8.1
2Р-Ч
Fractional Factorial Designs
/ 301
8.1.1
2p~l Fractional Factorial Design
/ 301
8.1.2
General W 4 Fractional Factorial Designs
/ 307
8.1.3
Statistical Analysis
/ 312
8.1.4
Minimum Aberration Designs
/ 316
8.2
Plackett-Burman Designs
/ 317
8.3
Hadamard
Designs
/ 323
8.4
Supersaturated Designs
/ 325
8.4.1
Construction of Supersaturated Designs
/ 325
8.4.2
Statistical Analysis
/ 327
8.5
Orthogonal Arrays
/ 329
8.6
Sequential Assemblies of Fractional Factorials
/ 333
8.6.1
Foldover of Resolution III Designs
/ 334
8.6.2
Foldover of Resolution IV Designs
/ 337
8.7
Chapter Summary
/ 338
Exercises
/ 339
9
Three-Level and Mixed-Level Factorial Experiments
351
9.1
Three-Level Full Factorial Designs
/ 351
9.1.1
Linear-Quadratic System
/ 353
9.1.2
Orthogonal Component System
/ 361
9.2
Three-Level Fractional Factorial Designs
/ 364
9.3
Mixed-Level Factorial Designs
/ 372
9.3.1
2рАч
Designs
/ 373
9.3.2
2p3« Designs
/ 378
9.4
Chapter Notes
/ 386
XU CONTENTS
9.4.1 Alternative
Derivations of Estimators of
Linear
and
Quadratic Effects
/ 386
9.5
Chapter Summary
/ 388
Exercises
/ 389
10
Experiments for Response Optimization
395
10.1
Response Surface Methodology
/ 396
10.1.1
Outline of Response Surface Methodology
/ 396
10.1.2
First-Order Experimentation Phase
/ 397
10.1.3
Second-Order Experimentation Phase
/ 402
10.2
Mixture Experiments
/412
10.2.1
Designs for Mixture Experiments
/ 414
10.2.2
Analysis of Mixture Experiments
/ 416
10.3
Taguchi Method of Quality Improvement
/ 419
10.3.1
Philosophy Underlying Taguchi Method
/ 422
10.3.2
Implementation of Taguchi Method
/ 425
10.3.3
Critique of Taguchi Method
/ 432
10.4
Chapter Summary
/ 436
Exercises
/ 437
11
Random and Mixed Crossed-Factors Experiments
448
11.1
One-Way Layouts
/ 449
11.1.1
Random-Effects Model
/ 449
11.1.2
Analysis of Variance
/ 450
11.1.3
Estimation of Variance Components
/ 452
11.2
Two-Way Layouts
/ 455
11.2.1
Random-Effects Model
/ 455
11.2.2
Mixed-Effects Model
/ 459
11.3
Three-Way Layouts
/ 464
11.3.1
Random- and Mixed-Effects Models
/ 464
11.3.2
Analysis of Variance
/ 465
11.3.3
Approximate
f
-Tests
/ 468
11.4
Chapter Notes
/ 472
11.4.1
Maximum Likelihood and Restricted Maximum
Likelihood (REML) Estimation of Variance
Components
/ 472
11.4.2
Derivations of Results for One- and Two-Way
Random-Effects Designs
/ 475
11.4.3
Relationship between Unrestricted and Restricted
Models
/ 478
CONTENTS
ХІІІ
11.5
Chapter Summary
/ 479
Exercises
/ 480
12
Nested, Crossed-Nested, and Split-Plot Experiments
487
12.1
Two-Stage Nested Designs
/ 488
12.1.1
Model
/ 488
12.1.2
Analysis of Variance
/ 489
12.2
Three-Stage Nested Designs
/ 490
12.2.1
Model
/ 491
12.2.2
Analysis of Variance
/ 492
12.3
Crossed and Nested Designs
/ 495
12.3.1
Model
/ 495
12.3.2
Analysis of Variance
/ 496
12.4
Split-Plot Designs
/ 501
12.4.1
Model
/ 504
12.4.2
Analysis of Variance
/ 505
12.4.3
Extensions of Split-Plot Designs
/ 508
12.5
Chapter Notes
/ 515
12.5.1
Derivations of E(MS) Expressions for Two-Stage
Nested Design of Section
12.1
with Both Factors
Random
/515
12.5.2
Derivations of E(MS) Expressions for Design of
Section
12.3
with Crossed and Nested Factors
/517
12.5.3
Derivations of E(MS) Expressions for Split-Plot
Design
/ 520
12.6
Chapter Summary
/ 523
Exercises
/ 524
13
Repeated Measures Experiments
536
13.1
Univariate Approach
/ 536
13.1.1
Model
/ 537
13.1.2
Univariate Analysis of Variance for
RM
Designs
/ 537
13.2
Multivariate Approach
/ 548
13.2.1
One-Way Multivariate Analysis of Variance
/ 548
13.2.2
Multivariate Analysis of Variance for
RM
Designs
/ 549
13.3
Chapter Notes
/ 555
13.3.1
Derivations of E(MS) Expressions for Repeated
Measures Design Assuming Compound Symmetry
/ 555
13.4
Chapter Summary
/558
Exercises
/ 559
XIV
CONTENTS
14.2.2
14.2.3
14.2.4
14.2.5
14
Theory of Linear Models with Fixed Effects
566
14.1
Basic Linear Model and Least Squares Estimation
/ 566
14.1.1
Geometric Interpretation of Least Squares
Estimation
/ 568
14.1.2
Least Squares Estimation in Singular Case
/ 570
14.1.3
Least Squares Estimation in Orthogonal Case
/ 572
14.2
Confidence Intervals and Hypothesis Tests
/ 573
14.2.1
Sampling Distribution of
β
I
573
Sampling Distribution of s2 I
574
Inferences on Scalar Parameters
/ 575
Inferences on Vector Parameters
/ 575
Extra Sum of Squares Method
/ 577
14.2.6
Analysis of Variance
/ 579
14.3
Power of F-Test
/ 583
14.4
Chapter Notes
/ 586
14.4.1
Proof of Theorem
14.1
(Gauss-Markov
Theorem)
/ 586
14.4.2
Proof of Theorem
14.2 / 586
14.5
Chapter Summary
/ 587
Exercises
/ 588
Appendix A Vector-Valued Random Variables and Some
Distribution Theory
595
A.
1
Mean Vector and Covariance Matrix of Random
Vector
/ 596
A.2 Covariance Matrix of Linear Transformation of
Random Vector
/ 597
A.3 Multivariate Normal Distribution
/ 598
A.4 Chi-Square, F-, and i-Distributions
/ 599
A.5 Distributions of Quadratic Forms
/ 601
A.6 Multivariate r-Distribution
/ 605
A.7 Multivariate Normal Sampling Distribution
Theory
/ 606
Appendix
В
Case Studies
608
B.I Case Study
1:
Effects of Field Strength and Flip
Angle on
MRI
Contrast
/ 608
B.I.I Introduction
/ 608
B.1.2 Design
/ 609
B.1.3 Data Analysis
/ 610
CONTENTS
XV
В.
1.4
Results
/ 612
B.2 Case Study
2:
Growing Stem Cells for Bone
Implants
/613
B.2.1 Introduction
/613
B.2.2 Design
/ 614
B.2.3 Data Analysis
/ 614
B.2.4 Results
/ 614
B.3 Case Study
3:
Router Bit Experiment
/ 619
B.3.1 Introduction
/619
B.3.2 Design
/619
B.3.3 Data Analysis
/ 623
B.3.4 Results
/ 624
Appendix
С
Statistical Tables
627
Answers to Selected Exercises
644
References
664
Index
675
|
| adam_txt |
Contents
Preface
xv
Abbreviations
xxi
1
Introduction
1
1.1
Observational Studies and Experiments
/ 1
1.2
Brief Historical Remarks
/ 4
1.3
Basic Terminology and Concepts of Experimentation
/ 5
1.4
Basic Principles of Experimentation
/ 9
1.4.1
How to Minimize Biases and Variability?
/ 9
1.4.2
Sequential Experimentation
/ 14
1.5
Chapter Summary
/ 15
Exercises
/ 16
2
Review of Elementary Statistics
20
2.1
Experiments for a Single Treatment
/ 20
2.1.1
Summary Statistics and Graphical Plots
/ 21
2.1.2
Confidence Intervals and Hypothesis Tests
/ 25
2.1.3
Power and Sample Size Calculation
/ 27
2.2
Experiments for Comparing Two Treatments
/ 28
2.2.1
Independent Samples Design
/ 29
2.2.2
Matched Pairs Design
/ 38
2.3
Linear Regression
/ 41
2.3.1
Simple Linear Regression
/ 42
2.3.2
Multiple Linear Regression
/ 50
2.4
Chapter Summary
/ 62
Exercises
/ 62
vii
VIU
CONTENTS
3 Single
Factor
Experiments:
Completely Randomized Designs
70
3.1
Summary Statistics and Graphical Displays
/71
3.2
Model
/ 73
3.3
Statistical Analysis
/ 75
3.3.1
Estimation
/ 75
3.3.2
Analysis of Variance
/ 76
3.3.3
Confidence Intervals and Hypothesis Tests
/ 78
3.4
Model Diagnostics
/ 79
3.4.1
Checking Homoscedasticity
/ 80
3.4.2
Checking Normality
/ 81
3.4.3
Checking Independence
/ 81
3.4.4
Checking Outliers
/ 81
3.5
Data Transformations
/ 85
3.6
Power of F-Test and Sample Size Determination
/ 87
3.7
Quantitative Treatment Factors
/ 90
3.8
One-Way Analysis of Covariance
/ 96
3.8.1
Randomized Block Design versus Analysis of
Covariance
/ 96
3.8.2
Model
/ 96
3.8.3
Statistical Analysis
/ 98
3.9
Chapter Notes
/ 106
3.9.1
Randomization Distribution of F-Statistic
/106
3.9.2
F-Test for Heteroscedastic Treatment
Variances
/ 108
3.9.3
Derivations of Formulas for Orthogonal
Polynomials
/110
3.9.4
Derivation of LS Estimators for One-Way Analysis
of Covariance
/ 112
3.10
Chapter Summary
/113
Exercises
/ 114
4
Single-Factor Experiments: Multiple Comparison and Selection
Procedures
126
4.1
Basic Concepts of Multiple Comparisons
/ 127
4.1.1
Family
/ 127
4.1.2
Family wise Error Rate
/ 128
4.1.3
Bonferroni Method
/ 129
4.1.4
Union-Intersection Method
/ 130
4.1.5
Closure Method
/131
CONTENTS
ІХ
4.2 Pairwise
Comparisons
/132
4.2.1
Least Significant Difference and Bonferroni
Procedures
/133
4.2.2
Tukey Procedure for Pairwise Comparisons
/134
4.2.3
Step-Down Procedures for Pairwise Comparisons
/136
4.3
Comparisons with a Control
/139
4.3.1
Dunnett Procedure for Comparisons with a
Control
/ 139
4.3.2
Step-Down Procedures for Comparisons with a
Control
/ 142
4.4
General Contrasts
/ 144
4.4.1
Tukey Procedure for Orthogonal Contrasts
/ 145
4.4.2
Scheffé
Procedure for All Contrasts
/ 146
4.5
Ranking and Selection Procedures
/ 148
4.5.1
Indifference-Zone Formulation
/148
4.5.2
Subset Selection Formulation
/ 154
4.5.3
Multiple Comparisons with the Best
/155
4.5.4
Connection between Multiple Comparisons with
Best and Selection of Best Treatment
/ 157
4.6
Chapter Summary
/ 158
Exercises
/159
5
Randomized Block Designs and Extensions
168
5.1
Randomized Block Designs
/ 169
5.1.1
Model
/ 169
5.1.2
Statistical Analysis
/ 171
5.1.3
Randomized Block Designs with Replicates
/177
5.2
Balanced Incomplete Block Designs
/180
5.2.1
Statistical Analysis
/182
5.2.2
Interblock Analysis
/ 185
5.3
Youden Square Designs
/ 188
5.3.1
Statistical Analysis
/ 189
5.4
Latin Square Designs
/ 192
5.4.1
Choosing a Latin Square
/ 192
5.4.2
Model
/ 195
5.4.3
Statistical Analysis
/ 195
5.4.4
Crossover Designs
/ 198
5.4.5
Graeco-Latin Square Designs
/ 202
5.5
Chapter Notes
/ 205
CONTENTS
5.5.1
Restriction
Error Model for Randomized Block
Designs
/ 205
5.5.2
Derivations of Formulas for BIB Design
/ 206
5.6
Chapter Summary
/211
Exercises
/212
General Factorial Experiments
224
6.1
Factorial versus One-Factor-at-a-Time Experiments
/ 225
6.2
Balanced Two-Way Layouts
/ 227
6.2.1
Summary Statistics and Graphical Plots
/ 227
6.2.2
Model
/ 230
6.2.3
Statistical Analysis
/ 231
6.2.4
Model Diagnostics
/ 235
6.2.5
Tukey's Test for Interaction for Singly Replicated
Two-Way Layouts
/ 236
6.3
Unbalanced Two-Way Layouts
/ 240
6.3.1
Statistical Analysis
/ 240
6.4
Chapter Notes
/ 245
6.4.1
Derivation of LS Estimators of Parameters for
Balanced Two-Way Layouts
/ 245
6.4.2
Derivation of ANOVA Sums of Squares and
F-Tests for Balanced Two-Way Layouts
/ 246
6.4.3
Three- and Higher Way Layouts
/ 248
6.5
Chapter Summary
/ 250
Exercises
/ 250
Two-Level Factorial Experiments
256
7.1
Estimation of Main Effects and Interactions
/ 257
7.1.1
22 Designs
/ 257
7.1.2
23 Designs
/ 261
7.1.3
V Designs
/ 266
7.2
Statistical Analysis
/ 267
7.2.1
Confidence Intervals and Hypothesis Tests
/ 267
7.2.2
Analysis of Variance
/ 268
7.2.3
Model Fitting and Diagnostics
/ 270
7.3
Single-Replicate Case
/ 272
7.3.1
Normal and Half-Normal Plots of Estimated
Effects
/ 272
7.3.2
Lenth Method
/ 278
CONTENTS
ХІ
7.3.3
Augmenting a 2P Design with Observations at the
Center Point
/ 279
7.4
2P Factorial Designs in Incomplete Blocks: Confounding of
Effects
/ 282
7.4.1
Construction of Designs
/ 282
7.4.2
Statistical Analysis
/ 286
7.5
Chapter Notes
/ 287
7.5.1
Yates
Algorithm
/ 287
7.5.2
Partial Confounding
/ 288
7.6
Chapter Summary
/ 289
Exercises
/ 290
8
Two-Level Fractional Factorial Experiments
300
8.1
2Р-Ч
Fractional Factorial Designs
/ 301
8.1.1
2p~l Fractional Factorial Design
/ 301
8.1.2
General W'4 Fractional Factorial Designs
/ 307
8.1.3
Statistical Analysis
/ 312
8.1.4
Minimum Aberration Designs
/ 316
8.2
Plackett-Burman Designs
/ 317
8.3
Hadamard
Designs
/ 323
8.4
Supersaturated Designs
/ 325
8.4.1
Construction of Supersaturated Designs
/ 325
8.4.2
Statistical Analysis
/ 327
8.5
Orthogonal Arrays
/ 329
8.6
Sequential Assemblies of Fractional Factorials
/ 333
8.6.1
Foldover of Resolution III Designs
/ 334
8.6.2
Foldover of Resolution IV Designs
/ 337
8.7
Chapter Summary
/ 338
Exercises
/ 339
9
Three-Level and Mixed-Level Factorial Experiments
351
9.1
Three-Level Full Factorial Designs
/ 351
9.1.1
Linear-Quadratic System
/ 353
9.1.2
Orthogonal Component System
/ 361
9.2
Three-Level Fractional Factorial Designs
/ 364
9.3
Mixed-Level Factorial Designs
/ 372
9.3.1
2рАч
Designs
/ 373
9.3.2
2p3« Designs
/ 378
9.4
Chapter Notes
/ 386
XU CONTENTS
9.4.1 Alternative
Derivations of Estimators of
Linear
and
Quadratic Effects
/ 386
9.5
Chapter Summary
/ 388
Exercises
/ 389
10
Experiments for Response Optimization
395
10.1
Response Surface Methodology
/ 396
10.1.1
Outline of Response Surface Methodology
/ 396
10.1.2
First-Order Experimentation Phase
/ 397
10.1.3
Second-Order Experimentation Phase
/ 402
10.2
Mixture Experiments
/412
10.2.1
Designs for Mixture Experiments
/ 414
10.2.2
Analysis of Mixture Experiments
/ 416
10.3
Taguchi Method of Quality Improvement
/ 419
10.3.1
Philosophy Underlying Taguchi Method
/ 422
10.3.2
Implementation of Taguchi Method
/ 425
10.3.3
Critique of Taguchi Method
/ 432
10.4
Chapter Summary
/ 436
Exercises
/ 437
11
Random and Mixed Crossed-Factors Experiments
448
11.1
One-Way Layouts
/ 449
11.1.1
Random-Effects Model
/ 449
11.1.2
Analysis of Variance
/ 450
11.1.3
Estimation of Variance Components
/ 452
11.2
Two-Way Layouts
/ 455
11.2.1
Random-Effects Model
/ 455
11.2.2
Mixed-Effects Model
/ 459
11.3
Three-Way Layouts
/ 464
11.3.1
Random- and Mixed-Effects Models
/ 464
11.3.2
Analysis of Variance
/ 465
11.3.3
Approximate
f
-Tests
/ 468
11.4
Chapter Notes
/ 472
11.4.1
Maximum Likelihood and Restricted Maximum
Likelihood (REML) Estimation of Variance
Components
/ 472
11.4.2
Derivations of Results for One- and Two-Way
Random-Effects Designs
/ 475
11.4.3
Relationship between Unrestricted and Restricted
Models
/ 478
CONTENTS
ХІІІ
11.5
Chapter Summary
/ 479
Exercises
/ 480
12
Nested, Crossed-Nested, and Split-Plot Experiments
487
12.1
Two-Stage Nested Designs
/ 488
12.1.1
Model
/ 488
12.1.2
Analysis of Variance
/ 489
12.2
Three-Stage Nested Designs
/ 490
12.2.1
Model
/ 491
12.2.2
Analysis of Variance
/ 492
12.3
Crossed and Nested Designs
/ 495
12.3.1
Model
/ 495
12.3.2
Analysis of Variance
/ 496
12.4
Split-Plot Designs
/ 501
12.4.1
Model
/ 504
12.4.2
Analysis of Variance
/ 505
12.4.3
Extensions of Split-Plot Designs
/ 508
12.5
Chapter Notes
/ 515
12.5.1
Derivations of E(MS) Expressions for Two-Stage
Nested Design of Section
12.1
with Both Factors
Random
/515
12.5.2
Derivations of E(MS) Expressions for Design of
Section
12.3
with Crossed and Nested Factors
/517
12.5.3
Derivations of E(MS) Expressions for Split-Plot
Design
/ 520
12.6
Chapter Summary
/ 523
Exercises
/ 524
13
Repeated Measures Experiments
536
13.1
Univariate Approach
/ 536
13.1.1
Model
/ 537
13.1.2
Univariate Analysis of Variance for
RM
Designs
/ 537
13.2
Multivariate Approach
/ 548
13.2.1
One-Way Multivariate Analysis of Variance
/ 548
13.2.2
Multivariate Analysis of Variance for
RM
Designs
/ 549
13.3
Chapter Notes
/ 555
13.3.1
Derivations of E(MS) Expressions for Repeated
Measures Design Assuming Compound Symmetry
/ 555
13.4
Chapter Summary
/558
Exercises
/ 559
XIV
CONTENTS
14.2.2
14.2.3
14.2.4
14.2.5
14
Theory of Linear Models with Fixed Effects
566
14.1
Basic Linear Model and Least Squares Estimation
/ 566
14.1.1
Geometric Interpretation of Least Squares
Estimation
/ 568
14.1.2
Least Squares Estimation in Singular Case
/ 570
14.1.3
Least Squares Estimation in Orthogonal Case
/ 572
14.2
Confidence Intervals and Hypothesis Tests
/ 573
14.2.1
Sampling Distribution of
β
I
573
Sampling Distribution of s2 I
574
Inferences on Scalar Parameters
/ 575
Inferences on Vector Parameters
/ 575
Extra Sum of Squares Method
/ 577
14.2.6
Analysis of Variance
/ 579
14.3
Power of F-Test
/ 583
14.4
Chapter Notes
/ 586
14.4.1
Proof of Theorem
14.1
(Gauss-Markov
Theorem)
/ 586
14.4.2
Proof of Theorem
14.2 / 586
14.5
Chapter Summary
/ 587
Exercises
/ 588
Appendix A Vector-Valued Random Variables and Some
Distribution Theory
595
A.
1
Mean Vector and Covariance Matrix of Random
Vector
/ 596
A.2 Covariance Matrix of Linear Transformation of
Random Vector
/ 597
A.3 Multivariate Normal Distribution
/ 598
A.4 Chi-Square, F-, and i-Distributions
/ 599
A.5 Distributions of Quadratic Forms
/ 601
A.6 Multivariate r-Distribution
/ 605
A.7 Multivariate Normal Sampling Distribution
Theory
/ 606
Appendix
В
Case Studies
608
B.I Case Study
1:
Effects of Field Strength and Flip
Angle on
MRI
Contrast
/ 608
B.I.I Introduction
/ 608
B.1.2 Design
/ 609
B.1.3 Data Analysis
/ 610
CONTENTS
XV
В.
1.4
Results
/ 612
B.2 Case Study
2:
Growing Stem Cells for Bone
Implants
/613
B.2.1 Introduction
/613
B.2.2 Design
/ 614
B.2.3 Data Analysis
/ 614
B.2.4 Results
/ 614
B.3 Case Study
3:
Router Bit Experiment
/ 619
B.3.1 Introduction
/619
B.3.2 Design
/619
B.3.3 Data Analysis
/ 623
B.3.4 Results
/ 624
Appendix
С
Statistical Tables
627
Answers to Selected Exercises
644
References
664
Index
675 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Tamhane, Ajit C. |
| author_facet | Tamhane, Ajit C. |
| author_role | aut |
| author_sort | Tamhane, Ajit C. |
| author_variant | a c t ac act |
| building | Verbundindex |
| bvnumber | BV035173734 |
| callnumber-first | Q - Science |
| callnumber-label | QA279 |
| callnumber-raw | QA279 |
| callnumber-search | QA279 |
| callnumber-sort | QA 3279 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 840 |
| ctrlnum | (OCoLC)212627345 (DE-599)BVBBV035173734 |
| dewey-full | 519.5/7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/7 |
| dewey-search | 519.5/7 |
| dewey-sort | 3519.5 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01728nam a2200433zc 4500</leader><controlfield tag="001">BV035173734</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20090825 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">081121s2009 xxud||| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2008009432</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780471750437</subfield><subfield code="c">cloth</subfield><subfield code="9">978-0-471-75043-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)212627345</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV035173734</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-578</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA279</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.5/7</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 840</subfield><subfield code="0">(DE-625)143261:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Tamhane, Ajit C.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Statistical analysis of designed experiments</subfield><subfield code="b">theory and applications</subfield><subfield code="c">Ajit C. Tamhane</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Hoboken, N.J.</subfield><subfield code="b">Wiley</subfield><subfield code="c">2009</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XXIV, 679 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Wiley series in probability and statistics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Experimental design</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Versuchsplanung</subfield><subfield code="0">(DE-588)4078859-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4123623-3</subfield><subfield code="a">Lehrbuch</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Versuchsplanung</subfield><subfield code="0">(DE-588)4078859-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/enhancements/fy0829/2008009432-d.html</subfield><subfield code="3">Publisher description</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/enhancements/fy0829/2008009432-t.html</subfield><subfield code="3">Table of contents only</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">Digitalisierung UB Bayreuth</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016980625&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016980625</subfield></datafield></record></collection> |
| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV035173734 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:55:17Z |
| indexdate | 2024-07-09T21:26:41Z |
| institution | BVB |
| isbn | 9780471750437 |
| language | English |
| lccn | 2008009432 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016980625 |
| oclc_num | 212627345 |
| open_access_boolean | |
| owner | DE-703 DE-11 DE-578 |
| owner_facet | DE-703 DE-11 DE-578 |
| physical | XXIV, 679 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Tamhane, Ajit C. Verfasser aut Statistical analysis of designed experiments theory and applications Ajit C. Tamhane Hoboken, N.J. Wiley 2009 XXIV, 679 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Includes bibliographical references and index Experimental design Versuchsplanung (DE-588)4078859-3 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Versuchsplanung (DE-588)4078859-3 s DE-604 http://www.loc.gov/catdir/enhancements/fy0829/2008009432-d.html Publisher description http://www.loc.gov/catdir/enhancements/fy0829/2008009432-t.html Table of contents only Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016980625&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tamhane, Ajit C. Statistical analysis of designed experiments theory and applications Experimental design Versuchsplanung (DE-588)4078859-3 gnd |
| subject_GND | (DE-588)4078859-3 (DE-588)4123623-3 |
| title | Statistical analysis of designed experiments theory and applications |
| title_auth | Statistical analysis of designed experiments theory and applications |
| title_exact_search | Statistical analysis of designed experiments theory and applications |
| title_exact_search_txtP | Statistical analysis of designed experiments theory and applications |
| title_full | Statistical analysis of designed experiments theory and applications Ajit C. Tamhane |
| title_fullStr | Statistical analysis of designed experiments theory and applications Ajit C. Tamhane |
| title_full_unstemmed | Statistical analysis of designed experiments theory and applications Ajit C. Tamhane |
| title_short | Statistical analysis of designed experiments |
| title_sort | statistical analysis of designed experiments theory and applications |
| title_sub | theory and applications |
| topic | Experimental design Versuchsplanung (DE-588)4078859-3 gnd |
| topic_facet | Experimental design Versuchsplanung Lehrbuch |
| url | http://www.loc.gov/catdir/enhancements/fy0829/2008009432-d.html http://www.loc.gov/catdir/enhancements/fy0829/2008009432-t.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016980625&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tamhaneajitc statisticalanalysisofdesignedexperimentstheoryandapplications |