Experimental designs using ANOVA:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Belmont, CA
Thomson, Brooks/Cole
2007
|
| Edition: | Internat. student ed. |
| Series: | Duxbury applied series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXI, 724 S. graph. Darst. |
| ISBN: | 0495110922 0534405142 |
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| 245 | 1 | 0 | |a Experimental designs using ANOVA |c Barbara G. Tabachnick ; Linda S. Fidell |
| 250 | |a Internat. student ed. | ||
| 264 | 1 | |a Belmont, CA |b Thomson, Brooks/Cole |c 2007 | |
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| 650 | 4 | |a Experimental design | |
| 650 | 4 | |a Analysis of variance | |
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| _version_ | 1804137793271627776 |
|---|---|
| adam_text | Titel: Experimental designs using ANOVA
Autor: Tabachnick, Barbara G
Jahr: 2007
Contents
Preface xix
1 Introduction 1
1.1 The Nature of Research 2
1.1.1 IVs and DVs 2
1.1.2 What Is an Experiment? 2
1.1.3 What If It Isn t an Experiment? 4
1.1.4 Relationship between Design and Analysis 5
1.1.5 Monitoring Processes to Aid in Experimental Design 6
1.2 Types of Research Designs 6
1.2.1 Randomized-Groups Designs 6
1.2.2 Repeated-Measures Designs 7
1.2.3 One- Way and Factorial Designs 8
1.2.4 Blocking Designs 9
1.2.5 Crossing and Nesting 9
1.3 Types of Treatments 11
1.3.1 Qualitative IVs 11
1.3.2 Quantitative IVs 11
vi Contents
1.4 Outcome Measures 12
1.4.1 Types of Outcome Measures 12
1.4.2 Number of Outcome Measures 13
1.5 Overview of Research Designs 13
1.5.1 Continuous Outcomes 13
1.5.2 Rank Order Outcomes 16
1.5.3 Discrete Outcomes 16
1.5.4 Time as an Outcome 17
1.6 Overview of Issues Encountered in Most Designs 17
1.6.1 Statistical Inference 17
1.6.2 Power 19
1.6.3 Effect Size 20
1.6.4 Parameter Estimates 20
1.6.5 To Test or Not to Test? 21
1.7 Generalizing Results 21
1.8 Computer Assistance 22
1.8.1 Programs for Statistical Analysis 22
1.8.2 Programs for Designing Experiments 24
1.9 Organization of the Book 24
1.10 Choosing a Design: Some Guidelines 25
1.11 Problem Sets 27
2 Organizing, Describing, and Screening Data 29
2.1 Organizing Data for a Computer 29
2.1.1 Discrete, Continuous, and Ordinal Data 30
2.1.2 Randomized-Groups Designs 31
2.1.3 Repeated-Measures Designs 32
2.2 Describing Data from One Variable 33
2.2.1 Discrete Variables 34
2.2.2 Ordinal Variables 35
2.2.3 Continuous Variables 37
Contents vii
2.3 Describing Relationships between Two Variables 53
2.3.1 Both Variables Discrete 53
2.3.2 Both Variables Continuous 56
2.3.3 One Discrete and One Continuous Variable 60
2.4 Problem Sets 67
3 Basic ANOVA: Logic of Analysis and Tests
of Assumptions 69
3.1 Introduction 69
3.2 Analysis of Variance 70
3.2.1 The General Linear Model 70
3.2.2 Generation of a Data Set 71
3.2.3 The Basic Analysis 73
3.3 The Regression Approach to ANOVA 82
3.3.1 Bivariate Regression and Basic ANOVA 82
3.3.2 Why Bother? 86
3.4 Assumptions of Analysis 86
3.4.1 Normality of Sampling Distribution ofMeans 86
3.4.2 Independence of Errors 87
3.4.3 Homogeneity of Variance 88
3.4.4 Absence of Outliers 89
3.5 Other Recurring Issues 90
3.5.1 Effect Size 90
3.5.2 Power 91
3.5.3 Comparisons 91
3.5.4 Orthogonality 92
3.5.5 Coding 92
3.5.6 Missing Values 93
3.5.7 Transformations 94
3.6 Overview of Remaining Chapters 96
3.7 Problem Sets 97
vi ii Contents
4 One-Way Randomized-Groups Analysis
of Variance, Fixed-Effects Designs 98
4.1 General Purpose and Description 98
4.2 Kinds of Research Questions 99
4.2.1 Effect of the IV 100
4.2.2 Specific Comparisons 100
4.2.3 Parameter Estimates 100
4.2.4 Effect Sizes 101
4.2.5 Power 101
4.3 Assumptions and Limitations 101
4.3.1 Theoretical Issues 101
4.3.2 Practical Issues 102
4.4 Fundamental Equations 102
4.4.1 Allocation of Cases 102
4.4.2 Partition of Variance 103
4.4.3 Traditional ANOVA Approach (Three Levels) 103
4.4.4 Regression Approach (Three Levels) 104
4.4.5 Computer Analyses of Small-Sample One-Way Design 108
4.5 Some Important Issues 111
4.5.1 Effect Size 111
4.5.2 Power and Sample Size 115
4.5.3 Unequal Sample Sizes 120
4.5.4 Homogeneity of Variance 122
4.5.5 Specific Comparisons 123
4.6 Complete Example of One-Way ANOVA 140
4.6.1 Evaluation of Assumptions 141
4.6.2 Planned Trend Analysis for One-Way Randomized-Groups Design 143
4.7 Comparison of Programs 148
4.7.1 SPSS Package 148
4.7.2 SAS System 148
4.7.3 SYSTAT System 151
4.8 Problem Sets 151
Contents ¡x
5 Factorial Randomized-Groups,
Fixed-Effects Designs 154
5.1 General Purpose and Description 154
5.2 Kinds of Research Questions 155
5.2.1 Main Effects of the IVs 155
5.2.2 Effects of Interactions among IVs 156
5.2.3 Specific Comparisons 156
5.2.4 Parameter Estimates 157
5.2.5 Effect Sizes 157
5.2.6 Power 157
5.3 Assumptions and Limitations 158
5.3.1 Theoretical Issues 158
5.3.2 Practical Issues 158
5.4 Fundamental Equations 159
5.4.1 Allocation of Cases 160
5.4.2 Partition of Sources of Variance 161
5.4.3 Traditional ANOVA Approach (3 X 3) 163
5.4.4 Regression Approach (3 X 3) 165
5.4.5 Computer A nalyses of Small-Sample Factorial
Design 170
5.5 Other Types of Randomized-Groups Designs 174
5.5.1 Higher-Order Factorial Designs 175
5.5.2 Factorial Design with a Single Control 180
5.6 Some Important Issues 181
5.6.1 Interpreting Interactions 181
5.6.2 Effect Size 187
5.6.3 Power and Sample Size 190
5.6.4 Specific Comparisons 192
5.6.5 Unequal Sample Sizes 216
5.7 Complete Example of Two-Way Randomized-Groups ANOVA 221
5.7.1 Evaluation of Assumptions 221
5.7.2 Randomized-Groups Analysis of Variance 225
X Contents
5.8 Comparison of Programs 236
5.8.1 SPSS Package 236
5.8.2 SAS System 239
5.8.3 SYSTATSystem 239
5.9 Problem Sets 240
6 Repeated-Measures Designs 242
6.1 General Purpose and Description 242
6.2 Kinds of Research Questions 243
6.2.1 Effect of the IVs 244
6.2.2 Effect of Interactions among IVs 244
6.2.3 Parameter Estimates 244
6.2.4 Effect Sizes 244
6.2.5 Power 245
6.2.6 Specific Comparisons 245
6.3 Assumptions and Limitations 245
6.3.1 Theoretical Issues 245
6.3.2 Practical Issues 246
6.4 Fundamental Equations 249
6.4.1 One-Way Repeated-Measures ANOVA 249
6.4.2 Factorial Repeated-Measures Designs 261
6.5 Types of Repeated-Measures Designs 280
6.5.1 Time as a Variable 280
6.5.2 Simultaneous Repeated Measures 281
6.5.3 Matched Randomized Blocks 281
6.6 Some Important Issues 282
6.6.1 Carryover Effects: Control of Extraneous Variables 282
6.6.2 Assumptions of Analysis: Independence of Errors, Sphericity,
Additivity, and Compound Symmetry 284
6.6.3 Power, Sample Size, and Relative Efficiency 288
6.6.4 Effect Size 289
6.6.5 Missing Data 291
6.6.6 Specific Comparisons 292
Contents x¡
6.7 Complete Example of Two-Way Repeated-Measures ANOVA 302
6.7.1 Evaluation of Assumptions 302
6.7.2 Planned Trend Analysis of Two-Way Repeated-Measures
Design 304
6.8 Comparison of Programs 312
6.8.1 SPSS Package 312
6.8.2 SAS System 313
6.8.3 SYSTATSystem 313
6.9 Problem Sets 314
7 Mixed Randomized-Repeated Designs 316
7.1 General Purpose and Description 316
7.2 Kinds of Research Questions 318
7.2.1 Effects of the IVs 318
7.2.2 Effects of Interactions among IVs 318
7.2.3 Parameter Estimates 318
7.2.4 Effect Sizes 318
7.2.5 Power 318
7.2.6 Specific Comparisons 319
7.3 Assumptions and Limitations 319
7.3.1 Theoretical Issues 319
7.3.2 Practical Issues 319
7.4 Fundamental Equations 321
7.4.1 Allocation of Cases 321
7.4.2 Partition of Sources of Variance 322
7.4.3 Traditional ANOVA for the Mixed Design 324
7.4.4 Regression Approach to the Mixed Design 32 7
7.4.5 Computer Analyses of Small-Sample Mixed Design 332
7.5 Types of Mixed Designs 338
7.5.1 The Pretest-Posttest Design 338
7.5.2 Expanding Mixed Designs 338
Contents
7.6 Some Important Issues 340
7.6.1 Comparisons on the Margins 340
7.6.2 Simple Main Effects Analysis 345
7.6.3 Simple Comparisons 348
7.6.4 Interaction Contrasts 349
7.6.5 Comparisons through the Regression Approach 351
7.7 Complete Example of Mixed Randomized-Repeated ANOVA
7.7.1 Evaluation of Assumptions 356
7.7.2 Three- Way Mixed Randomized-Repeated ANOVA 358
7.8 Comparison of Programs 369
7.8.1 SPSSPackage 369
7.8.2 SAS System 370
7.8.3 SYSTATSystem 370
7.9 Putting It All Together for Factorial Designs 371
7.9.1 Allocation of Cases 371
7.9.2 Assumptions of Analysis 371
7.9.3 Error Terms 371
7.9.4 Setup for Regression 373
7.9.5 Developing Computational Equations from Degrees
of Freedom 376
7.10 Problem Sets 377
8 Analysis of Covariance 379
8.1 General Purpose and Description 379
8.2 Kinds of Research Questions 382
8.2.1 Effect of the IV(s) 382
8.2.2 Effect of Interactions among IVs 383
8.2.3 Effects of Covariates 383
8.2.4 Parameter Estimates 383
8.2.5 Effect Sizes 383
8.2.6 Power 384
8.2.7 Specific Comparisons 384
Contents x¡¡¡
8.3 Assumptions and Limitations 384
8.3.1 Theoretical Issues 384
8.3.2 Practical Issues 385
8.4 Fundamental Equations 390
8.4.1 Allocation of Cases to Conditions 390
8.4.2 Partition of Sources of Variance 390
8.4.3 Traditional Approach with Three Levels and One Covariate 392
8.4.4 Computer Analyses of Small-Sample ANCOVA 394
8.4.5 Computer Analysis Using Regression Approach to ANCOVA 399
8.5 Types of Designs Using Covariates 401
8.5.1 Randomized-Groups Factorial 401
8.5.2 Repeated Measures 402
8.6 Some Important Issues 412
8.6.1 Multiple Covariates 412
8.6.2 Test of Homogeneity of Regression 418
8.6.3 Effect Size 423
8.6.4 Power 424
8.6.5 A djusted Means 424
8.6.6 Specific Comparisons 426
8.6.7 Alternatives to ANCOVA 430
8.7 Complete Examples of Analysis of Covariance 432
8.7.1 One- Way Analysis of Covariance with Five Levels and One Covariate 432
8.7.2 Mixed Randomized-Groups and Repeated-Measures Analysis
of Covariance 441
8.8 Comparison of Programs 473
8.8.1 SPSS Package 473
8.8.2 SAS System 473
8.8.3 SYSTATSystem 475
8.9 Problem Sets 475
9 Latin-Square Designs 478
9.1 General Purpose and Description 478
xiv Contents
9.2 Kinds of Research Questions 481
9.2.1 Effects of the IV(s) 481
9.2.2 Interactions among IVs 482
9.2.3 Parameter Estimates 482
9.2.4 Effect Sizes and Power 482
9.2.5 Specific Comparisons 483
9.3 Assumptions and Limitations 483
9.3.1 Theoretical Issues 483
9.3.2 Practical Issues 483
9.4 Fundamental Equations 485
9.4.1 Allocation of Cases 486
9.4.2 Partition of Sources of Variance 486
9.4.3 Traditional ANOVA Approach to 3 X 3 X 3 Latin Square 488
9.4.4 Regression Approach to 3 X 3 X 3 Latin Square 490
9.4.5 Computer Analyses of Small-Sample Latin Square
Example 492
9.5 Types of Latin-Square Designs 496
9.5.1 Replicated Randomized-Groups Designs 497
9.5.2 Replicated Repeated-Measures Designs 501
9.5.3 Less Commonly Encountered Designs 512
9.6 Some Important Issues 518
9.6.1 Sphericity in Repeated-Measures Designs 519
9.6.2 Choosing a Latin Square 521
9.6.3 Power, Effect Size, and Relative Efficiency 522
9.6.4 Specific Comparisons 525
9.6.5 Missing Data 527
9.7 Complete Examples of Latin-Square ANOVA 528
9.7.1 Complete Example of 4 X 4 X 4 Randomized-Groups
Latin-Square Analysis 528
9.7.2 Complete Example of a Repeated-Measures Crossover Design
with Multiple Trials 537
9.8 Comparison of Programs 548
9.8.1 SPSS Package 549
Contents xv
9.8.2 SAS System 549
9.8.3 SYSTATSystem 549
9.9 Problem Sets 549
10 Screening and Other Incomplete Designs 552
10.1 General Purpose and Description 552
10.2 Kinds of Research Questions 554
10.2.1 Effects of the IV(s) 554
10.2.2 Effects ofInteractions among IV(s) 554
10.2.3 Parameter Estimates 554
10.2.4 Effect Sizes and Power 555
10.2.5 Specific Comparisons 555
10.3 Assumptions and Limitations 555
10.3.1 Theoretical Issues 555
10.3.2 Practical Issues 556
10.4 Fundamental Equations 557
10.4.1 Allocation of Cases 558
10.4.2 Partition of Sources of Variance 559
10.4.3 Regression Approach to a 25 Half-Factorial ANOVA 560
10.4.4 Computer Analyses of the Small-Sample 25 1 Half-Factorial ANOVA 565
10.5 Types of Screening and Other Incomplete Designs 569
10.5.1 Resolution of Incomplete Designs 569
10.5.2 Fractional-Factorial Designs 569
10.5.3 Plackett-Burman Designs 575
10.5.4 Taguchi Designs 577
10.5.5 Response-Surface Methodology 583
10.5.6 Optimal Designs 595
10.6 Some Important Issues 598
10.6.1 Generating Screening and Other Incomplete Designs 598
10.6.2 Choosing among Screening and Other Incomplete Designs 603
10.7 Complete Example of a Central-Composite Design 605
10.7.1 Generating the Design 606
xvi Contents
10.7.2 Assumptions and Limitations 606
10.7.3 Three-Factor Central-Composite Design 609
10.8 Comparisons of Programs 613
10.8.1 SASADX 616
10.8.2 NCSS Design of Experiments 617
10.9 Problem Sets 617
11 Analysis of Variance with Random Effects 620
11.1 General Purpose and Description 620
11.2 Kinds of Research Questions 623
11.2.1 Effect of the IV(s) 623
11.2.2 Effects of Interactions among IVs 623
11.2.3 Specific Comparisons 623
11.2.4 Parameter Estimates 623
11.2.5 Effect Sizes 624
11.2.6 Power 624
11.3 Assumptions and Limitations 625
11.3.1 Theoretical Issues 625
11.3.2 Practical Issues 626
11.4 Fundamental Equations 627
11.4.1 Allocation of Cases 627
11.4.2 Partition of Sources of Variance 628
11.4.3 Traditional ANOVA Approach (One Treatment Factor and
One Level of Nesting) 630
11.4.4 Regression Approach (One Treatment Factor and
One Level of Nesting) 632
11.4.5 Computer Analyses of Small-Sample Nested Example 632
11.5 Types of Designs with Random Effects 638
11.5.1 Nested Designs 638
11.5.2 One-Way Random-Effects Design 644
11.5.3 Factorial Random-Effects Designs 644
11.5.4 Mixed Fixed-Random Designs 648
Contents xvii
11.6 Some Important Issues 656
11.6.1 Error Terms in Random-Effects ANOVA 65 7
11.6.2 Alternative Strategies to ANOVA 662
11.6.3 Trend Analysis with Unequal Spacing 664
11.6.4 Homogeneity of Covariance 667
11.6.5 Effect Size 668
11.7 Complete Example of Random-Effects Anova 668
11.7.1 Evaluation of Assumptions 669
11.7.2 ANOVA for Doubly Nested Design 676
11.8 Comparison of Programs 680
11.8.1 SAS System 680
11.8.2 SPSS Package 682
11.8.3 SYSTATSystem 683
11.9 Problem Sets 683
Appendix A Statistical Tables 685
A.1 Critical Values of F Distribution 686
A.2 Critical Values of y} Distribution 693
A.3 Critical Values of Studentized Range Statistic Distribution 694
A.4 Critical Values of Dunnett s ¿/-Statistic in Comparing Treatment Means
with a Control (1-sided test) 696
A.5 Coefficients of Orthogonal Polynomials 698
A.6 Critical Values of Fmax Distribution 699
Appendix B Research Designs for Complete Examples 700
B.1 Facets in Fly s Eyes 700
B.2 Bonding Strength of Periodontal Dressings 701
B.3 Reaction Time to Identify Figures 702
B.4 Auto Pollution Filter Noise 702
B.5 Wear Testing of Fabric Samples 703
B.6 Odors and Performance 703
B.7 Processing Time for ANOVA 704
B.8 Nambeware Polishing Times 704
B.9 Chest Deceleration Injuries in Automobile Crashes
B. 10 Fat Content of Eggs 705
References 706
Index 711
|
| adam_txt |
Titel: Experimental designs using ANOVA
Autor: Tabachnick, Barbara G
Jahr: 2007
Contents
Preface xix
1 Introduction 1
1.1 The Nature of Research 2
1.1.1 IVs and DVs 2
1.1.2 What Is an Experiment? 2
1.1.3 What If It Isn't an Experiment? 4
1.1.4 Relationship between Design and Analysis 5
1.1.5 Monitoring Processes to Aid in Experimental Design 6
1.2 Types of Research Designs 6
1.2.1 Randomized-Groups Designs 6
1.2.2 Repeated-Measures Designs 7
1.2.3 One- Way and Factorial Designs 8
1.2.4 Blocking Designs 9
1.2.5 Crossing and Nesting 9
1.3 Types of Treatments 11
1.3.1 Qualitative IVs 11
1.3.2 Quantitative IVs 11
vi Contents
1.4 Outcome Measures 12
1.4.1 Types of Outcome Measures 12
1.4.2 Number of Outcome Measures 13
1.5 Overview of Research Designs 13
1.5.1 Continuous Outcomes 13
1.5.2 Rank Order Outcomes 16
1.5.3 Discrete Outcomes 16
1.5.4 Time as an Outcome 17
1.6 Overview of Issues Encountered in Most Designs 17
1.6.1 Statistical Inference 17
1.6.2 Power 19
1.6.3 Effect Size 20
1.6.4 Parameter Estimates 20
1.6.5 To Test or Not to Test? 21
1.7 Generalizing Results 21
1.8 Computer Assistance 22
1.8.1 Programs for Statistical Analysis 22
1.8.2 Programs for Designing Experiments 24
1.9 Organization of the Book 24
1.10 Choosing a Design: Some Guidelines 25
1.11 Problem Sets 27
2 Organizing, Describing, and Screening Data 29
2.1 Organizing Data for a Computer 29
2.1.1 Discrete, Continuous, and Ordinal Data 30
2.1.2 Randomized-Groups Designs 31
2.1.3 Repeated-Measures Designs 32
2.2 Describing Data from One Variable 33
2.2.1 Discrete Variables 34
2.2.2 Ordinal Variables 35
2.2.3 Continuous Variables 37
Contents vii
2.3 Describing Relationships between Two Variables 53
2.3.1 Both Variables Discrete 53
2.3.2 Both Variables Continuous 56
2.3.3 One Discrete and One Continuous Variable 60
2.4 Problem Sets 67
3 Basic ANOVA: Logic of Analysis and Tests
of Assumptions 69
3.1 Introduction 69
3.2 Analysis of Variance 70
3.2.1 The General Linear Model 70
3.2.2 Generation of a Data Set 71
3.2.3 The Basic Analysis 73
3.3 The Regression Approach to ANOVA 82
3.3.1 Bivariate Regression and Basic ANOVA 82
3.3.2 Why Bother? 86
3.4 Assumptions of Analysis 86
3.4.1 Normality of Sampling Distribution ofMeans 86
3.4.2 Independence of Errors 87
3.4.3 Homogeneity of Variance 88
3.4.4 Absence of Outliers 89
3.5 Other Recurring Issues 90
3.5.1 Effect Size 90
3.5.2 Power 91
3.5.3 Comparisons 91
3.5.4 Orthogonality 92
3.5.5 Coding 92
3.5.6 Missing Values 93
3.5.7 Transformations 94
3.6 Overview of Remaining Chapters 96
3.7 Problem Sets 97
vi'ii Contents
4 One-Way Randomized-Groups Analysis
of Variance, Fixed-Effects Designs 98
4.1 General Purpose and Description 98
4.2 Kinds of Research Questions 99
4.2.1 Effect of the IV 100
4.2.2 Specific Comparisons 100
4.2.3 Parameter Estimates 100
4.2.4 Effect Sizes 101
4.2.5 Power 101
4.3 Assumptions and Limitations 101
4.3.1 Theoretical Issues 101
4.3.2 Practical Issues 102
4.4 Fundamental Equations 102
4.4.1 Allocation of Cases 102
4.4.2 Partition of Variance 103
4.4.3 Traditional ANOVA Approach (Three Levels) 103
4.4.4 Regression Approach (Three Levels) 104
4.4.5 Computer Analyses of Small-Sample One-Way Design 108
4.5 Some Important Issues 111
4.5.1 Effect Size 111
4.5.2 Power and Sample Size 115
4.5.3 Unequal Sample Sizes 120
4.5.4 Homogeneity of Variance 122
4.5.5 Specific Comparisons 123
4.6 Complete Example of One-Way ANOVA 140
4.6.1 Evaluation of Assumptions 141
4.6.2 Planned Trend Analysis for One-Way Randomized-Groups Design 143
4.7 Comparison of Programs 148
4.7.1 SPSS Package 148
4.7.2 SAS System 148
4.7.3 SYSTAT System 151
4.8 Problem Sets 151
Contents ¡x
5 Factorial Randomized-Groups,
Fixed-Effects Designs 154
5.1 General Purpose and Description 154
5.2 Kinds of Research Questions 155
5.2.1 Main Effects of the IVs 155
5.2.2 Effects of Interactions among IVs 156
5.2.3 Specific Comparisons 156
5.2.4 Parameter Estimates 157
5.2.5 Effect Sizes 157
5.2.6 Power 157
5.3 Assumptions and Limitations 158
5.3.1 Theoretical Issues 158
5.3.2 Practical Issues 158
5.4 Fundamental Equations 159
5.4.1 Allocation of Cases 160
5.4.2 Partition of Sources of Variance 161
5.4.3 Traditional ANOVA Approach (3 X 3) 163
5.4.4 Regression Approach (3 X 3) 165
5.4.5 Computer A nalyses of Small-Sample Factorial
Design 170
5.5 Other Types of Randomized-Groups Designs 174
5.5.1 Higher-Order Factorial Designs 175
5.5.2 Factorial Design with a Single Control 180
5.6 Some Important Issues 181
5.6.1 Interpreting Interactions 181
5.6.2 Effect Size 187
5.6.3 Power and Sample Size 190
5.6.4 Specific Comparisons 192
5.6.5 Unequal Sample Sizes 216
5.7 Complete Example of Two-Way Randomized-Groups ANOVA 221
5.7.1 Evaluation of Assumptions 221
5.7.2 Randomized-Groups Analysis of Variance 225
X Contents
5.8 Comparison of Programs 236
5.8.1 SPSS Package 236
5.8.2 SAS System 239
5.8.3 SYSTATSystem 239
5.9 Problem Sets 240
6 Repeated-Measures Designs 242
6.1 General Purpose and Description 242
6.2 Kinds of Research Questions 243
6.2.1 Effect of the IVs 244
6.2.2 Effect of Interactions among IVs 244
6.2.3 Parameter Estimates 244
6.2.4 Effect Sizes 244
6.2.5 Power 245
6.2.6 Specific Comparisons 245
6.3 Assumptions and Limitations 245
6.3.1 Theoretical Issues 245
6.3.2 Practical Issues 246
6.4 Fundamental Equations 249
6.4.1 One-Way Repeated-Measures ANOVA 249
6.4.2 Factorial Repeated-Measures Designs 261
6.5 Types of Repeated-Measures Designs 280
6.5.1 Time as a Variable 280
6.5.2 Simultaneous Repeated Measures 281
6.5.3 Matched Randomized Blocks 281
6.6 Some Important Issues 282
6.6.1 Carryover Effects: Control of Extraneous Variables 282
6.6.2 Assumptions of Analysis: Independence of Errors, Sphericity,
Additivity, and Compound Symmetry 284
6.6.3 Power, Sample Size, and Relative Efficiency 288
6.6.4 Effect Size 289
6.6.5 Missing Data 291
6.6.6 Specific Comparisons 292
Contents x¡
6.7 Complete Example of Two-Way Repeated-Measures ANOVA 302
6.7.1 Evaluation of Assumptions 302
6.7.2 Planned Trend Analysis of Two-Way Repeated-Measures
Design 304
6.8 Comparison of Programs 312
6.8.1 SPSS Package 312
6.8.2 SAS System 313
6.8.3 SYSTATSystem 313
6.9 Problem Sets 314
7 Mixed Randomized-Repeated Designs 316
7.1 General Purpose and Description 316
7.2 Kinds of Research Questions 318
7.2.1 Effects of the IVs 318
7.2.2 Effects of Interactions among IVs 318
7.2.3 Parameter Estimates 318
7.2.4 Effect Sizes 318
7.2.5 Power 318
7.2.6 Specific Comparisons 319
7.3 Assumptions and Limitations 319
7.3.1 Theoretical Issues 319
7.3.2 Practical Issues 319
7.4 Fundamental Equations 321
7.4.1 Allocation of Cases 321
7.4.2 Partition of Sources of Variance 322
7.4.3 Traditional ANOVA for the Mixed Design 324
7.4.4 Regression Approach to the Mixed Design 32 7
7.4.5 Computer Analyses of Small-Sample Mixed Design 332
7.5 Types of Mixed Designs 338
7.5.1 The Pretest-Posttest Design 338
7.5.2 Expanding Mixed Designs 338
Contents
7.6 Some Important Issues 340
7.6.1 Comparisons on the Margins 340
7.6.2 Simple Main Effects Analysis 345
7.6.3 Simple Comparisons 348
7.6.4 Interaction Contrasts 349
7.6.5 Comparisons through the Regression Approach 351
7.7 Complete Example of Mixed Randomized-Repeated ANOVA
7.7.1 Evaluation of Assumptions 356
7.7.2 Three- Way Mixed Randomized-Repeated ANOVA 358
7.8 Comparison of Programs 369
7.8.1 SPSSPackage 369
7.8.2 SAS System 370
7.8.3 SYSTATSystem 370
7.9 Putting It All Together for Factorial Designs 371
7.9.1 Allocation of Cases 371
7.9.2 Assumptions of Analysis 371
7.9.3 Error Terms 371
7.9.4 Setup for Regression 373
7.9.5 Developing Computational Equations from Degrees
of Freedom 376
7.10 Problem Sets 377
8 Analysis of Covariance 379
8.1 General Purpose and Description 379
8.2 Kinds of Research Questions 382
8.2.1 Effect of the IV(s) 382
8.2.2 Effect of Interactions among IVs 383
8.2.3 Effects of Covariates 383
8.2.4 Parameter Estimates 383
8.2.5 Effect Sizes 383
8.2.6 Power 384
8.2.7 Specific Comparisons 384
Contents x¡¡¡
8.3 Assumptions and Limitations 384
8.3.1 Theoretical Issues 384
8.3.2 Practical Issues 385
8.4 Fundamental Equations 390
8.4.1 Allocation of Cases to Conditions 390
8.4.2 Partition of Sources of Variance 390
8.4.3 Traditional Approach with Three Levels and One Covariate 392
8.4.4 Computer Analyses of Small-Sample ANCOVA 394
8.4.5 Computer Analysis Using Regression Approach to ANCOVA 399
8.5 Types of Designs Using Covariates 401
8.5.1 Randomized-Groups Factorial 401
8.5.2 Repeated Measures 402
8.6 Some Important Issues 412
8.6.1 Multiple Covariates 412
8.6.2 Test of Homogeneity of Regression 418
8.6.3 Effect Size 423
8.6.4 Power 424
8.6.5 A djusted Means 424
8.6.6 Specific Comparisons 426
8.6.7 Alternatives to ANCOVA 430
8.7 Complete Examples of Analysis of Covariance 432
8.7.1 One- Way Analysis of Covariance with Five Levels and One Covariate 432
8.7.2 Mixed Randomized-Groups and Repeated-Measures Analysis
of Covariance 441
8.8 Comparison of Programs 473
8.8.1 SPSS Package 473
8.8.2 SAS System 473
8.8.3 SYSTATSystem 475
8.9 Problem Sets 475
9 Latin-Square Designs 478
9.1 General Purpose and Description 478
xiv Contents
9.2 Kinds of Research Questions 481
9.2.1 Effects of the IV(s) 481
9.2.2 Interactions among IVs 482
9.2.3 Parameter Estimates 482
9.2.4 Effect Sizes and Power 482
9.2.5 Specific Comparisons 483
9.3 Assumptions and Limitations 483
9.3.1 Theoretical Issues 483
9.3.2 Practical Issues 483
9.4 Fundamental Equations 485
9.4.1 Allocation of Cases 486
9.4.2 Partition of Sources of Variance 486
9.4.3 Traditional ANOVA Approach to 3 X 3 X 3 Latin Square 488
9.4.4 Regression Approach to 3 X 3 X 3 Latin Square 490
9.4.5 Computer Analyses of Small-Sample Latin Square
Example 492
9.5 Types of Latin-Square Designs 496
9.5.1 Replicated Randomized-Groups Designs 497
9.5.2 Replicated Repeated-Measures Designs 501
9.5.3 Less Commonly Encountered Designs 512
9.6 Some Important Issues 518
9.6.1 Sphericity in Repeated-Measures Designs 519
9.6.2 Choosing a Latin Square 521
9.6.3 Power, Effect Size, and Relative Efficiency 522
9.6.4 Specific Comparisons 525
9.6.5 Missing Data 527
9.7 Complete Examples of Latin-Square ANOVA 528
9.7.1 Complete Example of 4 X 4 X 4 Randomized-Groups
Latin-Square Analysis 528
9.7.2 Complete Example of a Repeated-Measures Crossover Design
with Multiple Trials 537
9.8 Comparison of Programs 548
9.8.1 SPSS Package 549
Contents xv
9.8.2 SAS System 549
9.8.3 SYSTATSystem 549
9.9 Problem Sets 549
10 Screening and Other Incomplete Designs 552
10.1 General Purpose and Description 552
10.2 Kinds of Research Questions 554
10.2.1 Effects of the IV(s) 554
10.2.2 Effects ofInteractions among IV(s) 554
10.2.3 Parameter Estimates 554
10.2.4 Effect Sizes and Power 555
10.2.5 Specific Comparisons 555
10.3 Assumptions and Limitations 555
10.3.1 Theoretical Issues 555
10.3.2 Practical Issues 556
10.4 Fundamental Equations 557
10.4.1 Allocation of Cases 558
10.4.2 Partition of Sources of Variance 559
10.4.3 Regression Approach to a 25 Half-Factorial ANOVA 560
10.4.4 Computer Analyses of the Small-Sample 25"1 Half-Factorial ANOVA 565
10.5 Types of Screening and Other Incomplete Designs 569
10.5.1 Resolution of Incomplete Designs 569
10.5.2 Fractional-Factorial Designs 569
10.5.3 Plackett-Burman Designs 575
10.5.4 Taguchi Designs 577
10.5.5 Response-Surface Methodology 583
10.5.6 Optimal Designs 595
10.6 Some Important Issues 598
10.6.1 Generating Screening and Other Incomplete Designs 598
10.6.2 Choosing among Screening and Other Incomplete Designs 603
10.7 Complete Example of a Central-Composite Design 605
10.7.1 Generating the Design 606
xvi Contents
10.7.2 Assumptions and Limitations 606
10.7.3 Three-Factor Central-Composite Design 609
10.8 Comparisons of Programs 613
10.8.1 SASADX 616
10.8.2 NCSS Design of Experiments 617
10.9 Problem Sets 617
11 Analysis of Variance with Random Effects 620
11.1 General Purpose and Description 620
11.2 Kinds of Research Questions 623
11.2.1 Effect of the IV(s) 623
11.2.2 Effects of Interactions among IVs 623
11.2.3 Specific Comparisons 623
11.2.4 Parameter Estimates 623
11.2.5 Effect Sizes 624
11.2.6 Power 624
11.3 Assumptions and Limitations 625
11.3.1 Theoretical Issues 625
11.3.2 Practical Issues 626
11.4 Fundamental Equations 627
11.4.1 Allocation of Cases 627
11.4.2 Partition of Sources of Variance 628
11.4.3 Traditional ANOVA Approach (One Treatment Factor and
One Level of Nesting) 630
11.4.4 Regression Approach (One Treatment Factor and
One Level of Nesting) 632
11.4.5 Computer Analyses of Small-Sample Nested Example 632
11.5 Types of Designs with Random Effects 638
11.5.1 Nested Designs 638
11.5.2 One-Way Random-Effects Design 644
11.5.3 Factorial Random-Effects Designs 644
11.5.4 Mixed Fixed-Random Designs 648
Contents xvii
11.6 Some Important Issues 656
11.6.1 Error Terms in Random-Effects ANOVA 65 7
11.6.2 Alternative Strategies to ANOVA 662
11.6.3 Trend Analysis with Unequal Spacing 664
11.6.4 Homogeneity of Covariance 667
11.6.5 Effect Size 668
11.7 Complete Example of Random-Effects Anova 668
11.7.1 Evaluation of Assumptions 669
11.7.2 ANOVA for Doubly Nested Design 676
11.8 Comparison of Programs 680
11.8.1 SAS System 680
11.8.2 SPSS Package 682
11.8.3 SYSTATSystem 683
11.9 Problem Sets 683
Appendix A Statistical Tables 685
A.1 Critical Values of F Distribution 686
A.2 Critical Values of y} Distribution 693
A.3 Critical Values of Studentized Range Statistic Distribution 694
A.4 Critical Values of Dunnett's ¿/-Statistic in Comparing Treatment Means
with a Control (1-sided test) 696
A.5 Coefficients of Orthogonal Polynomials 698
A.6 Critical Values of Fmax Distribution 699
Appendix B Research Designs for Complete Examples 700
B.1 Facets in Fly's Eyes 700
B.2 Bonding Strength of Periodontal Dressings 701
B.3 Reaction Time to Identify Figures 702
B.4 Auto Pollution Filter Noise 702
B.5 Wear Testing of Fabric Samples 703
B.6 Odors and Performance 703
B.7 Processing Time for ANOVA 704
B.8 Nambeware Polishing Times 704
B.9 Chest Deceleration Injuries in Automobile Crashes
B. 10 Fat Content of Eggs 705
References 706
Index 711 |
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| author | Tabachnick, Barbara G. 1936- Fidell, Linda S. 1942- |
| author_GND | (DE-588)131432389 (DE-588)132341697 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | CM 4000 |
| ctrlnum | (OCoLC)613058793 (DE-599)BVBBV023407395 |
| discipline | Psychologie |
| discipline_str_mv | Psychologie |
| edition | Internat. student ed. |
| format | Book |
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| genre | Lehrbuch swd |
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| id | DE-604.BV023407395 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:26:06Z |
| indexdate | 2024-07-09T21:17:56Z |
| institution | BVB |
| isbn | 0495110922 0534405142 |
| language | English |
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| spelling | Tabachnick, Barbara G. 1936- Verfasser (DE-588)131432389 aut Experimental designs using ANOVA Barbara G. Tabachnick ; Linda S. Fidell Internat. student ed. Belmont, CA Thomson, Brooks/Cole 2007 XXI, 724 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Duxbury applied series Varianzanalyse swd Versuchsplanung swd Experimental design Analysis of variance Lehrbuch swd Fidell, Linda S. 1942- Verfasser (DE-588)132341697 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016590066&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tabachnick, Barbara G. 1936- Fidell, Linda S. 1942- Experimental designs using ANOVA Varianzanalyse swd Versuchsplanung swd Experimental design Analysis of variance |
| title | Experimental designs using ANOVA |
| title_auth | Experimental designs using ANOVA |
| title_exact_search | Experimental designs using ANOVA |
| title_exact_search_txtP | Experimental designs using ANOVA |
| title_full | Experimental designs using ANOVA Barbara G. Tabachnick ; Linda S. Fidell |
| title_fullStr | Experimental designs using ANOVA Barbara G. Tabachnick ; Linda S. Fidell |
| title_full_unstemmed | Experimental designs using ANOVA Barbara G. Tabachnick ; Linda S. Fidell |
| title_short | Experimental designs using ANOVA |
| title_sort | experimental designs using anova |
| topic | Varianzanalyse swd Versuchsplanung swd Experimental design Analysis of variance |
| topic_facet | Varianzanalyse Versuchsplanung Experimental design Analysis of variance Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016590066&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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