Statistical principles in experimental design:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a].
McGraw-Hill
1991
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | McGraw Hill series in psychology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 1057 S. graph. Darst. |
| ISBN: | 0070709823 |
Internformat
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| 100 | 1 | |a Winer, Ben James |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Statistical principles in experimental design |c B. J. Winer ; Donald R. Brown ; Kenneth M. Michels |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a New York [u.a]. |b McGraw-Hill |c 1991 | |
| 300 | |a XIII, 1057 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804122902434414592 |
|---|---|
| adam_text | CONTENTS
Preface »
1 Introduction to Design l
1.1 Introduction 1
1.2 The Control of Independent, Dependent, and Supplementary Variables 2
1.3 Experimental Design Basics 6
1.4 Summary 10
2 Principles of Estimation and Inference:
Means and Variances 12
2.1 Basic Terminology in Sampling 12
2.2 Basic Terminology in Statistical Estimation 13
2.3 Basic Terminology in Testing Statistical Hypotheses 17
2.4 Variables with Normal Distributions 20
2.5 Other Distributions—Chi Square, t, and F 28
2.6 Inferences Concerning Means 35
2.7 Inferences Concerning Pairs of Means 51
3 Design and Analysis of Single Factor Experiments:
Completely Randomized Design 74
3.1 Introduction 74
3.2 Definitions and Numerical Example 74
3.3 Structural Model: Model I (Fixed Constants) 82
3.4 Methods of Deriving Estimates and Their Expected Values: Model I 89
3.5 Structural Model—Model II (Variance Component Model) 92
3.6 Analysis of Variance Assumptions 100
3.7 Transformations 110
3.8 Unequal Sample Sizes 110
3.9 Power, Treatment Effect Size, and the Determination of Sample Size 120
3.10 Comparisons Among Treatment Means 140
vii
viii contents
3.11 Methods of Error Control for Sets of Multiple Comparisons 153
3.12 Comparing Comparison Methods 195
3.13 Treatment Magnitude—Dependent Variable Relationships:
Trend Analysis and Strength of Association 198
3.14 Randomized Complete Block Designs 210
3.15 Exercises 216
4 Single Factor Experiments Having Repeated
Measures on the Same Elements 220
4.1 Introduction 220
4.2 Notation and Computational Procedures 222
4.3 Numerical Example 228
4.4 Analysis of Variance Assumptions for Repeated Measures Designs 239
4.5 Statistical Models and the Assumptions 261
4.6 Measures of Association and Power 274
4.7 Hotelling s T2 Multivariate Analysis of Data That Do Not Meet the
Circularity Assumption 278
4.8 Topics Closely Related to Repeated Measures Anov 281
4.9 Exercises 282
5 Design and Analysis of Factorial Experiments:
Completely Randomized Designs 284
5.1 General Purpose 284
5.2 Terminology and Notation 286
5.3 Structural Model 291
5.4 Estimating Elements of the Model 298
5.5 Principles for Constructing F Ratios 311
5.6 Higher Order Factorial Experiments 313
5.7 Estimation and Tests of Significance for Three Factor Experiments 323
5.8 Simple Effects and Their Tests 326
5.9 Geometric Interpretation of Higher Order Interactions 333
5.10 Individual Comparisons 342
5.11 Partition of Main Effects and Interaction into Trend Components 348
5.12 The Case n = 1 and a Test for Nonadditivity 351
5.13 The Choice of a Scale of Measurement and Transformations 354
5.14 Nested Factors (Hierarchal Designs) 358
5.15 Split Plot Designs 365
5.16 Rules for Deriving the Expected Values of Mean Squares 369
5.17 Quasi F Ratios 374
5.18 Preliminary Tests on the Model and Pooling Procedures 377
5.19 Replicated Experiments 382
5.20 Unequal Cell Frequencies 385
5.21 Estimation of the Magnitude of Experimental Effects and Statistical
Power 405
5.22 Exercises 416
CONTENTS IX
6 Factorial Experiments—Computational
Procedures and Numerical Examples 419
6.1 General Purpose 419
6.2 p xq Factorial Experiment Having n Observations Per Cell 419
6.3 p x q Factorial Experiment—Unequal Cell Frequencies 438
6.4 Effect of Scale Measurement on Interaction 442
6.5 p x q x r Factorial Experiment Having n Observations Per Cell 445
6.6 Computational Procedures for Nested Factors 456
6.7 Factorial Experiment with a Single Control Group 460
6.8 Test for Nonadditivity 465
6.9 Computation of Trend Components 470
6.10 General Computational Formulas for Main Effects and Interactions 476
6.11 Missing Data 479
6.12 Special Computational Procedures when all Factors have Two Levels 481
6.13 Unequal Cell Frequencies—Least Squares Solution 486
6.14 Analysis of Variance in Terms of Polynomial Progression 492
6.15 Exercises 492
7 Multifactor Experiments Having Repeated
Measures on the Same Elements 497
7.1 General Purpose 497
7.2 Two Factor Experiment with Repeated Measures on One Factor 509
7.3 Three Factor Experiment with Repeated Measures (Case I) 531
7.4 Three Factor Experiment with Repeated Measures (Case II) 547
7.5 Other Multifactor Repeated Measure Plans 557
7.6 Tests on Trends 562
7.7 Unequal Group Size 575
7.8 Measures of Association and Statistical Power 580
7.9 Exercises 580
8 Factorial Experiments in which some
of the Interactions are Confounded 583
8.1 General Purpose 583
8.2 Assigning Treatments to Blocks 586
8.3 Methods for Obtaining and Confounding Interaction Components 590
8.4 Simplified Computational Procedures for 2* Factorial Experiments 603
8.5 Designs for 2* Experiments 607
8.6 Designs for 3* Experiments 625
8.7 Mixed Designs 647
8.8 Fractional Replications 661
8.9 Exercises 670
9 Latin Squares and Related Designs 674
9.1 Definition and Enumeration of Latin Square 674
9.2 Uses of Latin Squares 679
9.3 Analysis of Latin Square Designs—No Repeated Measures 687
9.4 Analysis of Greco Latin Squares 699
X CONTENTS
9.5 Analysis of Latin Squares—Repeated Measures 702
9.6 Exercises 735
10 Analysis of Covariance 739
10.1 General Purpose 739
10.2 Single Factor Experiment 744
10.3 Multiple Covariates 788
10.4 Factorial Experiment 800
10.5 Analysis of Covariance—Repeated Measures 820
10.6 Exercises 837
A Random Variables 841
A.I Random Variables and Probability Distributions 842
A.2 Normal distribution 850
A.3 Gamma and Chi Square Distributions 852
A.4 Beta and F Distributions 856
A.5 Student s t Distribution 863
A.6 Bivariate Normal Distributions 865
A.7 Multivariate Normal Distribution 868
A.8 Distribution of Quadratic Forms 873
B Vector and Matrix Algebra 876
B.I Vectors and Matrices 876
B.2 Vector and Matrix Equality 881
B.3 Matrix Transposition 881
B.4 Vector and Matrix Addition and Subtraction 882
B.5 Vector and Matrix Multiplication 883
B.6 Matrix Inversion 894
B.7 Linear Transformations and Solving Linear Equations 902
B.8 Basic Statistical Operations 906
C Linear Models: Regression and the Analysis
of Variance 911
C. 1 Linear Relations: Least Squares Procedures 912
C.2 The General Linear Model 941
C.3 The General Linear Model and the Analysis of Variance 954
D Tables 964
E Topics Closely Related to the Analysis of Variance 1011
E.I Use of Analysis of Variance to Estimate 1011
E.2 Analysis of Variance for Ranked Data 1024
E.3 Dichotomous Data 1027
E.4 Kruskal Wallis H Test 1028
E.5 Contingency Table with Repeated Measures 1030
E.6 Comparing Treatment Effects with a Control 1034
E.7 General Partition of Degrees of Freedom in a Contingency Table 1036
References i©4i
Index 1048
|
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| author_facet | Winer, Ben James Brown, Donald R. Michels, Kenneth M. |
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| discipline | Soziologie Psychologie Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| indexdate | 2024-07-09T17:21:15Z |
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| isbn | 0070709823 |
| language | English |
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| spelling | Winer, Ben James Verfasser aut Statistical principles in experimental design B. J. Winer ; Donald R. Brown ; Kenneth M. Michels 3. ed. New York [u.a]. McGraw-Hill 1991 XIII, 1057 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier McGraw Hill series in psychology Experimentelle Psychologie (DE-588)4016005-1 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Versuchsplanung (DE-588)4078859-3 gnd rswk-swf Experimentelle Psychologie (DE-588)4016005-1 s Statistik (DE-588)4056995-0 s DE-604 Versuchsplanung (DE-588)4078859-3 s 1\p DE-604 Brown, Donald R. Verfasser aut Michels, Kenneth M. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005632606&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Winer, Ben James Brown, Donald R. Michels, Kenneth M. Statistical principles in experimental design Experimentelle Psychologie (DE-588)4016005-1 gnd Statistik (DE-588)4056995-0 gnd Versuchsplanung (DE-588)4078859-3 gnd |
| subject_GND | (DE-588)4016005-1 (DE-588)4056995-0 (DE-588)4078859-3 |
| title | Statistical principles in experimental design |
| title_auth | Statistical principles in experimental design |
| title_exact_search | Statistical principles in experimental design |
| title_full | Statistical principles in experimental design B. J. Winer ; Donald R. Brown ; Kenneth M. Michels |
| title_fullStr | Statistical principles in experimental design B. J. Winer ; Donald R. Brown ; Kenneth M. Michels |
| title_full_unstemmed | Statistical principles in experimental design B. J. Winer ; Donald R. Brown ; Kenneth M. Michels |
| title_short | Statistical principles in experimental design |
| title_sort | statistical principles in experimental design |
| topic | Experimentelle Psychologie (DE-588)4016005-1 gnd Statistik (DE-588)4056995-0 gnd Versuchsplanung (DE-588)4078859-3 gnd |
| topic_facet | Experimentelle Psychologie Statistik Versuchsplanung |
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