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雷达卡
GLENN GAMST
University of La Verne
LAWRENCE S. MEYERS
California State University, Sacramento
A. J. GUARINO
Auburn University
Contents
Preface page xiii
SECTION 1. RESEARCH FOUNDATIONS
1 ANOVA AND RESEARCH DESIGN 3
1.1 What Is Analysis of Variance? 3
1.2 A Brief History of ANOVA 4
1.3 Dependent and Independent Variables 5
1.4 The Importance of Variation 6
1.5 Exploratory Research and Hypothesis Testing 7
2 MEASUREMENT, CENTRAL TENDENCY, AND VARIABILITY 9
2.1 Scales ofMeasurement 9
2.2 Central Tendency and Variability 12
2.3 TheMean as aMeasure of Central Tendency 13
2.4 TheMedian as aMeasure of Central Tendency 15
2.5 TheMode as aMeasure of Central Tendency 15
2.6 Range as aMeasure of Variability 16
2.7 Variance as aMeasure of Variability 16
2.8 Standard Deviation as aMeasure of Variability 19
Chapter 2 Exercises 20
SECTION 2. FOUNDATIONS OF ANALYSIS OF VARIANCE
3 ELEMENTS OF ANOVA 23
3.1 Partitioning of the Variance 23
3.2 A Simple Example Study 23
3.3 Sources of Variance 26
3.4 Sums of Squares 26
3.5 Degrees of Freedom 30
3.6 Mean Square 32
3.7 Where All This Leads 33
4 THE STATISTICAL SIGNIFICANCE OF F AND EFFECT STRENGTH 34
4.1 The F Ratio 34
4.2 The Sampling Distribution of F 35
4.3 The Area Under the Sampling Distribution 37
4.4 Statistical Significance 37
4.5 Explaining Variance: Strength of Effect 41
4.6 Reporting the Results 44
4.7 Statistical Power 45
4.8 The Limiting Case of ANOVA: The t Test 47
5 ANOVA ASSUMPTIONS 49
5.1 Overview 49
5.2 Independence of Errors 49
5.3 Normality of Errors 52
5.4 Homogeneity of Variance 57
5.5 SPSS Applications: Assumption Violation Detection and
Solution 60
5.6 SAS Applications: Assumption Violation Detection and
Solution 70
5.7 Communicating the Results 83
Chapter 5 Exercises 84
SECTION 3. BETWEEN-SUBJECTS DESIGNS
6 ONE-WAY BETWEEN-SUBJECTS DESIGN 87
6.1 Overview 87
6.2 A Numerical Example 87
6.3 Partitioning the Total Variance into Its Sources 89
6.4 Omnibus and Simplifying Analyses 90
6.5 Computing the Omnibus Analysis by Hand 91
6.6 Performing the Omnibus One-Way Between-Subjects ANOVA
in SPSS 98
6.7 The Output of the Omnibus One-Way Between-Subjects
ANOVA in SPSS 101
6.8 Performing the Omnibus One-Way Between-Subjects ANOVA
in SAS 102
6.9 The Output of the Omnibus One-Way Between-Subjects
ANOVA in SAS 107
6.10 Communicating the Results 110
Chapter 6 Exercises 111
7 MULTIPLE COMPARISON PROCEDURES 112
7.1 Overview 112
7.2 Planned Versus Unplanned Comparisons 112
7.3 Pairwise Versus Composite Comparisons 113
7.4 Orthogonal Versus Nonorthogonal Comparisons 114
7.5 Statistical Power 115
7.6 Alpha Inflation 117
7.7 General Categories ofMultiple Comparison Procedures 118
7.8 Post Hoc Tests 120
7.9 Computing a Tukey HSD Test by Hand 126
7.10 Performing a Tukey HSD Test in SPSS 128
7.11 The Tukey HSD Output from SPSS 129
7.12 Performing a Tukey HSD Test in SAS 132
7.13 The Tukey HSD Output from SAS 134
7.14 Communicating the Tukey Results 135
7.15 Preset Contrasts in SPSS 135
7.16 Performing Simple Contrasts in SPSS 139
7.17 The Simple Contrasts Output from SPSS 141
7.18 Performing Simple Contrasts in SAS 143
7.19 The Simple Contrasts Output from SAS 143
7.20 Communicating the Simple Contrast Results 144
7.21 Polynomial Contrasts (Trend Analysis) 145
7.22 Performing a Trend Analysis by Hand 150
7.23 Performing Polynomial Contrasts (Trend Analysis) in SPSS 152
7.24 Output for Polynomial Contrasts (Trend Analysis) in SPSS 154
7.25 Communicating the Results of the Trend Analysis 155
7.26 User-Defined Contrasts 155
7.27 Performing User-Defined (Planned) Comparisons by Hand 158
7.28 Performing User-Defined Contrasts in SPSS 162
7.29 Output from User-Defined Contrasts Analysis in SPSS 163
7.30 Communicating the Results of the Contrasts Analyses 164
7.31 Performing User-Defined Contrasts (Planned Comparisons) in
SAS 164
7.32 Output for Planned Comparisons in SAS 167
7.33 Communicating the Results of the Planned Comparisons 168
7.34 Performing Polynomial Contrasts (Trend Analysis) in SAS 169
7.35 Output for Polynomial Contrasts (Trend Analysis) in SAS 170
7.36 Communicating the Results of the Polynomial Contrasts 171
Chapter 7 Exercises 171
8 TWO-WAY BETWEEN-SUBJECTS DESIGN 172
8.1 Combining Two Independent Variables Factorially 172
8.2 A Numerical Example 173
8.3 Partitioning the Variance into Its Sources 174
8.4 Effects of Interest in This Design 176
8.5 The Interaction Effect 177
8.6 Precedence of Effects: Interactions SupercedeMain Effects 180
8.7 Computing an Omnibus Two-Factor Between-Subjects
ANOVA by Hand 180
8.8 Computing Simple Effects by Hand 185
8.9 Performing the Omnibus Analysis in SPSS 188
8.10 SPSS Output for the Omnibus Analysis 190
8.11 Performing the Post-ANOVA Analyses in SPSS 193
8.12 SPSS Output for the Post-ANOVA Analyses 197
8.13 Performing the Omnibus Analysis in SAS Enterprise Guide 200
8.14 SAS Output for the Omnibus Analysis 204
8.15 Performing the Post-ANOVA Analyses in SAS 206
8.16 SAS Output for the Post-ANOVA Analyses 207
8.17 Communicating the Results 209
Chapter 8 Exercises 209
9 THREE-WAY BETWEEN-SUBJECTS DESIGN 211
9.1 A Numerical Example of a Three-Way Design 211
9.2 Partitioning the Variance into Its Sources 212
9.3 Computing the Portions of the Summary Table 215
9.4 Precedence of Effects: Higher-Order Interactions, Lower-Order
Interactions,Main Effects 216
9.5 Computing by Hand the Omnibus Three-Way
Between-Subject Analysis 217
9.6 Performing the Omnibus Analysis in SPSS 218
9.7 SPSS Output for the Omnibus Analysis 222
9.8 Performing the Post-ANOVA Analyses in SPSS 224
9.9 SPSS Output for the Post-ANOVA Analyses in SPSS 228
9.10 Performing the Omnibus Analysis in SAS Enterprise Guide 231
9.11 SAS Output for the Omnibus Analysis 237
9.12 Performing the Post-ANOVA Analyses in SAS 238
9.13 SAS Output for the Post-ANOVA Analyses in SAS 240
9.14 Communicating the Results 242
Chapter 9 Exercises 243
SECTION 4. WITHIN-SUBJECTS DESIGNS
10 ONE-WAY WITHIN-SUBJECTS DESIGN 247
10.1 The Concept ofWithin-Subjects Variance 247
10.2 Nomenclature 247
10.3 Nature ofWithin-Subjects Variables 248
10.4 The Issue of Carry-Over Effects 249
10.5 Between- VersusWithin-Subjects Variance 251
10.6 A Numerical Example of a One-WayWithin-Subjects Design 253
10.7 Effect of Interest in This Design 253
10.8 The Error Term in a One-WayWithin-Subjects Design 254
10.9 Computing the Omnibus Analysis by Hand 256
10.10 Performing User-Defined (Planned) Comparisons by Hand 259
10.11 Performing the Omnibus Analysis in SPSS 262
10.12 SPSS Output for the Omnibus Analysis 266
10.13 Performing the Post-ANOVA Analysis in SPSS 270
10.14 SPSS Output for the Post-ANOVA Analysis 271
10.15 SPSS and SAS Data File Structures 273
10.16 Performing the Omnibus Analysis in SAS 275
10.17 SAS Output for the Omnibus Analysis 279
10.18 Performing the Post-ANOVA Analysis in SAS 280
10.19 SAS Output for the Post-ANOVA Analysis 280
10.20 Communicating the Results 285
Chapter 10 Exercises 285
11 TWO-WAY WITHIN-SUBJECTS DESIGN 287
11.1 Combining TwoWithin-Subjects Factors 287
11.2 A Numerical Example of a Two-WayWithin-Subjects Design 288
11.3 Partitioning the Variance into Its Sources 288
11.4 Effects of Interest in This Design 289
11.5 The Error Terms in a Two-WayWithin-Subjects Design 290
11.6 Computing the Omnibus Two-FactorWithin-Subjects
ANOVA by Hand 291
11.7 Performing the Omnibus Analysis in SPSS 299
11.8 SPSS Output for the Omnibus Analysis 305
11.9 Performing the Post-ANOVA Analysis in SPSS 308
11.10 SPSS Output for the Post-ANOVA Analysis 311
11.11 Performing the Omnibus Analysis in SAS 313
11.12 SAS Output from the Omnibus Analysis 318
11.13 Performing the Simple Effects Analysis in SAS 320
11.14 SAS Output from the Simple Effects Analysis 320
11.15 Performing the Post Hoc Analysis in SAS 321
11.16 SAS Output from the Post Hoc Analysis 321
11.17 Communicating the Results 323
Chapter 11 Exercises 323
12 THREE-WAY WITHIN-SUBJECTS DESIGN 325
12.1 A Numerical Example of a Three-WayWithin-Subjects Design 325
12.2 Partitioning the Variance into Its Sources 326
12.3 Effects of Interest in This Design 326
12.4 The Error Terms in a Three-WayWithin-Subjects Design 329
12.5 Computing the Omnibus Analysis 329
12.6 Performing the Omnibus Analysis in SPSS 329
12.7 SPSS Output for the Omnibus Analysis 337
12.8 Performing the Post-ANOVA Analysis in SPSS 341
12.9 SPSS Output for the Post-ANOVA Analysis 343
12.10 Performing the Omnibus Analysis in SAS 345
12.11 SAS Output from the Omnibus Analysis 349
12.12 Performing the Simple Effects Analysis in SAS 349
12.13 SAS Output from the Simple Effects Analysis 352
12.14 Performing the Post Hoc Analysis in SAS 353
12.15 SAS Output from the Post Hoc Analysis 355
12.16 Communicating the Results 357
Chapter 12 Exercises 357
SECTION 5. MIXED DESIGNS
13 SIMPLE MIXED DESIGN 361
13.1 Combining Between-Subjects andWithin-Subjects Factors 361
13.2 A Numerical Example of a Simple Mixed Design 362
13.3 Effects of Interest 363
13.4 Computing the Omnibus Analysis by Hand 364
13.5 Performing the Omnibus Analysis in SPSS 369
13.6 SPSS Output of the Omnibus Analysis 372
13.7 Performing the Post-ANOVA Analysis in SPSS 372
13.8 Output for the Post-ANOVA Analysis in SPSS 377
13.9 Performing the Omnibus Analysis in SAS 379
13.10 SAS Output of the Omnibus Analysis 385
13.11 Performing the Simple Effects Analysis in SAS 385
13.12 SAS Output from the Simple Effects Analysis 387
13.13 Performing the Post Hoc Analysis in SAS 387
13.14 SAS Output from the Post Hoc Analysis 388
13.15 Communicating the Results 389
Chapter 13 Exercises 389
14 COMPLEX MIXED DESIGN: TWO BETWEEN-SUBJECTS FACTORS AND
ONE WITHIN-SUBJECTS FACTOR 391
14.1 Combining Between- andWithin-Subjects Factors 391
14.2 A Numerical Example of a ComplexMixed Design 391
14.3 Effects of Interest 393
14.4 Computing the Omnibus ComplexMixed Design by Hand 393
14.5 Performing the Omnibus Analysis in SPSS 396
14.6 SPSS Output of the Omnibus Analysis 401
14.7 Performing the Post-ANOVA Analysis in SPSS 402
14.8 SPSS Output of the Omnibus Analysis 404
14.9 Performing the Omnibus Analysis in SAS 406
14.10 SAS Output of the Omnibus Analysis 410
14.11 Performing the Simple Effects Analysis in SAS 411
14.12 SAS Output from the Simple Effects Analysis 411
14.13 Communicating the Results 414
Chapter 14 Exercises 418
15 COMPLEX MIXED DESIGN: ONE BETWEEN-SUBJECTS FACTOR AND
TWOWITHIN-SUBJECTS FACTORS 420
15.1 A Numerical Example of a ComplexMixed Design 420
15.2 Effects of Interest 421
15.3 Computing the Omnibus ComplexMixed Design by Hand 424
15.4 Performing the Omnibus Analysis in SPSS 424
15.5 SPSS Output of the Omnibus Analysis 430
15.6 Performing the Post-ANOVA Analysis in SPSS 432
15.7 Output for the Post-ANOVA Analysis in SPSS 434
15.8 Performing the Omnibus Analysis in SAS 438
15.9 SAS Output of the Omnibus Analysis 444
15.10 Performing the Post-ANOVA Analysis in SAS 444
15.11 Output for the Post-ANOVA Analysis in SAS 445
15.12 Communicating the Results 449
Chapter 15 Exercises 449
SECTION 6. ADVANCED TOPICS
16 ANALYSIS OF COVARIANCE 453
16.1 Experimental and Statistical Control 453
16.2 A Simple Illustration of Covariance 453
16.3 The Effect of a Covariate on Group Differences 454
16.4 The Process of Performing ANCOVA 455
16.5 Assumptions of ANCOVA 458
16.6 Numerical Example of a One-Way ANCOVA 461
16.7 Performing the ANOVA in SPSS 463
16.8 Evaluating the ANCOVA Assumptions in SPSS 463
16.9 Performing the ANCOVA in SPSS 470
16.10 Performing the ANOVA in SAS 473
16.11 Evaluating the ANCOVA Assumptions in SAS 475
16.12 Performing the ANCOVA in SAS 481
16.13 Communicating the Results 485
Chapter 16 Exercises 486
17 ADVANCED TOPICS IN ANALYSIS OF VARIANCE 488
17.1 Interaction Comparisons 488
17.2 Fixed and Random Factors 490
17.3 Nested Designs 494
17.4 Latin Squares 495
17.5 Unequal Sample Size 496
17.6 Multivariate Analysis of Variance (MANOVA) 497
APPENDIXES
APPENDIXA. PRIMER ON SPSS 501
A.1 Historical Overview 501
A.2 Different Kinds of Files and Their Extensions 501
A.3 Opening SPSS 502
A.4 Saving SPSS Files 503
A.5 Setting Preferences 503
A.6 Creating New Data Files in SPSS 506
A.7 Variable View of the Data File 507
A.8 Data View of the Data File 513
A.9 Reading Data from an ExcelWorksheet 513
A.10 Reading Data from a Text File 514
A.11 Opening Saved Data Files 521
A.12 TheMain SPSSMenu 521
A.13 Performing Statistical Procedures in SPSS 522
A.14 Saving Output Files 526
APPENDIXB. PRIMER ON SAS 531
B.1 Historical Overview 531
B.2 Installing Enterprise Guide on Your Computer 531
B.3 Opening SAS Enterprise Guide 532
B.4 Entering Data Directly into SAS Enterprise Guide 533
B.5 Saving a Project 538
B.6 Constructing Your Data File in Excel 538
B.7 Importing Data from Excel 539
B.8 TheMain SASMenu 542
B.9 Performing Statistical Procedures in SAS Enterprise Guide 544
B.10 SAS Enterprise Guide Output 546
B.11 Saving the SAS Output File as a PDF Document 547
B.12 Additional Resources 550
APPENDIXC. TABLE OF CRITICAL F VALUES 551
APPENDIXD. DEVIATIONAL FORMULA FOR SUMS OF SQUARES 555
APPENDIXE. COEFFICIENTS OF ORTHOGONAL POLYNOMIALS 559
APPENDIXF. CRITICAL VALUES OF THE STUDENTIZED RANGE
STATISTIC 560
References 561
Author Index 567
Subject Index 569
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