Research Design & Statistical Analysis

Contents......Page 8
Preface......Page 14
1.1 Variability and the Need for Statistics......Page 22
1.2 Systematic Versus Random Variability......Page 24
1.4 Reducing Error Variance......Page 26
1.6 Concluding Remarks......Page 28
2.1 Introduction......Page 31
2.2 Exploring a Single Sample......Page 32
2.3 Comparing Two Data Sets......Page 39
2.4 Other Measures of Location and Spread: The Mean and Standard Deviation......Page 41
2.5 Standardized (Ζ) Scores......Page 48
2.6 Measures of the Shape of a Distribution......Page 49
2.7 Concluding Remarks......Page 54
3.2 Some Examples......Page 58
3.3 Linear Relations......Page 64
3.4 The Pearson Product-Moment Correlation Coefficient......Page 65
3.5 Linear Regression......Page 72
3.6 The Coefficient of Determination, r2......Page 75
3.7 Influential Data Points and Resistant Measures of Regression......Page 76
3.9 Concluding Remarks......Page 77
4.1 Introduction......Page 82
4.2 Discrete Random Variables......Page 83
4.3 Probability Distributions......Page 84
4.4 Some Elementary Probability......Page 88
4.5 The Binomial Distribution......Page 96
4.6 Means and Variances of Discrete Distributions......Page 100
4.7 Hypothesis Testing......Page 101
4.8 Independence and the Sign Test......Page 107
4.10 Concluding Remarks......Page 110
5.2 Continuous Random Variables......Page 121
5.3 The Normal Distribution......Page 123
5.4 Point Estimates of Population Parameters......Page 125
5.5 Inferences About Population Means: The One-Sample Case......Page 133
5.6 Inferences About Population Means: The Correlated-Samples Case......Page 138
5.7 The Power of the Ζ Test......Page 140
5.8 Hypothesis Tests and CIs......Page 143
5.9 Validity of Assumptions......Page 144
5.10 Comparing Means of Two Independent Populations......Page 146
5.11 The Normal Approximation to the Binomial Distribution......Page 149
5.12 Concluding Remarks......Page 150
6.1 Introduction......Page 161
6.2 Inferences About a Population Mean......Page 162
6.3 The Standardized Effect Size......Page 166
6.4 Power of the One-Sample t Test......Page 168
6.5 The t Distribution: Two Independent Groups......Page 173
6.6 Standardized Effect Size for Two Independent Means......Page 177
6.7 Power of the Test of Two Independent Means......Page 178
6.8 Assumptions Underlying the Two-Group t Test......Page 179
6.9 Contrasts Involving More than Two Means......Page 182
6.10 Correlated Scores or Independent Groups?......Page 186
6.11 Concluding Remarks......Page 188
7.1 Introduction......Page 194
7.2 The χ2 Distribution......Page 195
7.3 Inferences About the Population Variance......Page 196
7.4 The F Distribution......Page 200
7.5 Inferences About Population Variance Ratios......Page 203
7.6 Relations Among Distributions......Page 206
7.7 Concluding Remarks......Page 207
8.1 Introduction......Page 212
8.2 Exploring the Data......Page 214
8.3 The Analysis of Variance......Page 216
8.4 The Model for the One-Factor Design......Page 222
8.5 Assessing the Importance of the Independent Variable......Page 228
8.6 Power of the F Test......Page 233
8.7 Assumptions Underlying the F Test......Page 237
8.8 Concluding Remarks......Page 248
9.1 Introduction......Page 254
9.2 Definitions and Examples of Contrasts......Page 255
9.3 Calculations of the t Statistic for Testing Hypotheses About Contrasts......Page 256
9.4 The Proper Unit for the Control of Type 1 Error......Page 262
9.5 Planned Versus Post Hoc Contrasts......Page 264
9.6 Controlling the FWE for Families of K Planned Contrasts......Page 265
9.7 Testing All Pairwise Contrasts......Page 268
9.8 Comparing a – 1 Treatment Means with a Control: Dunnett's Test......Page 276
9.9 Controlling the Familywise Error Rate for Post Hoc Contrasts......Page 277
9.10 The Sum of Squares Associated with a Contrast......Page 279
9.11 Concluding Remarks......Page 281
10.1 Introduction......Page 288
10.2 Linear Trend......Page 289
10.3 Testing Nonlinear Trends......Page 295
10.4 Concluding Remarks......Page 301
11.1 Introduction......Page 305
11.2 A First Look at the Data......Page 306
11.3 Two-Factor Designs: The ANOVA......Page 309
11.4 The Structural Model and Expected Mean Squares......Page 316
11.5 Main Effect Contrasts......Page 318
11.6 More About Interaction......Page 319
11.7 Simple Effects......Page 323
11.8 Two-Factor Designs: Trend Analysis......Page 326
11.9 Concluding Remarks......Page 330
12.2 Measures of Effect Size......Page 336
12.3 Power of the F Test......Page 339
12.4 Unequal Cell Frequencies......Page 340
12.5 Three-Factor Designs......Page 345
12.7 Pooling in Factorial Designs......Page 353
12.8 Blocking to Reduce Error Variance......Page 356
12.9 Concluding Remarks......Page 357
13.1 Introduction......Page 363
13.2 The Additive Model and Expected Mean Squares for the S × A Design......Page 366
13.3 The Nonadditive Model for the S × A Design......Page 373
13.4 Hypothesis Tests Assuming Nonadditivity......Page 376
13.6 Multifactor Repeated-Measures Designs......Page 384
13.7 Fixed or Random Effects?......Page 392
13.8 Nonparametric Procedures for Repeated-Measures Designs......Page 393
13.9 Concluding Remarks......Page 398
14.2 One Between-Subjects and One Within-Subjects Factor......Page 407
14.3 Rules for Generating Expected Mean Squares......Page 413
14.4 Measures of Effect Size......Page 415
14.5 Power Calculations......Page 417
14.6 Contrasting Means in Mixed Designs......Page 418
14.7 Testing Simple Effects......Page 422
14.8 Pretest-Posttest Designs......Page 423
14.9 Additional Mixed Designs......Page 424
14.10 Concluding Remarks......Page 428
15.1 Introduction......Page 433
15.2 Example of an ANCOVA......Page 436
15.3 Assumptions and Interpretation in an ANCOVA......Page 443
15.4 Testing Homogeneity of Slopes......Page 448
15.5 More About ANCOVA Versus Treatments × Blocks......Page 449
15.6 Estimating Power in an ANCOVA......Page 451
15.8 Some Extensions of the ANCOVA......Page 452
15.9 Concluding Remarks......Page 453
16.1 Introduction......Page 457
16.2 Groups Within Treatments......Page 458
16.3 Groups Versus Individuals......Page 464
16.4 Extensions of the Groups-Within-Treatments Design......Page 466
16.5 Items Within Treatments......Page 470
16.6 Concluding Remarks......Page 473
17.1 Introduction......Page 478
17.2 Selecting a Latin Square......Page 480
17.3 The Single Latin Square......Page 482
17.4 The Replicated Latin Square Design......Page 490
17.5 Balancing Carry-Over Effects......Page 495
17.6 Greco-Latin Squares......Page 497
17.7 Concluding Remarks......Page 498
18.1 Introduction......Page 501
18.2 Further Issues in Understanding the Correlation Coefficient......Page 502
18.3 Inference About Correlation......Page 510
18.4 Partial Correlations......Page 522
18.5 Other Measures of Correlation......Page 525
18.6 Concluding Remarks......Page 532
19.1 Introduction......Page 540
19.2 Regression Toward the Mean......Page 541
19.3 Inference in Linear Regression......Page 543
19.4 An Example: Regressing Cholesterol Level on Age......Page 553
19.5 Checking for Violations of Assumptions......Page 555
19.6 Locating Outliers and Influential Data Points......Page 563
19.7 Testing Independent Slopes for Equality......Page 569
19.8 Repeated-Measures Designs......Page 570
19.10 Concluding Remarks......Page 572
20.1 Introduction......Page 583
20.2 A Regression Example with Several Predictor Variables......Page 584
20.3 The Nature of the Regression Coefficients......Page 593
20.4 The Multiple Correlation Coefficient and the Partitioning of Variability in Multiple Regression......Page 594
20.5 Inference in Multiple Regression......Page 601
20.6 Selecting the Best Regression Equation for Prediction......Page 612
20.7 Explanation Versus Prediction in Regression......Page 614
20.8 Testing for Curvilinearity in Regression......Page 619
20.9 Including Interaction Terms in Multiple Regression......Page 622
20.10 Multiple Regression in Repeated-Measures Designs......Page 628
20.11 Concluding Remarks......Page 629
21.1 Introduction......Page 635
21.2 One-Factor Designs......Page 636
21.3 Regression Analyses and Factorial Designs......Page 642
21.4 Using Categorical and Continuous Variables in the Same Analysis......Page 651
21.5 Coding Designs with Within-Subjects Factors......Page 655
21.6 Concluding Remarks......Page 658
Appendix A: Notation and Summation Operations......Page 662
Appendix B: Expected Values and Their Applications......Page 670
Appendix C: Statistical Tables......Page 674
Answers to Selected Exercises......Page 706
Endnotes......Page 742
References......Page 750
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