Essentials of Behavioral and Social Science Statistics

Preface xv

Acknowledgments xix

About the Companion Website xxi

Introduction 1

1 Basic Concepts in Research 3

1.1 The Scientific Method 3

1.2 The Goals of the Researcher 5

1.3 Types of Variables 7

1.4 Controlling Extraneous Variables 9

1.5 Validity Issues 16

1.6 Causality and Correlation 21

1.7 The Organization of the Textbook 23

Summary 24

Exercises 25

Part 1 Descriptive Statistics 29

2 The Nature, Scales, and Display of Measurements 31

2.1 The Nature of Measurement 31

2.2 Scales of Measurement 33

2.3 Types of Variables and Their Features 37

2.4 Using Tables to Organize Data 40

2.5 Using Graphs to Display Data 45

2.6 The Shape of Things to Come 52

Summary 55

Microsoft^® Excel and SPSS^® 57

Exercises 57

Work Problems 58

3 Measures of Central Tendency 61

3.1 Describing a Distribution of Scores 61

3.2 Parameters and Statistics 62

3.3 The Rounding Rule 62

3.4 The Mean 63

3.5 The Median 66

3.6 The Mode 69

3.7 Distribution Shape and Measures of Central Tendency 70

3.8 When to Use the Mean, Median, and Mode 71

Summary 74

Microsoft^® Excel and SPSS^® 75

Exercises 76

Work Problems 76

4 Measures of Variability 79

4.1 The Importance of Measures of Variability 79

4.2 The Range 79

4.3 The Mean Deviation 82

4.4 The Variance 84

4.5 The Standard Deviation 89

4.6 Simple Transformations of the Mean and Variance 91

4.7 Deciding Which Measure of Variability to Use 92

Summary 95

Microsoft^® Excel and SPSS^® 96

Exercises 97

Work Problems 98

5 The Normal Curve and Transformations 101

5.1 Percentile Rank 101

5.2 Normal Distributions 102

5.3 Standard Scores (z Scores) 106

Summary 116

Microsoft^® Excel and SPSS^® 117

Exercises 118

Work Problems 118

Part 2 Inferential Statistics: Theoretical Basis 121

6 Basic Concepts of Probability 123

6.1 Theoretical Support for Inferential Statistics 123

6.2 The Taming of Chance 124

6.3 What Is Probability? 126

6.4 The Addition Rule 130

6.5 The Multiplication Rule 133

6.6 Conditional Probabilities 136

Summary 141

Exercises 142

Work Problems 143

7 Hypothesis Testing and Sampling Distributions 147

7.1 Inferential Statistics 147

7.2 Hypothesis Testing 148

7.3 Sampling Distributions 153

7.4 Estimating the Features of Sampling Distributions 158

Summary 160

Exercises 162

Work Problems 163

Part 3 Inferential Statistics: z Test, t Tests, and Power 165

8 The Single-Sample z and t Tests 167

8.1 The Research Context 167

8.2 The Sampling Distribution for the Single-Sample z Test 168

8.3 Type I and Type II Errors 175

8.4 Is a Significant Finding “Significant?” 180

8.5 The Sampling Distribution for the Single-Sample t Test 182

8.6 Assumptions of the Single-Sample z and t Tests 188

8.7 Interval Estimation of the Population Mean 189

8.8 Formal Presentation of Findings 191

Summary 191

Microsoft^® Excel and SPSS^® 192

Exercises 193

Work Problems 194

9 The Independent- and Dependent-Samples t Tests 199

9.1 The Research Context for Between-Participants Designs 199

9.2 The Independent-Samples t Test 201

9.3 Assumptions of the Independent-Samples t Test 210

9.4 Interval Estimation for Independent Samples 210

9.5 The Research Context for Within-Participants Designs 211

9.6 The Dependent-Samples t Test 213

9.7 Assumptions of the Dependent-Samples t Test 218

9.8 Interval Estimation for Dependent Samples 218

9.9 Comparing the Two Tests 219

9.10 The Appropriateness of Unidirectional Tests 220

9.11 Formal Presentation of Findings 225

Summary 225

Microsoft^® Excel and SPSS^® 226

Exercises 228

Work Problems 230

10 Power Analysis and Hypothesis Testing 239

10.1 Decision-Making While Hypothesis Testing 239

10.2 Why Study Power? 240

10.3 The Five Factors that Influence Power 241

10.4 Decision Criteria that Influence Power 243

10.5 Determining Effect Size: The Achilles Heel of Power Analyses 247

10.6 Determining Sample Size for a Single-Sample Test 248

Summary 249

Exercises 250

Work Problems 251

Part 3 Review The z Test, t Tests, and Power Analysis 253

Part 4 Inferential Statistics: Analyses of Variance 257

11 One-Way Analysis of Variance 259

11.1 The Research Context 259

11.2 Hypotheses 261

11.3 The Conceptual Basis: Sources of Variation 262

11.4 The Assumptions 265

11.5 Computing the F Ratio 265

11.6 Testing Null Hypotheses 271

11.7 The ANOVA Summary Table 274

11.8 Measuring Effect Size 274

11.9 Locating the Source(s) of Significance 275

11.10 Formal Presentation of Findings 279

Summary 279

Microsoft^® Excel and SPSS^® 280

Exercises 281

Work Problems 283

12 Two-Way Analysis of Variance 289

12.1 The Research Context 289

12.2 The Logic of the Two-Way ANOVA 300

12.3 Definitional and Computational Formulas 303

12.4 The ANOVA Summary Table 306

12.5 Using the F Ratios to Test Null Hypotheses 307

12.6 The Assumptions 308

12.7 Measuring Effect Sizes 308

12.8 Multiple Comparisons 309

12.9 Interpreting the Factors in a Two-Way ANOVA 314

12.10 Formal Presentation of Findings 315

Summary 315

Microsoft^® Excel and SPSS^® 316

Exercises 317

Work Problems 320

13 Repeated-Measures Analysis of Variance 325

13.1 The Research Context 325

13.2 The Logic of the Repeated-Measures ANOVA 328

13.3 The Formulas 331

13.4 The ANOVA Summary Table 334

13.5 Using the F Ratio to Test the Null Hypothesis 335

13.6 Interpreting the Findings 335

13.7 The Assumptions 335

13.8 Measuring Effect Size 336

13.9 Locating the Source(s) of Statistical Evidence 337

13.10 Formal Presentation of Findings 338

Summary 339

Microsoft^® Excel and SPSS^® 339

Exercises 340

Work Problems 341

Part 4 Review Analyses of Variance 347

Part 5 Inferential Statistics: Bivariate Data and Chi-Square Tests 351

14 Linear Correlation 353

14.1 The Research Context 353

14.2 The Correlation Coefficient and Scatter Diagrams 356

14.3 The Coefficient of Determination, r² 362

14.4 Using the Pearson r for Hypothesis Testing 365

14.5 Misleading Correlation Coefficients 368

14.6 Formal Presentation of Findings 372

Summary 372

Microsoft^® Excel and SPSS^® 373

Exercises 374

Work Problems 376

15 Linear Regression 381

15.1 The Research Context 381

15.2 Overview of Regression 382

15.3 Establishing the Regression Line 386

15.4 Putting It All Together: A Worked Problem 396

15.5 The Pitfalls of Linear Regression 398

15.6 Formal Presentation of Findings 401

Summary 401

Microsoft^® Excel and SPSS^® 402

Exercises 403

Work Problems 404

16 Chi-Square Tests and Other Nonparametrics 409

16.1 The Research Context 409

16.2 The Goodness-of-Fit Chi-Square Test 410

16.3 The Chi-Square Sampling Distribution 416

16.4 The Chi-Square Test for Independence 418

16.5 The Chi-Square Test for a 2 × 2 Contingency Table 422

16.6 A Measure of Effect Size for Chi-Square Tests 423

16.7 Major Contributors to a Significant Chi-Square 424

16.8 Using the Chi-Square Test with Quantitative Variables 425

16.9 The Assumptions 426

16.10 Formal Presentation of Findings 426

16.11 Other Nonparametric Tests 426

Summary 429

Microsoft® Excel and SPSS^® 430

Exercises 431

Work Problems 432

Part 5 Review Bivariate Data and Chi-Square Tests 437

Appendix A Statistical Tables 433

Appendix B Answers to Exercises and Work Problems 461

Appendix c Instructions for Microsoft® Excel and SPSS® 533

References 565

Glossary 573

List of Selected Formulas 583

List of Symbols 589

Index 593