Analyzing Quantitative Data: An Introduction for Social Researchers

Preface xiii

Part I Summarizing Data 1

1 Data Organization 3

1.1 Introduction 3

1.2 Consideration of Variables 4

1.2.1 Units of Analysis 4

1.2.2 Variables 4

Roles of Variables 5

Variable Relationships 6

Causal Time Order 6

Intervening Variables 7

The Nature of Data 8

Categorical Variables 8

Continuous Variables 9

Levels of Measurement 11

1.2.3 Attributes 13

1.3 Coding 15

1.3.1 Coding Categorical Data 15

1.3.2 Coding Ordinal Data 17

1.4 Data Manipulations 18

1.4.1 Filtering Subjects 18

1.4.2 Splitting Datasets 19

1.4.3 Calculations with Data 19

Basic Operations 19

Combining Multiple Indicators 20

1.5 Conclusion 20

Statistical Resources for SPSS^® 21

Review Questions 29

2 Descriptive Statistics for Categorical Data 33

2.1 Introduction 33

2.2 Frequency Tables 35

2.2.1 Using Existing Categories 35

2.2.2 Creating Categories 35

2.3 Crosstabulations 37

2.3.1 Basic (Single-Layer) Crosstabulations 37

2.3.2 Multilayer Crosstabulations 39

Split Crosstabulations 40

Nested Crosstabulations 42

2.4 Graphs and Charts 44

2.4.1 Bar Graphs 45

Basic Bar Graphs 45

Clustered and Stacked Bar Graphs 46

2.4.2 Pie Charts 48

Basic Pie Chart 48

Paneled Pie Charts 48

2.5 Conclusion 50

Statistical Resources for SPSS 50

Review Questions 57

3 Descriptive Statistics for Continuous Data 63

3.1 Introduction 63

3.2 Frequencies 64

3.2.1 Frequency Histograms 64

Paneled Histograms 65

Stacked Histograms 67

Frequency Polygons 68

3.2.2 Stem-and-Leaf Charts 68

3.3 Measures of Central Tendency 70

3.3.1 Mean 70

3.3.2 Median 71

3.3.3 Mode 71

3.3.4 Deciding between Measures of Central Tendency 72

3.4 Measures of Dispersion 73

3.4.1 Maximum and Minimum 73

3.4.2 Range 73

3.4.3 Variance and Standard Deviation 75

Basic Formulas 76

Raw-Score Formulas 78

3.5 Standardized Scores 79

3.5.1 Computing Standardized Scores 80

3.5.2 Using Standardized Scores 82

3.6 Conclusion 88

Statistical Resources for SPSS 89

Review Questions 95

Part II Statistical Tests 101

4 Evaluating Statistical Significance 103

4.1 Introduction 103

4.2 Central Limit Theorem 104

4.2.1 Definition of the Central Limit Theorem 104

4.2.2 Demonstrating the Central Limit Theorem 106

4.2.3 Limitations of the Central Limit Theorem 107

4.3 Statistical Significance 107

4.3.1 The Importance of Good Sampling 108

Random Sampling 109

Sample Size 109

4.3.2 Identifying a Significant Difference 110

Probability Values 111

Alpha (α) and Critical Values 111

Confidence Intervals and Distribution Tails 112

Type I and Type II Errors 113

4.4 The Roles of Hypotheses 115

4.4.1 The Research and Null Hypotheses 116

Accepting the Null Hypothesis 117

Rejecting the Null Hypothesis 118

4.4.2 Unexpected Results 119

4.5 Conclusion 119

Statistical Resources for SPSS 120

Review Questions 122

5 The Chi-Square Test: Comparing Category Frequencies 125

5.1 Introduction 125

5.2 The Chi-Square Distribution 126

5.2.1 The Chi-Square Distribution versus the Normal Distribution 127

5.2.2 Variations of the Chi-Square Distribution 127

5.2.3 Chi-Square Probabilities 129

5.3 Performing Chi-Square Tests 130

5.3.1 One-Variable Chi-Square Test 131

The One-Variable Chi-Square Formula 132

Interpreting the One-Variable Calculated Chi-Square Value 134

5.3.2 Two-Variable Chi-Square Test 135

The Two-Variable Chi-Square Formula 136

Interpreting the Two-Variable Calculated Chi-Square Value 136

5.3.3 Three-or-More-Variable Chi-Square 139

Three-or-More-Variable Chi-Square Formulas 141

5.4 Post Hoc Testing 143

5.4.1 One-Variable Chi-Square Post Hoc Tests 144

5.4.2 Two-Variable Chi-Square Post Hoc Tests 144

5.4.3 Three-or-More-Variable Chi-Square Post Hoc Tests 145

5.5 Confidence Intervals 146

5.6 Explaining Results of the Chi-Square Test 147

5.7 Conclusion 148

Statistical Resources for SPSS 149

Review Questions 155

6 The t Test: Comparing Continuous-Variable Data Among Dichotomous Groups 159

6.1 Introduction 159

6.2 The t Distribution 160

6.3 Performing t Tests 161

6.3.1 One-Sample t Tests 162

One-Sample t-Test Formulas 162

Interpreting the One-Sample Calculated t Value 163

6.3.2 Paired (Dependent)-Samples t Test 165

Paired-Samples t-Test Formulas 166

Interpreting the Paired-Samples Calculated t Value 168

6.3.3 Independent-Samples t Test 169

Independent-Samples t-Test Formulas 169

Interpreting the Independent-Samples Calculated t Value 171

6.4 Confidence Intervals 172

6.5 Explaining Results of the t Test 173

6.6 Conclusion 174

Statistical Resources for SPSS 175

Review Questions 183

7 Analysis of Variance: Comparing Continuous-Variable Data Among Nondichotomous Groups 187

7.1 Introduction 187

7.2 The F Distribution 189

7.2.1 The F Distribution versus the Normal Distribution 189

7.2.2 Variations in the F Distribution 190

7.2.3 F Probabilities 191

7.3 Performing ANOVAs 192

7.3.1 One-Way ANOVA 192

One-Way ANOVA Formulas 193

Interpreting the One-Way Calculated F Value 197

7.3.2 Two-or-More-Way ANOVA 199

Factorial Designs 199

Main Effects and Interaction Effects 201

Two-Way ANOVA Formulas 205

Interpreting the Two-Way Calculated F Value 212

7.4 Post Hoc Testing 214

7.4.1 One-Way ANOVA Post Hoc Tests 215

7.4.2 Two-or-More-Way ANOVA Post Hoc Tests 216

7.5 Confidence Intervals 217

7.6 Explaining Results of the ANOVA 218

7.7 Conclusion 219

Statistical Resources for SPSS 220

Review Questions 226

8 Correlation and Regression: Comparing Changes Among Continuous-Variable Scores 231

8.1 Introduction 231

8.2 Bivariate Relationships 233

8.2.1 Bivariate Regression 234

8.2.2 Pairwise Correlation 238

The Pairwise Correlation Coefficient 238

The Coefficient of Determination 241

8.2.3 Curvilinear Relationships 242

8.3 Multivariate Relationships 244

8.3.1 Multiple Regression 245

8.3.2 Multiple Correlation 247

The Multiple-Correlation Coefficient 247

The Coefficient of Multiple Determination 248

8.3.3 Partial and Part Correlations 249

Partial Correlation 250

Part Correlation 252

8.4 The Phi Coefficient 253

8.5 Explaining Results of Correlation–Regression Analysis 255

8.5.1 Regression and Correlation 255

8.5.2 Relationships between Dichotomous Variables 257

8.6 Conclusion 258

Statistical Resources for SPSS 259

Review Questions 267

9 Advanced Statistical Analyses 273

9.1 Introduction 273

9.2 Repeated-Measures Analysis of Variance 274

9.2.1 Capabilities of Repeated-Measures ANOVA 274

9.2.2 Performing a Repeated-Measures ANOVA 275

9.3 Multiple Analysis of Variance 278

9.3.1 Capabilities of MANOVA 279

9.3.2 Performing a MANOVA 280

9.4 Analysis of Covariance 282

9.4.1 Capabilities of ANCOVA 283

9.4.2 Performing an ANCOVA 284

9.5 Discriminant Analysis 286

9.5.1 Capabilities of Discriminant Analysis 287

9.5.2 Performing a Discriminant Analysis 289

9.6 Conclusion 290

Statistical Resources for SPSS 290

Review Questions 299

Part III Applying Data 303

10 Drawing Conclusions 305

10.1 Introduction 305

10.2 Accepting and Rejecting Hypotheses 306

10.2.1 The Null Hypothesis–Research Hypothesis Relationship 306

10.2.2 Matching Null and Research Hypotheses 307

10.2.3 Different Null and Research Hypotheses 308

10.3 Drawing Conclusions from Results 310

10.3.1 Summarizing 311

10.3.2 Reflecting 313

10.3.3 Speculating 314

10.4 Cautions 315

10.4.1 Alternate Explanations of Causation 316

10.4.2 High Alpha Values 319

10.4.3 The Ecological Fallacy 320

10.4.4 Reductionism 322

10.5 Conclusion 323

Review Questions 324

11 Writing Research Reports 327

11.1 Introduction 327

11.2 Tone 328

11.2.1 Language 329

11.2.2 Presentation of Facts 332

11.3 Sections of the Research Report 334

11.3.1 Presentation of Hypothesis 334

Filling a Gap in Knowledge 335

Building on Past Research 336

Contradicting Past Findings 336

Connecting Past Findings 338

11.3.2 Description of Methods 339

Subjects 339

Population 339

Sampling Methods 340

Measures 341

Procedure 342

11.3.3 Presentation of Results 344

11.3.4 Presentation of Conclusions 348

11.4 Conclusion 348

Review Questions 348

Appendixes 353

Appendix A: Z-Score Table 355

Appendix B: Table for Critical χ² Values 357

Appendix C: Table for Critical t Values 359

Appendix D: Table for Critical F Values 361

References 369

Answers to Review Questions 371

Index 391