A user-friendly, hands-on guide to recognizing and conducting proper research techniques in data collection
Offering a unique approach to numerical research methods, Analyzing Quantitative Data: An Introduction for Social Researchers presents readers with the necessary statistical applications for carrying out the key phases of conducting and evaluating a research project. The book guides readers through the steps of data analysis, from organizing raw data to utilizing descriptive statistics and tests of significance, drawing valid conclusions, and writing research reports. The author successfully provides a presentation that is accessible and hands-on rather than heavily theoretical, outlining the key quantitative processes and the use of software to successfully draw valid conclusions from gathered data.
In its discussion of methods for organizing data, the book includes suggestions for coding and entry into spreadsheets or databases while also introducing commonly used descriptive statistics and clarifying their roles in data analysis. Next, inferential statistics is explored in-depth with explanations of and instructions for performing chi-square tests, t-tests, analyses of variance, correlation and regression analyses, and a number of advanced statistical procedures. Each chapter contains explanations of when to use the tests described, relevant formulas, and sample computations. The book concludes with guidance on extracting meaningful conclusions from statistical tests and writing research reports that describe procedures and analyses.
Throughout the book, Statistical Resources for SPSS® sections provide fundamental instruction for using SPSS® to obtain the results presented. Where necessary, the author provides basic theoretical explanations for distributions and background information regarding formulas. Each chapter concludes with practice problems, and a related website features derivations of the book's formulas along with additional resources for performing the discussed processes.
Analyzing Quantitative Data is an excellent book for social sciences courses on data analysis and research methods at the upper-undergraduate and graduate levels. It also serves as a valuable reference for applied statisticians and practitioners working in the fields of education, medicine, business and public service who analyze, interpret, and evaluate data in their daily work.
Table of Contents:
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
