Full Description
Introduction to Statistics in Criminal Justice and Criminology: A Practical Approach to Calculating, Using, and Interpreting Data provides students with a clear, structured path to the quantitative tools that shape empirical inquiry in the field. Written by an interdisciplinary team spanning criminal justice, psychology, mathematics, and computer science, this textbook emphasizes the practical purposes of statistical thinking while explaining how data is organized, described, compared, and analyzed to answer meaningful research questions.
Each chapter opens with a relatable scenario that frames key concepts, guiding students from foundational topics such as descriptive statistics and normal distributions to applications including hypothesis testing, chi-square analysis, regression, ANOVA, and survival analysis. Step-by-step examples, end-of-chapter problems, and intuitive visual displays reinforce learning. A companion software tool strengthens computational literacy, allowing students to work through calculations aligned with chapter material.
Designed for undergraduate and graduate courses in criminal justice statistics, this textbook supports required quantitative training across criminal justice curricula. Students gain the skills to interpret research findings, evaluate evidence critically, and engage in data-informed study and professional practice throughout their careers.
Contents
About the Authors xiii
Acknowledgements xv
1 Introduction 1
1.1 Statistics 1
1.2 Types of Statistics: Descriptive and Inferential 1
1.3 Basic Statistical Concepts and Terminology 2
1.3.1 Population, Element, Census, and Sample 2
1.3.2 Data and Variables 3
1.3.3 Variable Types 4
1.3.4 Levels of Variables and Scales 4
1.3.5 Nominal Scales 4
1.3.6 Ordinal Scales 5
1.3.7 Interval Scales 6
1.3.8 Ratio Scales 6
1.3.9 Likert Scales 6
1.3.10 The Hierarchy of Measurement Scales 7
1.4 Dependent and Independent Variables 10
1.5 Practical Application of Statistics 11
1.6 Introduction to SAS 11
1.7 Summary 12
1.8 Exercises 12
1.9 Answers to Exercises 14
References 16
2 Organizing and Describing Data 17
2.1 The Jail Report 17
2.2 Organizing and Describing Data 17
2.3 Frequency Distributions 18
2.3.1 Absolute Frequency Distributions 18
2.3.2 Relative Frequency Distributions 19
2.3.3 Relative Frequency Distributions 20
2.3.4 Cumulative Relative Frequency Distributions 22
2.3.5 Interval Frequency Distributions 23
2.3.6 Frequency Distributions in SAS 26
2.4 Visual Techniques 27
2.4.1 Bar Graphs 28
2.4.2 Bar Graphs in SAS 30
2.4.3 Pie Charts 31
2.4.4 Pie Charts in SAS 33
2.4.5 Histograms 33
2.4.6 Histograms in SAS 33
2.4.7 Polygons 35
2.4.8 Polygons in SAS 36
2.5 Properties of Distributions 37
2.5.1 Central Tendency 37
2.5.2 Variability 37
2.5.3 Skewness 37
2.5.4 Kurtosis 39
2.6 Summary 41
2.7 Exercises 42
2.8 Answers to Exercises 43
References 47
3 Comparative Statistics 48
3.1 Re-electing the County Sheriff 48
3.1.1 Comparative Statistics 48
3.1.2 Crime Rates 49
3.1.3 Crime-Specific Rates 51
3.1.4 Percent Change 52
3.2 Trend Analyses 54
3.3 Summary 61
3.4 Importing Data from a Database in SAS 62
3.5 Exercises 62
3.6 Answers to Exercises 65
References 68
4 Descriptive Statistics: Measures of Central Tendency and Variability 69
4.1 Analysis of Domestic Violence Cases 69
4.2 Measures of Central Tendency 69
4.3 Central Tendency 70
4.4 The Mean 70
4.4.1 Calculating the Mean 70
4.4.2 Computing the Mean from Frequency Distributions 72
4.4.3 Estimating the Mean of an Interval Frequency Distribution 73
4.5 The Median 75
4.5.1 Calculating the Median 75
4.5.2 Computing the Median from Frequency Distributions 76
4.5.3 Estimating the Median of an Interval Frequency Distribution 76
4.6 The Mode 76
4.6.1 Calculating the Mode 76
4.6.2 Calculating the Mode from a Frequency Distribution 77
4.6.3 Comparing the Mean, Median, and Mode: Skewness 77
4.7 When to Use Measures of Central Tendency: A Final Word 83
4.7.1 Comparing Mean, Median, and Mode 84
4.8 Characteristics of the Mean and Median 84
4.9 Variability 85
4.10 The Range 86
4.11 Measures of Deviation 87
4.12 Variance 87
4.13 Standard Deviation 88
4.13.1 Standard Deviation from Samples 89
4.13.1.1 When to Use the Sample or Population Standard Deviation 89
4.13.1.2 What Type of Data Should You Use When You Calculate a Standard Deviation? 89
4.14 Calculating Central Tendencies and Variability in SAS 90
4.15 Summary 93
4.16 Exercises 93
4.17 Answers to Exercises 95
5 Normal Distributions 98
5.1 Theoretical Distributions 98
5.1.1 Characterizing Shapes 98
5.2 Normal Distribution PDF 99
5.3 Binomial Distribution PMF 100
5.4 The Standard Normal Distribution 104
5.4.1 Z-Scores 105
5.5 Properties of Z-Scores 106
5.5.1 A Unitless Metric 106
5.5.2 Indication of Relative Standing 107
5.5.3 Standardization 109
5.5.4 Z-Scores and Probability 109
5.5.5 Standard Normal in SAS 114
5.6 Summary 116
5.7 Exercises 116
5.8 Answers to Exercises 117
6 Hypothesis Testing: z- andt-Tests 119
6.1 Introduction 119
6.2 Hypothesis Testing, One Sample z 120
6.2.1 Comparing Means in Hypothesis Testing 120
6.2.2 Sampling Distributions 120
6.2.3 Confidence Intervals (CI) 124
6.2.4 The Central Limit Theorem (CLT) 126
6.2.5 The Sampling Distribution of the Mean and z-Scores 126
6.2.6 The Single Sample z-Test 127
6.2.7 Hypothesis Testing 128
6.2.8 Level of Significance (Alpha) 129
6.2.9 Type I and Type II Errors 130
6.2.10 Type II Error 131
6.2.11 Steps in Testing for Statistical Significance 131
6.3 Hypothesis Testing, One Sample t 131
6.3.1 Single Sample t-Test 131
6.3.2 Hypothesis Testing 132
6.3.3 Degrees of Freedom 132
6.3.4 The Sampling Distribution of t 133
6.3.5 One Sample t-Test and Confidence Intervals in SAS 134
6.3.6 Independent Samples (or Unpaired) t-Test 135
6.3.6.1 Assumptions 137
6.3.6.2 The Steps in Testing the Hypothesis That Two Teaching Methods Do Not Differ in Their Effectiveness 138
6.3.7 Independent Sample t-Test in SAS 139
6.3.8 t-Test for Related (Paired) Samples 139
6.3.8.1 Paired t-Test in SAS 142
6.4 Summary 143
6.5 Exercises 144
6.6 Answers to Exercises 145
7 Analyzing Categorical Data: Chi-Square Test 152
7.1 Comparing Proportions 152
7.1.1 Comparing Proportions-One Sample 152
7.1.2 Confidence Interval for One-Sample Proportions 152
7.1.3 Hypothesis Testing for One-Sample Proportions 153
7.2 Comparing Proportions - Two Samples 155
7.2.1 Confidence Interval for Two-Sample Proportions 155
7.2.2 Hypothesis Test for Two-Sample Proportions 156
7.3 The Chi-Square Test 156
7.3.1 Chi-Square Goodness of Fit Test 157
7.3.2 Chi-Square Goodness of Fit Test in SAS 159
7.3.3 Chi-Square Test of Independence 159
7.3.3.1 Hypotheses for Chi-Square Test of Independence 162
7.3.4 Chi-Square Test of Independence in SAS 164
7.4 Summary 166
7.5 Exercises 166
7.6 Answers to Exercises 167
Reference 175
8 Correlation Coefficient 176
8.1 Relationships Between Variables 176
8.1.1 Pearson Correlation Coefficient 177
8.1.2 Relationships Between Variables 177
8.1.3 Scatter Diagrams 177
8.1.4 Meaning of Covariation 179
8.1.5 Interpretation of Covariance 179
8.1.6 The Calculation of Covariance 180
8.1.7 Finding the Correlation Coefficient Covariance Formula 181
8.1.8 Computational Formula 182
8.1.9 Pearson r as a General Measure of Association 183
8.1.10 The Range and Direction of Pearson's r 184
8.1.11 The Strength of Pearson's r 184
8.1.12 A Picture of Perfection 185
8.2 Interpreting the Meaning and Significance of r 185
8.2.1 The Effect of Outlying Scores on Pearson's r 186
8.2.2 Testing the Statistical Significance of r 186
8.2.3 Using SAS to Calculate Correlations 187
8.2.4 Nonlinear Relationships 188
8.2.5 A Scatterplot Depicting the Nonlinear Relationship Between Anxiety and the Percentage of Target Center Hits During Weapons Qualifications 188
8.2.5.1 Important Messages About Correlation Coefficient 188
8.3 Summary 189
8.4 Exercises 193
8.5 Answers to Exercises 193
9 Linear Regression and Prediction 196
9.1 The Concept of Prediction 196
9.2 Basic Assumptions and Terminology 197
9.2.1 A Linear Regression Problem 197
9.2.2 The Formula for a Straight Line 200
9.2.3 Finding the Regression Line 201
9.3 Linear Regression Using SAS 203
9.3.1 The REG Procedure 204
9.3.2 The Accuracy of Prediction 205
9.3.3 Linear Regression with Z-Scores 207
9.3.4 Taking Another Look at Prediction Error 209
9.4 Multiple Linear Regression 211
9.4.1 Multiple Regression in SAS 216
9.4.1.1 Regression to the Mean 216
9.5 Summary 218
9.6 Exercises 218
9.7 Answers to Exercises 219
Reference 222
10 Analysis of Variance 223
10.1 Introduction 223
10.1.1 Inmate Fights on Tier 3 223
10.2 A Return to Variance 224
10.2.1 The Context For ANOVA 224
10.2.2 ANOVA: Basic Concepts and Terminology 225
10.2.3 ANOVA Terminology and Computational Terms 226
10.2.4 A Simple ANOVA Problem 228
10.3 Steps in Hypothesis Testing 229
10.3.1 Computing ANOVA for the Tier 3 Study 230
10.3.2 Hypotheses 230
10.3.3 Steps in ANOVA Testing 231
10.3.4 The Research Question 231
10.3.5 ANOVA Calculations 231
10.3.6 Conclusion 232
10.3.7 Scores by Treatment Group 232
10.3.8 Assumptions for Conducting ANOVA 234
10.3.9 After ANOVA: Comparing Group Means 235
10.3.10 Computing the Amount of Explained Variance 236
10.4 ANOVA in SAS 237
10.5 Summary 239
10.6 Exercises 239
10.7 Answers to Exercises 241
11 Survival Analysis 249
11.1 Introduction 249
11.1.1 Recidivism Analyses 249
11.1.2 Survival Analysis 249
11.1.3 Censored Data 250
11.2 Survival Function 250
11.2.1 The Kaplan-Meier Method 252
11.2.2 Using SAS to Estimate the Survival Function 255
11.2.3 Log-Rank Test 257
11.2.4 Log-Rank Test in SAS 259
11.2.5 Cox Proportional Model 259
11.2.6 Using SAS to Calculate the Cox Proportional Hazard Model 263
11.3 Summary 263
11.4 Exercises 263
11.5 Answers to Exercises 265
Appendices 268
Index 295
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