Basic Statistics in Criminology and Criminal Justice

Description

Preface Acknowledgments Contents About the Authors Chapter 1: Introduction: Statistics as a Research Tool The Purpose of Statistics Is to Clarify Statistics Are Used to Solve Problems Basic Principles Apply Across Statistical Techniques The Uses of Statistics Descriptive Statistics Inferential Statistics Chapter Summary Key Terms References Chapter 2: Measurement: The Basic Building Block of Research Science and Measurement: Classification as a First Step in Research Levels of Measurement Nominal Scales Ordinal Scales Interval and Ratio Scales Relating Interval, Ordinal, and Nominal Scales: The Importance of Collecting Data at the Highest Level Possible What Is a Good Measure? Chapter Summary Key Terms Exercises Computer Exercises SPSS Stata R Problems References Chapter 3: Representing and Displaying Data Frequency Distributions, Bar Charts, and Histograms The Bar Chart The Grouped Bar Chart Histograms for Continuous and Discrete Data Box plots for Interval and Ratio Data Time Series Data Chapter Summary Key Terms Symbols and Formulas Exercises Computer Exercises SPSS Frequency Distributions and Histograms Bar Charts Line Graphs Stata Frequency Distributions and Histograms Bar Charts Line Graphs R Frequency Distributions and Histograms Bar Charts Line Graphs Problems References Chapter 4: Describing the Typical Case: Measures of Central Tendency The Mode: Central Tendency in Nominal Scales The Median: Taking into Account Position The Mean: Adding Value to Position Comparing Results Gained Using the Mean and Median Other Characteristics of the Mean Using the Mean for Non-interval/Ratio Scales Statistics in Practice: Comparing the Median and the Mean Chapter Summary Key Terms Symbols and Formulas Exercises Computer Exercises SPSS Recoding Variables in SPSS Identifying Outliers in SPSS Stata Recoding Variables in Stata Identifying Outliers in Stata R Recoding Variables and Missing Values in R Identifying Outliers in R Problems References Chapter 5: How Typical Is the Typical Case? Measuring Dispersion Measures of Dispersion for Nominal- and Ordinal-Level Data The Proportion in the Modal Category The Percentage in the Modal Category The Variation Ratio Index of Qualitative Variation Measuring Dispersion in Interval/Ratio Scales: The Range, Interquartile Range, Variance, and Standard Deviation The Variance The Standard Deviation Characteristics of the Variance and Standard Deviation The Coefficient of Relative Variation A Note on the Mean Deviation Chapter Summary Key Terms Symbols and Formulas Exercises Computer Exercises SPSS Stata R Problems Reference Chapter 6: The Logic of Statistical Inference: Making Statements About Populations from Sample Statistics The Dilemma: Making Statements About Populations from Sample Statistics The Research Hypothesis The Null Hypothesis Risks of Error in Hypothesis Testing Risks of Error and Statistical Levels of Significance Departing from Conventional Significance Criteria Chapter Summary Key Terms Symbols Exercises References Chapter 7: Defining the Observed Significance Level of a Test: A Simple Example Using the Binomial Distribution The Fair Coin Toss Sampling Distributions and Probability Distributions The Multiplication Rule Different Ways of Getting Similar Results Solving More Complex Problems The Binomial Distribution Using the Binomial Distribution to Estimate the Observed Significance Level of a Test Chapter Summary Key Terms Symbols and Formulas Exercises Computer Exercises SPSS Stata R Problems Chapter 8: Steps in a Statistical Test: Using the Binomial Distribution to Make Decisions About Hypotheses The Problem: The Impact of Problem-Oriented Policing on Disorderly Activity at Violent-Crime Hot Spots Assumptions: Laying the Foundations for Statistical Inference Level of Measurement Shape of the Population Distribution Sampling Method The Hypotheses Hypotheses Stating All of the Assumptions Assumptions Hypotheses Selecting a Sampling Distribution Significance Level and Rejection Region Choosing a One-Tailed or a Two-Tailed Rejection Region The Test Statistic Making a Decision Chapter Summary Key Terms Exercises Computer Exercises SPSS Stata R Problems References Chapter 9: Chi-Square: A Test Commonly Used for Nominal-Level Measures Testing Hypotheses Concerning the Roll of a Die The Chi-Square Distribution Calculating the Chi-Square Statistic Linking the Chi-Square Statistic to Probabilities: The Chi-Square Table A Substantive Example: The Relationship Between Assault Victims and Offenders The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Relating Two Nominal-Scale Measures in a Chi-Square Test A Substantive Example: Type of Sanction and Recidivism Among Convicted White-Collar Criminals The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Extending the Chi-Square Test to Multicategory Variables: The Example of Cell Allocations in Prison The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Extending the Chi-Square Test to a Relationship Between Two Ordinal Variables: Identification with Fathers and Delinquent Acts The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision The Use of Chi-Square When Samples Are Small: A Final Note Chapter Summary Key Terms Symbols and Formulas Exercises Computer Exercises SPSS Stata R Problems References Chapter 10: The Normal Distribution and Its Application to Tests of Statistical Significance The Normal Frequency Distribution (Normal Curve) Characteristics of the Normal Frequency Distribution z-Scores Developing Tests of Statistical Significance Based on the Standard Normal Distribution: The Single-Sample z-Test for Known Pop... The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Applying Normal Sampling Distributions to Non-normal Populations Comparing a Sample to an Unknown Population: The Single-Sample z-Test for Proportions Computing the Mean and Standard Deviation for the Sampling Distribution of a Proportion Testing Hypotheses with the Normal Distribution: The Case of a New Prison Program The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Limitations of the z-Test on a Proportion Comparing a Sample to an Unknown Population: The Single-Sample t-Test for Means Testing Hypotheses with the t Distribution The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Confidence Intervals Constructing Confidence Intervals Confidence Intervals for Sample Means Confidence Intervals for Sample Proportions Chapter Summary Key Terms Symbols and Formulas Exercises References Chapter 11: Comparing Means and Proportions in Two Samples to Test Hypotheses About Population Parameters Comparing Means The Case of Anxiety Among Police Officers and Firefighters The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Constructing Confidence Intervals for Differences of Means Bail in Los Angeles County: Another Example of the Two-Sample t-Test for Hypotheses About Population Mean Differences The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Sensitivity Analysis Comparing Proportions: The Two-Sample z-Test for Differences Between Population Proportions The Case of Drug Testing and Pretrial Misconduct The Sampling Distribution Significance Level and Rejection Region The Decision The t-Test for Dependent (Paired) Samples The Effect of Police Presence on High-Crime Street Segments The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Nonparametric Alternative to the t-Test Mann-Whitney U: Nonparametric Test for Two Independent Samples Bail in Los Angeles County Redux: The Mann-Whitney U Wilcoxon Signed-Rank Test for Dependent Samples The Effect of Police Presence Near High-Crime Street Segments Redux: The Wilcoxon Signed-Rank Test Effect Size Measures for Comparing Two Means: Cohen´s d A Note on Using the t-Test for Ordinal Scales with a Limited Number of Categories Chapter Summary Key Terms Symbols and Formulas Exercises Computer Exercises SPSS Independent Sample t-Test Dependent Sample t-Test Stata Independent Sample t-Test Dependent Sample t-Test R Independent Sample t-Test Dependent Sample t-Test Problems References Chapter 12: Comparing Means Among More Than Two Samples to Test Hypotheses about Populations: Analysis of Variance Analysis of Variance Computing the Variance Between and Within Groups A Substantive Example: Age and White-Collar Crimes The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Another ANOVA Example: Race and Bail Amounts Among Felony Drug Defendants The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Defining the Strength of the Relationship Observed Making Pairwise Comparisons Between the Groups Studied Tukey´s Honestly Significant Difference (HSD) Test Bonferroni Post Hoc Pairwise t-Tests A Nonparametric Alternative: The Kruskal-Wallis Test The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Chapter Summary Key Terms Symbols and Formulas Exercises Computer Exercises SPSS ANOVA Tukey´s HSD Kruskal-Wallis Test Stata ANOVA Tukey´s HSD Kruskal-Wallis Test R ANOVA Tukey´s HSD Kruskal-Wallis Test Problems References Chapter 13: Measures of Association for Nominal and Ordinal Variables Distinguishing Statistical Significance and Strength of Relationship: The Example of the Chi-Square Statistic Measures of Association for Nominal Variables Measures of Association Based on the Chi-Square Statistic The Phi Coefficient The Risk Ratio and Odds Ratio Cramer´s V Proportional Reduction in Error Measures: Tau and Lambda Statistical Significance of Measures of Association for Nominal Variables The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Measures of Association for Ordinal-Level Variables Gamma Kendall´s τb and τc Somers´ d A Substantive Example: Affectional Identification with Father and Level of Delinquency Note on the Use of Measures of Association for Ordinal Variables Statistical Significance of Measures of Association for Ordinal Variables The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Choosing the Best Measure of Association for Nominal- and Ordinal-Level Variables Chapter Summary Key Terms Symbols and Formulas Exercises Computer Exercises SPSS Stata R Problems References Chapter 14: Measuring Association for Scaled Data: Pearson´s Correlation Coefficient Measuring Association Between Two Interval- or Ratio-Level Variables Pearson´s Correlation Coefficient The Calculation A Substantive Example: Crime and Unemployment in California Nonlinear Relationships and Pearson´s r Beware of Outliers Spearman´s Correlation Coefficient Testing the Statistical Significance of Pearson´s r Statistical Significance of r: The Case of Age and Number of Arrests The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Statistical Significance of r: Unemployment and Crime in California The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Testing the Statistical Significance of Spearman´s r The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Using Pearson´s r When One or Both Variables are Dichotomous or Ordinal The Correlation Coefficient for Two Dichotomous Variables The Correlation Coefficient for One Dichotomous Variable and One Interval- or Ratio-level Variable Confidence Intervals for the Correlation Coefficient Chapter Summary Key Terms Symbols and Formulas Exercises Computer Exercises SPSS Correlation Coefficients Scatter plots Stata Correlation Coefficients Scatter plots R Correlation Coefficients Scatter plots Problems References Chapter 15: An Introduction to Bivariate Regression Estimating the Influence of One Variable on Another: The Regression Coefficient Calculating the Regression Coefficient A Substantive Example: Unemployment and Burglary in California Prediction in Regression: Building the Regression Line The Y-Intercept The Regression Line Predictions Beyond the Distribution Observed in a Sample Predicting Burglary Rates from Unemployment Rates in California Choosing the Best Line of Prediction Based on Regression Error Evaluating the Regression Model Percent of Variance Explained Percent of Variance Explained: Unemployment Rates and Burglary Rates in California Statistical Significance of the Regression Coefficient: The Case of Age and Number of Arrests The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision Testing the Statistical Significance of the Regression Coefficient for Unemployment Rates and Burglary Rates in California The Sampling Distribution Significance Level and Rejection Region The Test Statistic The Decision The F-Test for the Overall Regression Age and Number of Arrests Unemployment Rates and Burglary Rates in California Chapter Summary Key Terms Symbols and Formulas Exercises Computer Exercises SPSS Stata R Problems Reference Appendix 1: Factorials Appendix 2: Appendix 3: Areas of the Appendix 4: Appendix 5: Appendix 6: Critical Appendix 7: Appendix 8: Fisher Index