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Statistics for Criminology and Criminal Justice Statistics for Criminology and Criminal Justice Third Edition 2 3 Statistics for Criminology and Criminal Justice Third Edition Jacinta M. Gau University of Central Florida 4 FOR INFORMATION: SAGE Publications, Inc. 2455 Teller Road Thousand Oaks, California 91320 E-mail: [email protected] SAGE Publications Ltd. 1 Oliver’s Yard 55 City Road London EC1Y 1SP United Kingdom SAGE Publications India Pvt. Ltd. B 1/I 1 Mohan Cooperative Industrial Area Mathura Road, New Delhi 110 044 India SAGE Publications Asia-Pacific Pte. Ltd. 3 Church Street #10–04 Samsung Hub Singapore 049483 Copyright © 2019 by SAGE Publications, Inc. All rights reserved. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. Printed in the United States of America Library of Congress Cataloging-in-Publication Data Names: Gau, Jacinta M., author. Title: Statistics for criminology and criminal justice / Jacinta M. Gau, University of Central Florida. Description: Third edition. | Los Angeles : SAGE, [2019] | Includes bibliographical references and index. Identifiers: LCCN 2017045048 | ISBN 9781506391786 (pbk. : alk. paper) Subjects: LCSH: Criminal statistics. | Statistical methods. Classification: LCC HV7415 .G38 2019 | DDC 519.5—dc23 LC record available at https://lccn.loc.gov/2017045048 All trademarks depicted within this book, including trademarks appearing as part of a screenshot, figure, or other image are included solely for the purpose of illustration and are the property of their respective holders. The use of the trademarks in no way indicates any relationship with, or endorsement by, the holders of said trademarks. SPSS is a registered trademark of International Business Machines Corporation. This book is printed on acid-free paper. Acquisitions Editor: Jessica Miller Editorial Assistant: Rebecca Lee e-Learning Editor: Laura Kirkhuff Production Editor: Karen Wiley Copy Editor: Alison Hope 5 https://lccn.loc.gov/2017045048 Typesetter: C&M Digitals (P) Ltd. Proofreader: Wendy Jo Dymond Indexer: Beth Nauman-Montana Cover Designer: Janet Kiesel Marketing Manager: Jillian Oelsen 6 Brief Contents Preface to the Third Edition Acknowledgments About the Author Part I Descriptive Statistics Chapter 1 Introduction to the Use of Statistics in Criminal Justice and Criminology Chapter 2 Types of Variables and Levels of Measurement Chapter 3 Organizing, Displaying, and Presenting Data Chapter 4 Measures of Central Tendency Chapter 5 Measures of Dispersion Part II Probability and Distributions Chapter 6 Probability Chapter 7 Population, Sample, and Sampling Distributions Chapter 8 Point Estimates and Confidence Intervals Part III Hypothesis Testing Chapter 9 Hypothesis Testing: A Conceptual Introduction Chapter 10 Hypothesis Testing With Two Categorical Variables: Chi-Square Chapter 11 Hypothesis Testing With Two Population Means or Proportions Chapter 12 Hypothesis Testing With Three or More Population Means: Analysis of Variance Chapter 13 Hypothesis Testing With Two Continuous Variables: Correlation Chapter 14 Introduction to Regression Analysis Appendix A Review of Basic Mathematical Techniques Appendix B Standard Normal (z) Distribution Appendix C t Distribution Appendix D Chi-Square (χ²) Distribution Appendix E F Distribution Glossary Answers to Learning Checks Answers to Review Problems References Index 7 Detailed Contents Preface to the Third Edition Acknowledgments About the Author Part I Descriptive Statistics Chapter 1 Introduction to the Use of Statistics in Criminal Justice and Criminology ▶ Research Example 1.1: What Do Criminal Justice and Criminology Researchers Study? ▶ Data Sources 1.1: The Uniform Crime Reports ▶ Data Sources 1.2: The National Crime Victimization Survey Science: Basic Terms and Concepts Types of Scientific Research in Criminal Justice and Criminology Software Packages for Statistical Analysis Organization of the Book Review Problems Chapter 2 Types of Variables and Levels of Measurement Units of Analysis Independent Variables and Dependent Variables ▶ Research Example 2.1: Choosing Variables for a Study on Police Use of Conductive Energy Devices ▶ Research Example 2.2: Units of Analysis Relationships Between Variables: A Cautionary Note ▶ Research Example 2.3: The Problem of Omitted Variables Levels of Measurement The Categorical Level of Measurement: Nominal and Ordinal Variables ▶ Data Sources 2.1: The Police–Public Contact Survey ▶ Data Sources 2.2: The General Social Survey The Continuous Level of Measurement: Interval and Ratio Variables ▶ Data Sources 2.3: The Bureau of Justice Statistics Chapter Summary Review Problems Chapter 3 Organizing, Displaying, and Presenting Data Data Distributions Univariate Displays: Frequencies, Proportions, and Percentages Univariate Displays: Rates Bivariate Displays: Contingency Tables ▶ Data Sources 3.1: The Census of Jails ▶ Research Example 3.1: Does Sexual-Assault Victimization Differ Between Female and Male Jail Inmates? Do Victim Impact Statements Influence Jurors’ Likelihood of 8 Sentencing Murder Defendants to Death? Graphs and Charts Categorical Variables: Pie Charts ▶ Data Sources 3.2: The Law Enforcement Management and Administrative Statistics Survey Categorical Variables: Bar Graphs Continuous Variables: Histograms ▶ Research Example 3.2: Are Women’s Violent-Crime Commission Rates Rising? Continuous Variables: Frequency Polygons Longitudinal Variables: Line Charts Grouped Data ▶ Data Sources 3.3: CQ Press’s State Factfinder Series SPSS Chapter Summary Review Problems Chapter 4 Measures of Central Tendency The Mode ▶ Research Example 4.1: Are People Convicted of Homicide More Violent in Prison Than People Convicted of Other Types of Offenses? Do Latino Drug Traffickers’ National Origin and Immigration Status Affect the Sentences They Receive? The Median The Mean ▶ Research Example 4.2: How Do Offenders’ Criminal Trajectories Impact the Effectiveness or Incarceration? Can Good Parenting Practices Reduce the Criminogenic Impact of Youths’ Time Spent in Unstructured Activities? Using the Mean and Median to Determine Distribution Shape Deviation Scores and the Mean as the Midpoint of the Magnitudes SPSS Chapter Summary Review Problems Chapter 5 Measures of Dispersion The Variation Ratio The Range The Variance The Standard Deviation The Standard Deviation and the Normal Curve ▶ Research Example 5.1: Does the South Have a Culture of Honor That Increases Gun Violence? Do Neighborhoods With Higher Immigrant Concentrations Experience More Crime? ▶ Research Example 5.2: Why Does Punishment Often Increase—Rather Than Reduce— 9 Criminal Offending? SPSS Chapter Summary Review Problems Part II Probability and Distributions Chapter 6 Probability Discrete Probability: The Binomial Probability Distribution ▶ Research Example 6.1: Are Police Officers Less Likely to Arrest an Assault Suspect When the Suspect and the Alleged Victim Are Intimate Partners? Successes and Sample Size: N and r The Number of Ways r Can Occur, Given N: The Combination The Probability of Success and the Probability of Failure: p and q Putting It All Together: Using the Binomial Coefficient to Construct the Binomial Probability Distribution Continuous Probability: The Standard Normal Curve ▶ Research Example 6.2: What Predicts Correctional Officers’ Job Stress and Job Satisfaction? The z Table and Area Under the Standard Normal Curve Chapter Summary Review Problems Chapter 7 Population, Sample, and Sampling Distributions Empirical Distributions: Population and Sample Distributions Theoretical Distributions: Sampling Distributions Sample Size and the Sampling Distribution: The z and t Distributions Chapter Summary Review Problems Chapter 8 Point Estimates and Confidence Intervals The Level of Confidence: The Probability of Being Correct Confidence Intervals for Means With Large Samples Confidence Intervals for Means With Small Samples ▶ Research Example 8.1: Do Criminal Trials Retraumatize Victims of Violent Crimes? ▶ Data Sources 8.1: The Firearm Injury Surveillance Study, 1993–2013 Confidence Intervals With Proportions and Percentages ▶ Research Example 8.2: What Factors Influence Repeat Offenders’ Completion of a “Driving Under the Influence” Court Program? How Extensively Do News Media Stories Distort Public Perceptions About Racial Minorities’ Criminal Involvement? ▶ Research Example 8.3: Is There a Relationship Between Unintended Pregnancy and Intimate Partner Violence? Why Do Suspects Confess to Police? Chapter Summary 10 Review Problems Part III Hypothesis Testing Chapter 9 Hypothesis Testing: A Conceptual Introduction Sample Statistics and Population Parameters: Sampling Error or True Difference? Null and Alternative Hypotheses Chapter Summary Review Problems Chapter 10 Hypothesis Testing With Two Categorical Variables: Chi-Square ▶ Research Example 10.1: How Do Criminologists’ and Criminal Justice Researchers’ Attitudes About the Criminal Justice System Compare to the Public’s Attitudes? Conceptual Basis of the Chi-Square Test: Statistical Dependence and Independence The Chi-Square Test of Independence ▶ Research Example 10.2: Do Victim or Offender Race Influence the Probability That a Homicide Will Be Cleared and That a Case Will Be Tried as Death-Eligible? Measures of Association SPSS Chapter Summary Review Problems Chapter 11 Hypothesis Testing With Two Population Means or Proportions ▶ Research Example 11.1: Do Multiple Homicide Offenders Specialize in Killing? Two-Population Tests for Differences Between Means: t Tests Independent-Samples t Tests ▶ Data Sources 11.1: Juvenile Defendants in Criminal Courts Dependent-Samples t Tests ▶ Research Example 11.2: Do Mentally Ill Offenders’ Crimes Cost More? ▶ Research Example 11.3: Do Targeted Interventions Reduce Crime? Two-Population Tests for Differences Between Proportions ▶ Research Example 11.4: Does the Gender Gap in Offending Rates Differ Between Male and Female Drug Abusers? SPSS Chapter Summary Review Problems Chapter 12 Hypothesis Testing With Three or More Population Means: Analysis of Variance ANOVA: Different Types of Variances ▶ Research Example 12.1: Do Asian Defendants Benefit From a “Model Minority” Stereotype? ▶ Research Example 12.2: Are Juveniles Who Are Transferred to Adult Courts Seen as More Threatening? When the Null Is Rejected: A Measure of Association and Post Hoc Tests ▶ Research Example 12.3: Does Crime Vary Spatially and Temporally in Accordance With 11 Routine Activities Theory? SPSS Chapter Summary Review Problems Chapter 13 Hypothesis Testing With Two Continuous Variables: Correlation ▶ Research Example 13.1: Part 1: Is Perceived Risk of Internet Fraud Victimization Related to Online Purchases? ▶ Research Example 13.2: Do Prisoners’ Criminal Thinking Patterns Predict Misconduct? Do Good Recruits Make Good Cops? Beyond Statistical Significance: Sign, Magnitude, and Coefficient of Determination SPSS ▶ Research Example 13.1, Continued: Part 2: Is Perceived Risk of Internet Fraud Victimization Related to Online Purchases? Chapter Summary Review Problems Chapter 14 Introduction to Regression Analysis One Independent Variable and One Dependent Variable: Bivariate Regression Inferential Regression Analysis: Testing for the Significance of b Beyond Statistical Significance: How Well Does the Independent Variable Perform as a Predictor of the Dependent Variable? Standardized Slope Coefficients: Beta Weights The Quality of Prediction: The Coefficient of Determination Adding More Independent Variables: Multiple Regression ▶ Research Example 14.1: Does Childhood Intelligence Predict the Emergence of Self- Control? Ordinary Least Squares Regression in SPSS ▶ Research Example 14.2: Does Having a Close Black Friend Reduce Whites’ Concerns About Crime? ▶ Research Example 14.3: Do Multiple Homicide Offenders Specialize in Killing? Alternatives to Ordinary Least Squares Regression ▶ Research Example 14.4: Is Police Academy Performance a Predictor of Effectiveness on the Job? Chapter Summary Review Problems Appendix A Review of Basic Mathematical Techniques Appendix B Standard Normal (z) Distribution Appendix C t Distribution Appendix D Chi-Square (c²) Distribution Appendix E F Distribution Glossary 12 Answers to Learning Checks Answers to Review Problems References Index 13 Preface to the Third Edition In 2002, James Comey, the newly appointed U.S. attorney for the Southern District of New York who would later become the director of the Federal Bureau of Investigation, entered a room filled with high-powered criminal prosecutors. He asked the members of the group to raise their hands if they had never lost a case. Proud, eager prosecutors across the room threw their hands into the air, expecting a pat on the back. Comey’s response befuddled them. Instead of praising them, he called them chickens (that is not quite the term he used, but close enough) and told them the only reason they had never lost is that the

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