Measuring Crime

Behind the Statistics

Sharon L. Lohr

• Publisher: Chapman and Hall/CRC
• Year: 2019
• ISBN:
  9780429574948
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Every day, newspapers, magazines, web sites, and social media feature articles about the prevalence of crime. Some of these contradict each other; others use inaccurate statistics. Many people who see wildly diverging statistics conclude that no statistics should be trusted. However, the essence of the statistical discipline is that all statistics should be accompanied by a measure of their accuracy. This book looks at crime statistics from a statistical point of view, and evaluates the different sources of crime statistics with respect to completeness (i.e. missing data), measurement error, and sampling variability. The goal of the book is to promote statistical reasoning about statistics.

CHAPTER 1

Thinking Statistically about Crime

THE HEADLINE of the February 2018 news story drew me in: “94%: Sexual misconduct in Hollywood is staggering.” The story continued:

The first number you see is 94% — and your eyes pop with incredulity. But it’s true: Almost every one of hundreds of women questioned in an exclusive survey by USA TODAY said they have experienced some form of sexual harassment or assault during their careers in Hollywood.

Almost all of the women who participated in the survey said they experienced sexual harassment or assault. But what about women who did not participate?

We can’t tell from this survey. The USA Today story acknowledged this: “As a self-selected sample, it is not scientifically representative of the entire industry.”

Why don’t the results from this survey generalize to all women who work in Hollywood?

•E-mail invitations for the survey were sent only to members of two advocacy organizations: The Creative Coalition, and Women in Film and Television. All survey participants have joined an organization that raises awareness about issues such as public funding for the arts and gender parity in the screen industries. Their experiences and perceptions likely differ from those of non-joiners.

•Altogether, 843 women participated in the survey. The story does not say how many were asked to participate, so we do not know what percentage of women responded to the survey invitation. Often, persons who choose to respond to surveys are particularly engaged in the topic or have strong opinions. The women who responded to the survey invitation may have had different experiences than the women who did not elect to participate.

A survey administered to a conveniently chosen sample is often cheaper and easier to conduct than a survey that is statistically representative. The USA Today survey provided timely context about fall 2017 news stories concerning sexual assault in Hollywood by asking a large number of people about their experiences. It demonstrated that the women who had come forward publicly were not the only ones with accounts of harassment and assault, and gave a voice to the survey participants.

However, the statistics from the survey apply only to the women who participated in it. It is correct to say that 94% of the 843 women who responded to this survey reported having experienced sexual harassment or assault—according to the survey’s definitions and questions about those events—during their careers.

The study does not tell us what percentage of women in Hollywood have been sexually harassed or assaulted. That number might be 94%. It might be something else. The statistical procedures used in the survey do not allow us to assess how accurately the statistics describe all women in Hollywood.

STATISTICAL REASONING

Where do crime statistics come from, and how can you tell whether they are accurate?

Statisticians employ standard principles and procedures to collect data and to calculate and interpret statistics. This book illustrates how those principles apply to data sources and statistics about US crime rates, and tells you what to look for when evaluating a statistic.

The same principles apply to other statistics you encounter, from any field of study: political polls, unemployment rates, transportation use, size of bald eagle populations, agricultural production, diabetes prevalence, literacy rates, health care expenditures— the list goes on.

All statistics about crime, even the ones that appear to be exact counts such as number of homicides, are estimates. Statistical reasoning methods allow us to quantify uncertainty about estimates and tell how accurate they are likely to be.

WHY DO WE NEED ACCURATE CRIME STATISTICS?

You hear about crime all the time. Almost every edition of a newspaper contains at least one crime report. Stories about crime get high ratings—“If it bleeds, it leads”—and it is natural when you see one account after another to think that crime is everywhere.

Stories are memorable. But statistics tell us whether the stories are isolated events or reflect trends in society. When there are no high-quality statistics, people tend to extrapolate from personal experiences (“I know three people who were robbed last year— crime is really going up”) and opinions.

Accurate crime statistics help answer questions such as:

•How much crime has occurred, and what types of crime are increasing or decreasing?

•Who are the victims and offenders?

•What are the costs of crime to victims and to society?

•What crime-prevention and crime-reduction strategies are effective?

•Where should law enforcement resources be allocated?

WHAT IS ACCURACY?

Any discussion of the accuracy of a statistic has to begin with the question: accurate compared to what? Suppose that there existed an omniscient statistician, who knows about every crime that is committed (even the so-called “perfect crimes” that are undetected), and knows the hearts and intentions of every perpetrator and victim. From a statistical point of view, a crime rate calculated by this omniscient statistician is about as good as one can possibly have. We’ll call this rate the “true value.”

But the true value depends on what is defined to be a crime. The USA Today survey described at the beginning of the chapter included nine types of experiences as harassment or assault, ranging from “having someone make unwelcome sexual comments, jokes or gestures about you” to “being forced to do a sexual act.” Different definitions would have led to different answers.

A crime rate statistic has a numerator and a denominator— for example, a violent crime rate might be reported as 382 violent crimes per 100,000 inhabitants of the area. The definition used for crime determines the numerator of a crime rate statistic. Crime rates also depend on who is included in the denominator. Are children included? Prison inmates? Nursing home residents? Members of the armed forces? Some sexual assault statistics consider both sexes; others consider only women; others consider only women who are attending a college or university.

The set of persons or entities to whom the statistics are intended to apply is called the population. We would expect statistics about different populations to differ.

STATISTICAL PROPERTIES

Even if the same crime definitions and populations are used, crime statistics from different sources or samples are expected to vary. Almost every statistic deviates from the true value it estimates, usually for one or more of the following reasons:

Missing data. Almost all data collections fail to obtain some data, and for crime statistics this problem is of particular concern because often the missing data belong to crime victims. Undetected murders (such as deaths mistakenly ascribed to natural causes) will cause homicide statistics to be too low. Robberies not reported to the police will be missing from the law enforcement statistics for that crime.

Some surveys ask people about criminal victimizations they have experienced. If persons who are willing to answer the survey questions are more likely to be crime victims than those who decline to participate, then the victimization rate estimated from the survey data may be too high. The survey estimates may be too low if persons who agree to participate in the survey are less likely to be crime victims than persons who are asked to be in the survey but do not take part.

Measurement error. Measurement error occurs when an entry in the data set differs from the true value. Misclassifying a robbery as a purse-snatching is an example of a measurement error in police records. In surveys, measurement errors can occur because a question is worded confusingly or is misinterpreted, or because one interviewer might elicit a different response than another interviewer, or because the person responding to the survey does not tell the truth or has faulty memory.

Statisticians use the term “error” for anything that causes a statistic to deviate from its true value, but measurement errors should not be interpreted to mean “mistakes.” Rather, they should be viewed as sources of uncertainty about statistics. Some measurement errors are indeed the result of mistakes, as when someone types the wrong value in the database, but others can occur simply because people interpret a question in various ways.

Sampling variability. Some crime statistics come from randomly selected samples of households, persons, businesses, or records. The statistic calculated depends on the particular sample that was drawn. If a different sample had been drawn, a different value of the statistic would have been obtained, and that leads to variability from sample to sample.

If you have taken a statistics class, sampling variability is probably the type of error you learned about—and it is often the only measure of uncertainty that is reported for crime statistics. But effects of missing data and measurement errors should also be considered when interpreting a statistic.

WHAT THIS BOOK IS ABOUT

This book is about the statistical ideas needed to interpret statistics about crime rates: definitions of crime, populations, missing data, measurement error, and variability.

These factors affect all statistics. The two national sources of homicide statistics—one set obtained from death certificates and the other from law enforcement agency reports—show parallel trends over time but have different numbers of homicides. Chapter 2 outlines some of the reasons for these differences, including different definitions, missing data, and classification error.

Law enforcement agency statistics on crimes such as assault and burglary are also estimates. The Federal Bureau of Investigation (FBI) collects and tabulates statistics from US law enforcement agencies on violent and property crimes. The statistic on the back cover about violent crime decreasing by 0.9 percent from 2016 to 2017 comes from the FBI’s Uniform Crime Reporting System discussed in Chapter 3. The chapter describes crime classification errors and some of the statistical methods that can be used to measure and reduce them.

Of course, the FBI statistics include only crimes that are known to and recorded by the police. These statistics cannot tell us about crimes that are not reported to the police.

Surveys, however, can provide information on crimes not known to the police. They ask people about crimes that happened to them, and then ask whether they reported those crimes to the police. The US National Crime Victimization Survey (NCVS), the subject of Chapters 4 through 6, has surveyed US residents age 12 and older every year since 1973.

The NCVS is just one of many surveys that have been taken about crime. Some surveys give more accurate estimates than others. Chapter 5 explains why results from randomly selected samples can be generalized to a population and describes the procedure used to select the NCVS sample.

Chapter 6 describes the weighting methods used to try to compensate for missing data from persons who do not respond to a survey. It also discusses measurement errors in surveys: how do you ask questions and conduct the survey to elicit accurate responses?

Chapter 7 summarizes the statistical principles from the first six chapters, distilling them into eight questions that you can ask to assess the quality of any statistic you encounter. The remaining chapters of the book apply the...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Table of Contents
• Preface
• CHAPTER 1 ■ Thinking Statistically about Crime
• CHAPTER 2 ■ Homicide
• CHAPTER 3 ■ Police Statistics
• CHAPTER 4 ■ National Crime Victimization Survey
• CHAPTER 5 ■ Sampling Principles and the NCVS
• CHAPTER 6 ■ NCVS Measurement and Missing Data
• CHAPTER 7 ■ Judging the Quality of a Statistic
• CHAPTER 8 ■ Sexual Assault
• CHAPTER 9 ■ Fraud and Identity Theft
• CHAPTER 10 ■ Big Data and Crime Statistics
• CHAPTER 11 ■ Crime Statistics, 1915 and Beyond
• Glossary and Acronyms
• For Further Reading
• Index