What You'll Learn
The Concept
Numbers give criminal justice debates an appearance of precision that the underlying data often do not support. A city that reports 500 homicides sounds more dangerous than one that reports 200 — until you learn that the first city has four times the population. Raw counts without denominators are nearly meaningless for comparison.
A crime rate expresses the number of crimes per unit of population, typically per 100,000 residents. This allows comparisons across jurisdictions of different sizes. But the choice of denominator matters. A city's residential population may undercount the people actually present — commuters, tourists, and visitors are exposed to crime but not counted in the denominator. Researchers sometimes use ambient population estimates to address this problem.
Rates can also be misleading when the underlying counts are small. A county that records two homicides one year and four the next has experienced a 100 percent increase — a figure that sounds alarming but reflects a change of two events. Small-number instability is a persistent problem in local crime statistics, particularly for rare offenses.
Statistical significance answers a narrow question: how likely is it that an observed result would occur by chance if there were actually no effect? A p-value below 0.05 is conventionally treated as statistically significant, meaning the result would occur by chance less than 5 percent of the time under the null hypothesis. This threshold is arbitrary and widely misunderstood. A statistically significant result is not necessarily important, and a non-significant result does not prove that no effect exists.
A confidence interval provides a range of values within which the true population parameter likely falls, given the sample data and a specified confidence level. A 95 percent confidence interval does not mean there is a 95 percent probability that the true value falls within that range — it means that if the study were repeated many times, 95 percent of the resulting intervals would contain the true value. Wide confidence intervals reflect uncertainty; narrow intervals reflect precision.
Effect size measures the magnitude of a relationship or difference, independent of sample size. A large study can detect a very small effect with high statistical significance. Whether that effect is large enough to matter — to justify a policy change, a budget allocation, or a program expansion — is a substantive judgment, not a statistical one. Cohen's d, odds ratios, and relative risk are common effect-size measures in criminal justice research.
Correlation describes the statistical association between two variables. When crime rates and ice cream sales both rise in summer, they are correlated — but ice cream does not cause crime. Both are driven by a third variable: warm weather and increased outdoor activity. Confounding is the rule rather than the exception in observational criminal justice research, which is why establishing causation requires more than demonstrating an association.
Base rates are frequently ignored in criminal justice policy debates. If a risk-assessment instrument correctly identifies 80 percent of people who will reoffend, it sounds impressive — until you learn that only 10 percent of the population actually reoffends. In that case, the instrument will generate many false positives: people flagged as high-risk who would not have reoffended. Understanding base rates is essential for evaluating predictive tools, screening programs, and profiling strategies.
Selective presentation of statistics is common in advocacy and policy debates. Relative risk figures — 'twice as likely' — sound dramatic but may reflect a small absolute difference. Absolute risk figures — 'an increase from 1 percent to 2 percent' — provide context. Cherry-picking time periods, comparison jurisdictions, or outcome measures can make almost any policy appear successful or unsuccessful. Students should ask: what time period was selected, what comparison was used, and what outcomes were measured?
Applied Example: Interpreting a Use-of-Force Disparity Report
A city releases a report showing that Black residents are stopped by police at three times the rate of white residents. A critic argues this proves racial bias. A defender argues it reflects differences in crime rates by neighborhood. Both claims require further analysis. The relevant questions include: Are stops being compared to residential population, crime rates, or some other benchmark? Are the neighborhoods being compared similar in other relevant respects? What is the outcome of the stops — are they producing arrests, or are most stops resulting in no action? Statistics describe a pattern; they do not by themselves explain it.
Why It Matters
For Police Officers
Officers who understand statistics can evaluate departmental reports, research findings, and media coverage critically. When a study claims that a new program reduced crime by 40 percent, understanding rates, denominators, and effect sizes helps officers assess whether the claim is meaningful.
For Students
Statistical literacy is a core competency for criminal justice students. Policy debates about policing, sentencing, and corrections are saturated with statistics that are frequently misrepresented. Students who can evaluate these claims independently are better prepared for graduate study, policy work, and professional practice.
Think About It
A news report states that violent crime increased 50 percent in a city last year. What additional information would you need before concluding that the city has become significantly more dangerous?
Why is a statistically significant result not necessarily a practically important one? Give an example from criminal justice.
How can the same disparity data be used to support opposite conclusions in a policy debate? What does this suggest about the role of statistics in criminal justice advocacy?
What is the difference between relative risk and absolute risk, and why does the distinction matter for evaluating criminal justice programs?
How should a researcher account for small-number instability when reporting crime trends in a small jurisdiction?
Sources & Further Reading
Huff, D. (1954). How to Lie with Statistics. W. W. Norton.
Weisburd, D., & Britt, C. (2014). Statistics in Criminal Justice (4th ed.). Springer.
Bureau of Justice Statistics. (2023). Criminal Victimization, 2022. U.S. Department of Justice. https://bjs.ojp.gov/library/publications/criminal-victimization-2022
Gelman, A., & Loken, E. (2014). The statistical crisis in science. American Scientist, 102(6), 460–465.
Zimring, F. E. (2007). The Great American Crime Decline. Oxford University Press.
Lum, C., Koper, C. S., & Telep, C. W. (2011). The evidence-based policing matrix. Journal of Experimental Criminology, 7(1), 3–26.