Introduction
At first glance, census data should be unrelated to public safety data. At its heart, the U.S. Census Bureau gathers population data.1 However, population data provides important context for understanding other measured quantities. Moreover, it allows comparisons between cities, counties, or states, of varying size.
The Census Bureau recently released a new set of population estimates last month. For many uses, a location’s total population is adequate. Nevertheless, for specific research applications, it can be useful to separate the population by age, sex, and race. Data can be obtained using American FactFinder2 or its data directory3 At present, here is what is available for 2016:
- At the state level, population estimates are divided by sex, race, Hispanic origin, and
individual year of age.
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- At the county level, population estimates are divided by sex, race, and
age group.
Ages are usually grouped into 5-year increments: 0-4, 5-9, etc.
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- At the place level (city, town, etc), total population is available. download
Census data becomes the basis for converting counts to “rates.” These are just variations of percentages, often for situations that are rather infrequent. In other words, some events are counted, divided by the total population, and then multiplied by the appropriate power of 10. The rarer the event, the higher the power of ten.
Examples
Rates derived using census data have many applications. Here are a few examples with approximately half focusing on public safety settings.
Crime. As discussed in previous posts, each law enforcement agency provides its annual crime reports to the FBI. There is no valid basis to directly comparing total crime in different cities of varying sizes, or between a municipaltiy and a state or national average, without first converting to a standardized rate (crimes per 100,000).
Incarceration. Nationally reported crimes and other offenses can lead to arrest and eventual imprisonment. The Bureau of Justice Statistics measures the number of persons in local jails, and in state and federal prisons. This is converted to an incarceration rate measured per 100,000 residents. Adults and juveniles are measured separately. In addition, probation and parole is also measured as a community supervision rate. The bureau’s report titled Correctional Populations in the United States shows rates analyzed by state and gender. Similar information can be obtained at The Sentencing Project which also focuses on racial disparities in incarceration rates.
Foster care. Through no fault of their own, children may be removed from their homes and placed into the foster care system. The U.S. Department of Health and Human Services’ Children’s Bureau monitors the number of children in the foster care system on an annual basis as well as the number of children entering foster care each year. Researchers use the census bureau’s population estimates for children to convert foster care counts to rates measured per 1,000 children. These rates vary by location, both between states and among counties within the same state. There are also obvious differences in the rates of children entering foster care by age. The Kids Count Data Center has a well-designed site that includes foster care data, including rates for each state.
Fire fatality. Switching from examples of crime and child placement to a different aspect of public safety, let’s take a look at the fire service. Overall fire deaths are quite rare. The U.S. Fire Administration reports on both firefighter and civilian fire fatalities. (Civilian) Fire Death Rates are measured as deaths per million population. In 2014, there were 3,428 fire deaths, or a fire death rate of 10.7 deaths per million people. If you follow the link, you will notice a section separating fire rates by age, clearly relying on groups used by standard census data.
The USFA’s comprehensive report on Fire in the United States provides even greater detail on fire death rates separated by gender and race. Data downloadInfant mortality. Continuing the last example’s fixation on death, infant mortality is a measure of child welfare that has been used internationally for at least half a century. This mortality rate measures infant deaths per 1,000 live births. The national infant mortality rates is 5.9 per 1,000 births. The Centers for Disease Control and Prevention’s (CDC) National Center for Health Statistics shows variation in infant mortality rates by state. Here’s an alternate graphic at America’s Health Rankings.
Lyme disease. True to its name, the CDC maintains a system to monitor serious diseases. As many of these diseases are quite rare, they are converted to rates before comparing the number of cases in different parts of the country. For example, Lyme disease is measured as confirmed cases per 100,000 persons. Nationally, Lyme disease occurs at a rate of 8.5 per 100,000 persons, but can rise to more than 5 times that rate for many states in New England.
Public transportation Finally, on a more positive note, the U.S. Department of Department of Transportation’s Federal Transit Administration reports on monthly ridership for public transportation systems throughout the country. For comparison, total annual trips can be measured per person within a given metropolitan area. Unlike prior examples where lower rates are preferred, here the opposite is the case. Reuben Fischer-Baum wrote an article for Five Thirty Eight on public transit rates in 2014 which provides plenty of detail. Unfortunately, some of the links no longer work. Here is an alternate link to access monthly ridership data from the National Transit Database. The raw data in in this report by the American Public Transportation Association may be easier to follow.
Rates & Significant Figures
In most cases, rates are only shown to two or three significant figures. Simple error estimates associated with these rates render remaining digits meaningless. For example, the New Orleans’ property crime rate of 3,874 crimes per 100,000 people is equivalent to 3,900 crimes per 100,000.
Here is a “back of the envelope” statistical calculation. Assume that the annual number of crimes occurring within a population approximates a Poisson distribution. Then, an error estimate \(E\) for a specific crime rate would use a number \(Z\) of standard deviations within the following formula:
\[E = Z \times \sqrt{crime} \times \frac{10^5}{population} = rate \times \frac{Z}{\sqrt{crime}}\].
A recent post showed crime rates for seven cities in 2015. Let’s show the total reported property crimes, the associated crime rates, and error estimates. We’ll use a value of 2 for \(Z\). Within this estimate, New Orleans’ property crime rate is only accurate to within 63 crimes per 100,000 people. Note how errors decrease as city populations increase.