# Population Density and Concentration

Categories: Data Analysis, Quantitative

This is an excerpt from Chapter 11 of Frank Donnelly’s Exploring The U.S. Census.

Population Density

Population density measures how many people there are by unit of area and is used for understanding how crowded a place is. To calculate it, you divide the population by the total land area:

For example, based on the population and land area of New Jersey in 2010:

New Jersey has been the most densely populated state in the country for quite some time, given its small geographic size relative to its population. In contrast, given its large size and small population, Alaska is the least densely populated state in the nation with 1.2 people per square mile.

The Census Bureau publishes data on population density but doesn’t make it easy to find. Table GHT-PCT from decennial SF1 file provides population and housing unit counts, land and water areas in square miles, and population and housing unit density. Land and water areas are also published in several other places, and you can use it to calculate density yourself. These sources include the geographic header file in the FTP files, the gazetteer files, and as attributes in the TIGER Line shapefiles. In these sources, the attributes are labeled ALAND and AWATER, and the units are in square meters. To calculate results in square miles, you need to multiply the square meters by this conversion factor: 0.00000038610.

Land and water areas are remeasured for all geographies every 10 years and do change over time due to natural processes like erosion and rising sea levels and because of revisions to boundaries. Land and water areas for legal geographies such as counties and places are updated between the 10-year census if there are changes to political boundaries due to annexation, incorporation, or dissolution.

Population Concentration

Population density is useful for measuring how crowded a place is, but it doesn’t tell us anything about the distribution of the population within that place. Some areas within New Jersey and Alaska are more crowded than others, as population density is not uniform across these states. The Hoover Index is used to measure population concentration, and the statistic can be interpreted as the percentage of people that would have to move in order for the population to be evenly distributed. An index value of 0 indicates that the population is evenly distributed across an area, while a value of 100 indicates that the entire population is concentrated in one place (Rogerson & Plane, 2013).

Calculating the index for a place requires data on population and land area for that place as a whole and for all components or subareas of that place. To calculate the index for states, we can use counties as subareas. To do the calculation, calculate the proportion of the state’s total population and land area that’s in each county, take the absolute value of the difference between the population and land area proportions for each county, sum those county results for the state, and multiply by 50.

You can easily do this calculation in a spreadsheet. In Figure 11.1, the state’s values appear in the sheet as totals that can be referenced in the formulas. The proportions of population and land area for each county are calculated first in dedicated columns (E and F), with the absolute value of the difference between them in a third column (G). An absolute value is simply the nonnegative value of any number, representing that value’s distance from zero. The spreadsheet formula ABS is used to compute it. This column is summed and multiplied by 50 to obtain the index for the state.

New Jersey has a Hoover index of 38.6, which means that the population of the state is relatively evenly distributed. About 39 out of 100 people in New Jersey would have to move from a more densely populated to a less densely populated county in order for the state’s population to be equally distributed. In contrast, the index for Alaska is 73.2, which indicates that the state’s population is highly concentrated in certain areas. This makes sense, as two thirds of Alaskans live in the Anchorage metropolitan area.

The choice of the subarea has a large impact on the index. For the results to be meaningful, each area should have a reasonable number of subareas, subareas must nest within the larger areas, and ideally subareas should be relatively compact and not vary too widely in geographic area. Counties are a good choice for creating a state-based index, while county subdivisions (minor civil divisions and census county divisions) may be appropriate for measuring concentration at the county level. A geography like a ZIP Code Tabulation Area (ZCTA) would be a poor choice as it violates all these rules.

References

Rogerson, P. A., & Plane, D. A. (2013). The Hoover Index of population and demographic components of change: An article in memory of Andy Isserman. International Regional Science Review36(1), 97–114.

Exploring the U.S. Census

Frank Donnelly’s new book, Exploring the US Census: Your Guide to America’s Data, aims to give social science students and researchers alike the tools to understand, extract, process, and analyze data from the decennial census, the American Community Survey, and other data collected by the U.S. Census Bureau.