The Secret Life of Polygons
Understanding the relative accuracy of user-defined areas
By Douglas Skuta, Economist, Esri Data Development Team, and Lynn Wombold, Esri Chief Demographer

Data users who define sites using a polygon rather than a standard geographic area, such as a county or metropolitan area, benefit from Esri's use of block-level updates.

Figure 1: Site outside Phoenix, Arizona, in 2000, showing blocks included in the area and 2000 block weights based on housing weights

Demographic data is tabulated and reported for standard geographic areas that range in size from states to census blocks. Standard geography encompasses areas that are predefined for a specific purpose: government entities like states, counties, or incorporated places; postal delivery areas (ZIP Codes or carrier routes); political areas such as congressional districts and voting districts; and statistical areas like tracts and block groups that are designed to report census data for neighborhoods or blocks, the smallest areas for which data is tabulated from the census.

Despite the versatility of the areas for which data is routinely reported or estimated, most data users prefer to define their own areas or polygons. Approximately 80 percent of the users who access Business Analyst Online, Esri's online reporting system, define their own polygons rather than use standard geographic areas.

Understanding Estimate Methodology

To understand the relative accuracy of estimates for user-defined polygons, it is useful to know how data is estimated for ad hoc polygons. Estimates for any area can be retrieved if the component census geography is known. First, the boundaries of the site are identified. Any shape is possible—circle, square, or polygon. Circles are common and easily defined by a radius from a given point. However, circles may be modified to represent a trade area more realistically by incorporating natural features, such as rivers and mountains, or drive times to capture the traffic flow.

Next, the underlying census geographic areas for a site are located via centroids. Expressed as latitude/longitude coordinates, centroids approximate the geographic centers of areas as small as blocks. If the centroid of a block falls within the site, it is completely included. Blocks are aggregated, and the ratio of block totals to their respective block groups is used to apportion demographic characteristics to the site. Data is apportioned from the block groups using differential weights: population, households, housing units, or businesses specific to the data in question.

Blocks are the smallest geographic areas, but only complete count census data is reported by block. Block groups are the smallest areas for which complete count and sample data from Census 2000 are reported. The combination provides the full range of census detail for estimating data for any site.

To date, this technique has applied the relationship between the blocks and the block groups from the most recent census. For most areas, the application provides a good estimate for the polygon. If the relationship between the component blocks and the block group has changed significantly since 2000, then the estimate cannot incorporate that change unless both the blocks and block groups are updated. Since that data is now eight years old, it can limit estimates for areas that are changing rapidly or preclude estimates of areas that had no population or housing at the time of the last census.

Dealing with Differences in Data Currency

The map in Figure 1 shows a sample area located northwest of Phoenix, Arizona. In 2000, this area was primarily desert. The site includes 18 block points, but only one block had housing and a weight relative to its block group of 0.19 percent in 2000. Housing in this block group has almost tripled since 2000. However, using the 2000 ratio would yield an estimate of only 19 housing units in 2008.

Figure 2: Site outside Phoenix, Arizona, in 2008, showing blocks included in the area and 2008 block weights based on housing weights

To counteract the inconsistency of current data for block groups and eight-year-old data for blocks, Esri has updated the data critical to capturing current information for sites that are experiencing change. Enhanced site analysis is now available in Esri's Business Analyst software suite with a current database of the block weights used to retrieve information for user-defined polygons.

The map in Figure 2 shows the effect of using 2008 block weights when looking at housing development for the Phoenix sample area. Updating the block weights increases the estimated housing units for this site to more than 2,400.

The Importance of Blocks

The integration of demographic and spatial analysis has not only enabled the development of more accurate block group totals, it has also provided the opportunity to assess block totals. Blocks have attracted virtually no interest among data users. As the lowest common denominator in the geographic hierarchy that progresses to block groups, tracts, counties and states, blocks are too small for the tabulation of most census variables. However, blocks are the key to estimating data for polygons.

Extending the ABA Technique

Esri has developed a current database of the block weights used to retrieve information for polygons by extending the application of its Address-Based Allocation (ABA) technique to the block level. In addition to ABA, Esri employed block counts from special censuses that have been contracted by some local governments since 2000. All block-level updates are also moderated with geographic limiters such as local density thresholds and the identification of uninhabitable areas.

Updating the relationship between blocks and block groups for areas that are experiencing change is critical to capturing current trends in polygons. Revising the block weights not only improves estimation of data in blocks that are experiencing growth but also in adjacent blocks, where growth has not occurred, due to the shift in the relative weights. The result: data users who define a site as a polygon can be confident of the appropriateness of the data captured.

For more information about Address-Based Allocation, see Esri's Demographic Update Methodology at www.esri.com/data/esri_data/demographic.html.

About the Authors

Douglas A. Skuta, who joined Esri in September 2000, has more than 10 years of analytical experience in statistical programming and econometric methods. He contributes to the development and updating of Esri's demographic databases and consumer segmentation systems. He also works on custom site selection and profiling projects for Esri's retail and real estate clients. Prior to joining Esri, he served as an economist in the branch of Development and Applications Research for the Current Employment Statistics Survey at the U.S. Bureau of Labor Statistics in Washington, D.C. Skuta holds a bachelor of arts degree in economics from Hillsdale College in Hillsdale, Michigan, and a master's degree in economics from Ohio University in Athens, Ohio.

Lynn Wombold, chief demographer at Esri, manages data development including the processing of census data and the development of unique databases such as the demographic forecasts, consumer spending, Retail MarketPlace, and Community Tapestry market segmentation system as well as the acquisition and integration of third-party data. She is also responsible for custom analysis and modeling projects. With more than 31 years of experience, her areas of expertise include population estimates and projections, state and local demography, census data, survey research, and consumer data. Prior to joining Esri, she worked for CACI Marketing Systems and was the senior demographer at the University of New Mexico. Wombold holds degrees in sociology, with a specialty in demographic studies from Bowling Green State University in Ohio. She has received CACI's Eagle Award for Technical Excellence and Encore Achievers. The author of numerous articles for industry publications, she frequently presents papers on demography.