Abstract
The American Community Survey (ACS) is a U.S. Census Bureau product designed to provide accurate and timely demographic and economic indicators on an annual basis for both large and small geographic areas within the United States. Operational plans call for ACS to serve not only as a substitute for the decennial census long-form, but as a means of providing annual data at the national, state, county, and subcounty levels. In addition to being highly ambitious, this approach represents a major change in how data are collected and interpreted. Two of the major questions facing the ACS are its functionality and usability. This paper explores the latter of these two questions by examining “persons per household (PPH),” a variable of high interest to demographers and others preparing regular post-censal population estimates. The data used in this exploration are taken from 18 of the counties that formed the set of 1999 ACS test sites. The examination proceeds by first comparing 1-year ACS PPH estimates to Census 2010 PPH values along with extrapolated estimates generated using a geometric model based on PPH change between the 1990 and 2000 census counts. Both sets of estimates are then compared to annual 2001–2009 PPH interpolated estimates generated by a geometric model based on PPH from the 2000 census to the 2010 census. The ACS PPH estimates represent what could be called the “statistical perspective” because variations in the estimates of specific variables over time and space are viewed largely by statisticians with an eye toward sample error. The model-based PPH estimates represent a “demographic perspective” because PPH estimates are largely viewed by demographers as varying systematically and changing relatively slowly over time, an orientation stemming from theory and empirical evidence that PPH estimates respond to demographic and related determinants. The comparisons suggest that the ACS PPH estimates exhibit too much “noisy” variation for a given area over time to be usable by demographers and others preparing post-censal population estimates. These findings should be confirmed through further analysis and suggestions are provided for the directions this research could take. We conclude by noting that the statistical and demographic perspectives are not incompatible and that one of the aims of our paper is to encourage the U.S. Census Bureau to consider ways to improve the usability of the 1-year ACS PPH estimates.
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Notes
The population data available from the ACS are not the “official” estimates of the U.S. Census Bureau. However, along with the official estimates, the ACS data are being used to drive a portion of the geographic allocation of billions of federal funds (Blumerman and Vidal 2009; Reamer 2010b; Wetrogan 2005).
This is a finding of no small interest if in fact the 2010 ACS PPH estimates are informed in some manner by the 2010 Census. We point out that the documentation of the PEP preliminary estimates for 2010 suggest that these estimates are not informed by 2010 Census results (U.S. Census Bureau, no date 2) and the documentation for the ACS suggests only that the 2010 ACS data would be informed by 2000 Census data and subsequent PEP estimates and not at this point in time, by 2010 Census data (U.S. Census Bureau 2009a). Thus, it appears that the 2010 1-year ACS estimates are not informed by the 2010 Census results. However, we note that in 10 of the 18 counties there are pronounced reversals in the direction of change observed between 2009 and 2010 compared to the period 2008–2009 trend for the 1 year-ACS PPH estimates and that these pronounced reversals bring the 2010 ACS PPH estimates much closer to the 2010 census PPH values than the 2008–2009 trends and 2009 PPH estimates suggest they would have been. These pronounced reversals are seen for the following 10 counties: Pima County, AZ (Exhibit 1), San Francisco County, CA (Exhibit 3), Broward County, FL (Exhibit 5), Lake County, IL (Exhibit 6), Hampden County, MA (Exhibit 9), Douglas County, NE (Exhibit 11), Rockland County, NY (Exhibit 13), Multnomah County, OR (Exhibit 15), Schuylkill County, PA (Exhibit 16), and Sevier County, TN (Exhibit 17). These pronounced changes suggest some sort of “external” influence on the ACS data and while we can only speculate, given the information we have seen on the development of the 2010 ACS data, the 2010 census seems to be a logical suspect.
Continuing to the remaining eight counties, there would appear to be little if any reason, however, to suspect an external influence. We find that in two cases, the reversals are pronounced, but they serve to “over-correct” in that the 2010 PPH estimates are farther away from the corresponding 2010 census PPH values than were the 2009 PPH estimates. These are Black Hawk County, IA (Exhibit 7) and Yakima County, WA (Exhibit 18). In one case, Jefferson County, AR (Exhibit 2), there is a reversal but it is not pronounced, while in two others, Calvert County, MD (Exhibit 8) and Madison County, MS (Exhibit 10), 2010 ACS PPH estimates are closer to the census 2010 PPH values than the 2009 ACS PPH estimates but the moves do not involve a reversal of direction from the trend observed between 2008 and 2009. In Franklin County, OH (Exhibit 14), there is basically no change from the 2009 ACS PPH estimate to the 2010 ACS PPH estimate while in two counties, Tulare, CA (Exhibit 4) and Bronx, NY (Exhibit 12), the changes observed between 2009 and 2010 move their 2009 PPH estimates away from the corresponding 2010 census PPH values.
As noted in the text, we also used the census 2010 PPH values as a basis for comparing the accuracy of the 1-year 2010 ACS PPH estimates to the accuracy of PPH estimates generated by the geometric method for all of the 807 counties for which ACS data are available. The latter were developed in the same manner as the estimates discussed in Table 3: the 1990–2000 trends in PPH values were extrapolated to 2010 using the geometric model. At 6.85%, the MAPE of the ACS PPH estimates is higher than the MAPE for the geometric model, 5.83%, indicating that the ACS is less accurate than the geometric model not only for the 18 test counties, but for all counties. We also found that the 90% margins of error provided by the Census Bureau for the 2010 1-year ACS PPH estimates contained the 2010 census PPH values in only 64% (515) of the 807 counties. This is a better showing than the 39% observed for the 18 test counties, but one would intuitively expect it to be higher than 64% for the entire universe of ACS counties in that 90% margins of error are used. These data and results are in an excel file that is available from the authors.
This is because there is an expectation on the part of both these demographers and the stakeholders that PPH estimates should exhibit systematic changes unless there is compelling substantive evidence (e.g., the PPH estimates jumped because of a surge of in-migrants with high fertility and large family sizes) to the contrary. If such PPH estimates are used in the absence of compelling substantive evidence justifying their temporal instability then it appears that the risk of challenges and related administrative and legal actions increases (see, e.g., Walashek and Swanson 2006), especially when these estimates are used to allocate resources, which is often the case (National Research Council 1980, 2003; Scire 2007).
We need to make two points here. First, we selected Jefferson County as an example simply because it illustrates that using inferential statistics to identify change in the ACS PPH neither yields trends that are consistent with demographic theory nor annual PPH estimates that would be useful as input into the HUM for purposes of making annual population estimates. In point of fact, for all of the 18 counties statistical inference yields annual changes in the ACS PPH estimates that neither conform to demographic theory nor provide annual PPH estimates that would be useful as input into the HUM, as can be seen in Appendix Table 6.
The second point is that some may argue that in using statistical inference to identify PPH changes, we are actually making “multiple comparisons,” which require adjustments. In response, we argue that most multiple comparison adjustments (e.g., analysis of variance) are not appropriate because these adjustments are generally designed to be used when three or more simultaneous comparisons are being made (Iversen and Norpoth 1973; Toothaker 1993), which is not the case for an analyst attempting to use the ACS PPH estimates over the course of a decade. Instead, such an analyst would be only going out 1 year at a time and making a comparison of the most current ACS PPH estimate against the ACS PPH estimate in use, which through the decade would yield a series of pair-wise comparisons rather than three or more simultaneous comparisons. Of course, the one in use might be from 2 years ago if the previous two comparisons indicated “no change,” but the point holds: it is a series of pair-wise comparisons that would be made, not three or more comparisons simultaneously.
In making a series of pair-wise comparisons, one adjustment that could be made is the Bonferroni correction (Hough and Swanson 2006; Kirk 1968; Perenger 1998), which is designed to reduce the probability of making a Type I error. An analyst seeking to use the ACS PPH estimates over the course of a decade can quickly estimate the probability of making a Type I error. Since the Census Bureau is using a 90% confidence interval, the corresponding alpha level in a series of pair-wise T-tests would be .10 (α = .10). Given this, the probability of making at least one Type I error in making nine pair-wise comparisons (2001 compared to 2000, 2002 compared to 2001,…, 2008–2007, and 2009–2008) over the course of a decade is 1 − (.9)9 ≈ .67. That, is we have a 67% chance of stating that a change in PPH has occurred when in fact it is not, if all nine pair-wise comparisons are made. Assuming in advance that nine comparisons would be made, the analyst could employ the Bonferroni correction, which is ά = α/n, where α = the alpha level (.10), n = the number of pair-wise comparisons to be made (for which we can use nine, which is the maximum), and ά = the corrected alpha level (Hough and Swanson 2006). In this situation with α = .10 and n = 9, the analyst would find ά ≈ 0.01 ≈ .10/9. This would correspond to adjusting the margins of error from 90 to 99%. This can be done as follows: MOE′ = 2.576/1.645*MOE (U.S. Census Bureau 2009b, A12). Appendix Table 7 shows the results of using the Bonferroni correction to make this adjustment in the MOEs for all of the 18 counties over the period from 2001 to 2009.
As can be seen in Appendix Tables 6 and 7, whether or not an attempt is made to correct for multiple comparisons, the results in either case generally do not make demographic sense for any of the 18 counties. That is, the annual “change” in the ACS PPH estimates is either abrupt and discontinuous or non-existent. In either case, the change is neither consistent with the demographic theory underlying PPH change over time nor the needs of an analyst in terms of PPH estimates being used as input to the HUM for purposes of making annual population estimates. Continuing with our example of Jefferson County, if we use the Bonferroni correction to adjust the 90% margins of error provided by the U.S. Census Bureau for 1-year ACS PPH estimates, from 2001 to 2009 (with the adjusted 2001 MOE being compared to the 2000 census PPH of 2.66), we get, respectively: 2.66, 2.66, 2.66, 2.53, 2.53, 2.53, 2.53, 2.53, and 2.53. Thus, we would have no change in the 2000 census PPH of 2.66 from 2001 to 2003, then an abrupt decrease to 2.53 in 2004, followed by a constant PPH of 2.53 through 2009.
As a final note, we have looked into procedures designed to deal with detecting temporal change from other perspectives, including change-point analysis (Bai 1997; Bai and Perron 2003) and interrupted time series (Lewis-Beck 1986). These techniques appear to be ill-suited for use here since the 1-year ACS PPH estimates do not appear to be able to provide the requisite quality for an historical time series that could be used as a basis for developing models.
By a “substantive difference” we mean an “important difference.” This is not the same as “statistical significance.” The developer of the T-test, W.S. Gossett (aka “Student”), was acutely aware of the difference between statistical significance and an important difference since he was trying to brew high quality beer for the Guinness Brewery at reasonable prices (Ziliak and McCloskey 2008). However, this important distinction was late to come both to R.A. Fisher, and to J. Neyman and E. Pearson, whose ideas became widespread and literally “ritualized” into the practice of statistical testing without conveying the idea of taking into account whether or not there was an “important difference” (Hubbard and Bayarri 2003; Ziliak and McCloskey 2008); unfortunately, the ritualized nature of statistical testing exacerbated this by placing “statistical significance” as the only result worth reporting in scientific research (Ziliak and McCloskey 2008).
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Swanson, D.A., Hough, G.C. An Evaluation of Persons per Household (PPH) Estimates Generated by the American Community Survey: A Demographic Perspective. Popul Res Policy Rev 31, 235–266 (2012). https://doi.org/10.1007/s11113-012-9227-8
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DOI: https://doi.org/10.1007/s11113-012-9227-8