by the original design, but also by nonresponse and, in the case of the ACS, by the extent of CAPI subsampling that is done for personal visit follow-up to contain costs.
Tables 2-7a, 2-7b, and 2-7c provide rough, approximate estimates of sampling error for an estimated 15 percent poor school-age children from the ACS (1-year, 3-year, and 5-year period estimates) and the 2000 long-form sample for areas ranging in population from 500 to 2.5 million people. The calculations assume that school-age children are 20 percent of the total population and that areas with 3,000 or fewer people are oversampled. The calculations take account—for both the ACS and the long-form sample—of the added sampling error from household nonresponse but not the added error from item nonresponse.
Specifically, Table 2-7a shows relative standard errors—that is, the standard error as a percentage of the estimate, also called the coefficient of variation (see Box 2-5). Table 2-7b shows approximate 90 percent margins of error (MOEs) plus or minus the estimate of 15 percent poor school-age children for each size area (90 percent MOEs are 1.65 times the corresponding standard error). Finally, Table 2-7c translates the MOEs into 90 percent confidence intervals surrounding the 15 percent school-age poverty estimates.
The tables and text use 90 percent MOEs and confidence levels to follow the long-standing practice of Census Bureau publications; however, this practice is not standard in statistical work. It gives smaller MOEs and confidence intervals than is the case when the 95 percent standard is used: with the 95 percent standard, the MOEs and confidence intervals would be about 20 percent larger.
The panel developed the sampling error estimates in the tables by starting with a generalized variance estimation function provided by the Census Bureau for the 2000 long-form sample; we then computed the sampling error estimates for the ACS as multiples of the long-form-sample estimates (see notes at the end of Table 2-7c). The multiplication factors are derived from Census Bureau research with the ACS test sites, the C2SS, and the 2001–2004 ACS test surveys.
For the 2005 ACS, the Census Bureau directly estimated the sampling errors for specific estimates, including not only school-age poverty, but also other characteristics, using a repeated replication method (U.S. Census Bureau, 2006:Ch.12). The 2005 ACS data were only recently released, however, and the panel was not able to analyze their sampling errors; moreover, these estimates pertain only to areas with 65,000 or more people. Nevertheless, an unsystematic examination of the sampling errors for selected 2005 ACS poverty estimates suggests that they are similar to those shown in Tables 2-7a, 2-7b, and 2-7c.