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• #### Committee on National Statistics 331-332

of a population group in an area. The formula for estimating the coefficient of variation is very unstable for estimates of small proportions, and the estimated coefficients can be misleadingly large.

Table 2-7a shows that estimates from the 2000 long-form sample of 15 percent poor school-age children meet the 12 percent standard of precision for areas with a minimum population between 20,000 and 25,000 people (4,000–5,000 school-age children), but estimates from accumulated ACS 5-year data meet this standard only for areas with at least 50,000 people (10,000 school-age children). Estimates from the ACS 3-year and 1-year data meet this standard only for areas with at least 80,000 people (16,000 school-age children) and 250,000 people (50,000 school-age children), respectively.

The relative standard errors in Table 2-7a are calculated for estimates of 15 percent poor children among all school-age children. The latter group, in turn, is assumed to be 20 percent of the total population, so that poor school-age children are only 3 percent of the total population. If, instead, the table were to provide relative standard errors for estimates of 15 percent poor people—including all children and adults—among the total population, then the levels of precision shown would be considerably improved (see Table 2-8). Thus, the long-form sample would provide estimates that meet the 12 percent or less precision standard for areas as small as 1,500 people, while estimates from accumulated ACS 5-year data would meet this standard for areas as small as 10,000 people. Estimates from accumulated ACS 3-year and 1-year data would meet this standard for areas as small as about 15,000 and 50,000 people, respectively (see Table 2-8). In other words, simple one-way tabulations from the ACS may meet common standards for precision for relatively small areas, although that is not likely to be the case once another variable is introduced, such as age or race.

Users should not simply rely on commonly cited precision standards in deciding whether to use particular estimates. They also need to take into account the specific requirements of their application. For example, deciding which subset of school districts should receive additional funding directed to low-income students may require a narrower confidence interval than the standard. Thus, a 90 percent confidence interval of 12 to 18 percent poor school-age children, which corresponds to a 12 percent relative standard error for an estimate of 15 percent poor school-age children, may be too wide an interval for purposes of fund allocation. Still, for some applications, a ballpark estimate with an even wider confidence interval may suffice.

In deciding which set of ACS estimates is best suited for a particular application, users will need to make trade-offs between timeliness and sampling error. For example, a user could decide that a 3-year period estimate is preferable to a 1-year period estimate for a large city or county in order to achieve a greater level of precision. Alternatively, a user could decide that

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