8

Population Estimates

The SAIPE Program uses population estimates from the Census Bureau 's postcensal population estimates program to form predictor variables in the state and county models of poor school-age children–the state population under age 65 in the state model and the county population under age 18 in the county model. In addition, state population estimates of noninstitutionalized children aged 5-17 are used to convert estimates of the proportion of poor school-age children from the state model to estimates of the number poor (see Chapter 4).

For the two-stage allocation procedure that the Department of Education used to allocate Title I funds prior to school year 1999-2000, the Census Bureau provided not only estimates of the number of poor school-age children in each county from the SAIPE Program, but also county estimates for the 5-17 age group to use as denominators for calculating the proportion of poor school-age children. (Estimates were also provided for Puerto Rico.) Both numbers and proportions are needed to determine eligibility and allocation amounts for basic and concentration grants (see Chapter 2).1 The population estimates of school-age children that accompanied the 1993 county model estimates pertain to July

1  

The Census Bureau also makes available on its web site estimated proportions of poor school-age children in which the denominators are estimates of related children aged 5-17 in each county. These estimates are developed by multiplying the estimates from the Census Bureau's population estimates program for the noninstitutionalized population aged 5-17 by the ratio of related children aged 5-17 to noninstitutionalized children aged 5-17 for each county in the 1990 census.



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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology 8 Population Estimates The SAIPE Program uses population estimates from the Census Bureau 's postcensal population estimates program to form predictor variables in the state and county models of poor school-age children–the state population under age 65 in the state model and the county population under age 18 in the county model. In addition, state population estimates of noninstitutionalized children aged 5-17 are used to convert estimates of the proportion of poor school-age children from the state model to estimates of the number poor (see Chapter 4). For the two-stage allocation procedure that the Department of Education used to allocate Title I funds prior to school year 1999-2000, the Census Bureau provided not only estimates of the number of poor school-age children in each county from the SAIPE Program, but also county estimates for the 5-17 age group to use as denominators for calculating the proportion of poor school-age children. (Estimates were also provided for Puerto Rico.) Both numbers and proportions are needed to determine eligibility and allocation amounts for basic and concentration grants (see Chapter 2).1 The population estimates of school-age children that accompanied the 1993 county model estimates pertain to July 1   The Census Bureau also makes available on its web site estimated proportions of poor school-age children in which the denominators are estimates of related children aged 5-17 in each county. These estimates are developed by multiplying the estimates from the Census Bureau's population estimates program for the noninstitutionalized population aged 5-17 by the ratio of related children aged 5-17 to noninstitutionalized children aged 5-17 for each county in the 1990 census.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology 1994; those that accompanied the 1995 county model estimates pertain to July 1996. To enable the Department of Education to make direct allocations to school districts, the Census Bureau was charged to produce estimates at the school district level not only of poor school-age children in 1995, but also of the total population and total number of school-age children as of July 1996. Estimates of total school-age children are needed to compute poverty rates for school districts, which are a factor in the Title I allocation formulas. Estimates of total population are needed so that a state knows which districts have fewer than 20,000 people if it wants to take advantage of the provision in the legislation that permits states to aggregate the Title I allocations for these districts and to redistribute the funds on some other approved basis. The Census Bureau currently develops county age estimates within the framework of total population estimates for counties and population estimates by age for states. School district estimates of total population and school-age children are developed by using a shares procedure, similar to that used for school district estimates of poor school-age children. In this procedure, 1990 census data for school districts are applied to updated county population estimates. METHODS FOR POPULATION ESTIMATES This section describes the methods that the Census Bureau used to develop the following population estimates: county estimates of total population for 1994 and 1996; county estimates of the population by age for 1994 and 1996; and school district estimates of total population and school-age children for 1996. The descriptions of methods for county estimates of total population and population by age briefly summarize the methods used for the corresponding estimates for states (for more detail, see Long, 1993; Sink, 1996; U.S. Census Bureau, 1995b).2 County Estimates of Total Population In a process that begins anew with each decennial census, county estimates of total population are developed by updating the population estimates for the preceding year with data on births, deaths, net immigration from abroad, and net internal migration. The method is a component method, in which the numbers of births and deaths are based on reported vital statistics for each county; reports of 2   Estimates for Puerto Rico are developed separately. The basic methodology for 1994 and 1996 estimates used registered births by sex, registered deaths by age and sex, and estimates of annual intercensal net migration by age and sex from an analysis using the natural rate of increase for the 1980-1990 period and the reported 1990 census population by age and sex (Reed, 1996).

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology the Immigration and Naturalization Service are used to estimate net immigration from abroad; and administrative records are used to estimate net migration among counties. Net migration of people under 65 years of age is estimated for each county from a year-to-year match of IRS federal income tax returns; for people aged 65 and over, net migration is estimated for each county from the change in Medicare enrollment (U.S. Census Bureau, 1995). Estimates are developed separately for household and group quarters populations. The county population totals are summed for each state to provide estimates of the total population of each state. All county and state population totals are then adjusted to sum to independently derived estimates of the total U.S. population.3 The county estimates are also reviewed locally under the Census Bureau's Federal-State Cooperative Population Estimates (FSCPE) Program. Operationally, the county total population estimates are the sum of the estimates for four groups: Household population under age 65 (HHP < 65); Household population age 65 and over (HHP65+); Group quarters population under age 65 (GQ < 65); and Group quarters population age 65 and over (GQ65+). Household Population Under Age 65 The estimates for the household population under age 65 use a component method for year t to measure the change in each component of population change during the 12-month period preceding the estimate date, as follows: HHP < 65t = HHP < 65t−1 + NI + NMIG + NETMOVE − AGE. (1) NI is natural increase (births and deaths for people under age 65), which is estimated from a combination of vital statistics data from the National Center for Health Statistics (NCHS) and from state agencies that participate in the FSCPE Program. Each of these sources has some problems. The FSCPE does not 3   The national-level population estimates are not adjusted for net undercount in the census, but the methodology includes an “inflation-deflation ” procedure so that the undercount patterns for age groups are consistent between the estimates and the census. In this procedure the census counts for age groups are first adjusted (inflated) for net undercount as estimated from demographic analysis. Then the adjusted counts are carried forward by subtracting deaths, adding net immigration, and making the group 1 year older for each year of the estimates (births are added for the age group under 1 year). As a last step, the estimates are deflated, using the net undercount rates that apply to the updated age group. As an example, census counts for men age 20 are inflated using the relatively high net undercount rate for that age. After the updating is carried out over, say, 10 years, the resulting estimates are deflated by using the net undercount rate for men age 30, which is a smaller rate than the rate for men age 20.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology include all states, and the NCHS data exhibit some peculiarities (e.g., birth records are not always properly assigned to place of residence in such areas as Washington, D.C., in which births often occur in hospitals that are not in the county of residence, and in areas with military bases). NMIG, net internal migration, is estimated from data on IRS tax returns matched year to year on the basis of the social security number of the filer. A migration rate is developed from the net flow of exemptions (the tax filer and his or her dependents) on the matched tax returns. The rate is calculated as the difference in the number of exemptions entering the county minus the number leaving the county, as a proportion of the number of exemptions at the start of the period. This rate is then applied to the migration base [HHP < 65t−1 + 0.5(NI + NETMOVE) − AGE]. Coverage of the IRS data (i.e., the proportion of exemptions to estimated population) varies across counties, as do matching rates. NETMOVE is nondomestic net movements, mainly international immigration and emigration. It is estimated with a variety of data, and the totals generally are small. Legal immigrants and refugees (about 800,000 per year nationwide) are assigned to a county of residence on the basis of Immigration and Naturalization Service data about their intended place of residence, although they may not reside at the indicated place. Undocumented immigrants (estimated at 225,000 annually) are assigned to a county on the basis of the 1990 census distribution of the foreign born population. Estimates are also made of emigrants (about 195,000 per year). Net inmigrants from Puerto Rico (only about 7,000 annually because there is almost an equal number of outmigrants each year) were previously estimated from passenger traffic data from the San Juan airport. However, this method became increasingly untenable, and the current procedure uses estimates of migration of Puerto Ricans to the rest of the world, which include an assumption of the U.S. share. The U.S. share is allocated to counties on the basis of 1990 census data on place of residence. Estimates of the net movement in and out of the country of military and federal civilian and military dependents are based on data from the Department of Defense (DoD) and the Office of Personnel Management. County station strength data from DoD, which are used to allocate military personnel to counties, are modified in some locations (e.g., the Washington, D.C., area). Lastly, AGE is an estimate of the number of persons in the county who aged from 64 to 65 during the year. Except for internal migration, all components are controlled to national totals. Household Population Age 65 and Over The estimates for the household population age 65 and over use a component method in which: HHP65+t = HHP65+t−1 + NI65+ + NMIG65+ + NETMOVE65+. (2)

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology NI65+ is natural increase (decrease), which is estimated as the number of persons who aged from 64 to 65 during the year (AGE in equation(1)) minus deaths in the population aged 65 and over. NMIG65+ is internal migration, which is estimated from Medicare enrollment data. A migration rate is estimated as [(actual Medicare enrollment t−1− expected Medicare enrollment) / actual enrollmentt−1]. Expected Medicare enrollment is [actual enrollmentt−1 + (NI65+t−1 x the 1990 Medicare coverage ratio)].4 The estimated migration rate is then applied to the migration base, HHP65+t−1 + 0.5(NIt−1 + NETMOVEt−1). NETMOVE65+ is other net movements (legal immigrants, undocumented immigrants, refugees, emigrants, net entrants from Puerto Rico), which are estimated as described above for the household population under age 65. Group Quarters Population Under Age 65 and Age 65 and Over Group quarters populations for both age groups (under age 65 and age 65 and over) are estimated as the 1990 census group quarters population plus the difference between the current group quarters report (GQR) minus the 1990 GQR figure. The GQR is compiled annually from data obtained from the FSCPE, DoD, Veterans Administration, and colleges by type of group quarters: correctional facility, juvenile facility, nursing home, other institutional, college, military quarters, and other noninstitutional. County Estimates by Age County age estimates are prepared in a two-step procedure. In the first step, estimates of total county population are developed as described above. Separately, estimates of state populations by single years of age, sex, race, and Hispanic origin are developed. The state age estimates (which are controlled to the state total population estimates) use a component method in which migration rates by age for people under age 65 are derived from school enrollment data (U.S. Census Bureau, 1987).5 In the second step, the county age estimates are developed by using a raking-ratio adjustment of the numbers from the previous census. In this approach, the 4   Previously, the method simply used the change in Medicare enrollment to estimate the migration rate for the population aged 65 and over directly; the current method preserves the county variation in Medicare coverage. 5   Recently, the Census Bureau developed experimental state estimates of the population by age, sex, race, and Hispanic origin by a cohort-component method in which federal income tax returns are used to estimate net migration on the basis of estimates of gross inmigration and gross outmigration (see National Research Council, 2000:Ch.3). For this experimental method, the resulting state agesex-race-Hispanic origin estimates are controlled to the state age-sex population estimates developed as described in the text.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology beginning matrix of counts for each county by age, sex, race, and Hispanic origin from the previous census is simultaneously adjusted to agree with the postcensal estimate of the total county population and the postcensal estimates for the applicable state by age, sex, race, and Hispanic origin. Beginning with the revised county age estimates for 1994, this adjustment is carried out separately for persons in each age group who were in group quarters in the census and persons who were not in group quarters. The raking-ratio procedure used for county age estimates assumes that the age distribution of each county within a state changes in the same manner as that state's age distribution. Errors in the county estimates of an age group can arise from errors in this assumption, errors in the derivation of the state estimates of age groups, and errors in the derivation of the county estimates of total population. School District Population Estimates The Census Bureau uses a shares approach, similar to that used for distributing the number of poor school-age children among the school districts in a county, to estimate the total population and total school-age population for school districts. The method for producing 1996 estimates of total population and total school-age children for districts involved the following steps: retabulate the 1990 census data according to 1995-1996 school district boundaries, determine the 1990 census county share in each district or part of a district for total population and total school-age children, and apply those shares to the Census Bureau's 1996 county estimates of total population and total school-age children, respectively, derived by the procedures described above. Unlike the situation with poor school-age children, the 1990 census school district shares for total population and school-age population are based on data from the complete count (short form) and are not subject to sampling error. EVALUATION OF COUNTY ESTIMATES The Census Bureau has an active program to develop and review the performance of its demographically based state and county population estimates, including evaluating the estimates at 10-year intervals by comparing them with the decennial census. These comparisons provide an indication of the differences, but they are not perfect measures of accuracy and precision because the standard (i.e., the decennial census) itself is flawed, notably from net population undercount, which varies by age group across time and place (see Robinson et al., 1993). The Census Bureau's methods and data for producing postcensal population estimates have generally improved over time, but three patterns of differences, which are practically inevitable, continue to affect the state and county estimates

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology (see Davis, 1994). First, the proportional differences of the estimates in comparison with the census are larger on average for small areas than for large ones. Second, the proportional differences tend to be larger for areas in which the population is changing rapidly than for areas that are more stable. Third, the proportional differences for age groups tend to be higher than those for the total population. Comparisons with 1990 Census County Estimates The Census Bureau conducted an evaluation of the county estimates of total population and children aged 5-17 by comparison with the 1990 census numbers for all counties and for categories of counties. Updated estimates for counties by age were produced by ratio adjusting the 1980 census county age numbers to 1990 county total population estimates and 1990 state age estimates, as described above. The resulting 1990 county age estimates were compared with the 1990 census county age numbers. Tables 8-1 to 8-8 show the average proportional algebraic difference and the average proportional absolute difference, expressed as percents, between the 1990 county population estimates for people aged 5-17, developed by raking the 1980 census estimates as described above, and the 1990 census numbers.6 The two measures are shown for all counties and for counties grouped into categories for the following characteristics: population size in 1990; population growth from 1980 to 1990; percentage of black and other nonwhite population in 1990; percentage of Hispanic population in 1990; percentage of poor population in 1990; percentage of group quarters residents in 1990; census geographic division; and metropolitan status. Also shown is the percentage of counties with negative differences (underpredictions relative to the census). The overall average proportional absolute difference in the 1990 county estimates of people aged 5-17 is 6.3 percent (shown in Table 8-1). By comparison, for 1990 county estimates of total population, prepared using the Census Bureau's current estimation procedure, it is 3.6 percent (Davis, 1994).7 The average proportional absolute differences do not seem to be concentrated in any 6   The average proportional absolute difference is computed as the sum for all counties n (or all counties in a category) of the absolute difference between the estimate and the 1990 census figure for each county as a proportion of the census figure for each county, divided by the number of counties, or ∑ [(|Ymodel i − Ycensus i |) / Ycensus i ] / n. The average proportional algebraic difference is computed similarly, except that the sign of the difference (positive or negative) is considered in the computation. 7   The average absolute differences for 1990 county estimates of children aged 5-17 and the total population are smaller than the average proportional absolute differences–the average absolute differences are 4.9 percent and 2.3 percent of the county average school-age and total population, respectively (see Table 8-9 and Table 8-10).

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology TABLE 8-1 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Population Size in 1990 Population Size, 1990 Counties (Number)a Average Proportional Algebraic Differenceb Average Proportional Absolute Differenceb Percentage of Counties with Negative Differences All 3,140 −0.4 (8.7) 6.3 (6.1) 56.2 1,000,000 and over 30 1.5 (6.5) 5.2 (4.1) 46.7 500,000 to 1,000,000 67 1.7 (5.1) 4.4 (3.2) 29.9 100,000 to 500,000 361 0.9 (5.9) 4.6 (3.8) 50.4 50,000 to 100,000 384 0.6 (7.3) 5.6 (4.7) 51.3 10,000 to 50,000 1,543 −0.5 (7.7) 6.0 (4.8) 56.9 5,000 to 10,000 457 −1.5 (9.0) 7.2 (5.6) 61.7 2,500 to 5,000 180 −3.2 (10.5) 8.4 (7.0) 67.2 Less than 2,500 118 0.0 (21.2) 12.4 (17.2) 59.0 aExcludes Kalawao County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. bDifferences are in percent. See text for formulas. Standard deviations are in parentheses. SOURCE: Data from U.S. Census Bureau. TABLE 8-2 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Growth Rate, 1980-1990 Population Growth Rate, 1980-1990 Counties (Number)a Average Proportional Algebraic Differenceb Average Proportional Absolute Differenceb Percentage of Counties with Negative Differences All 3,140 −0.4 (8.7) 6.3 (6.1) 56.2 Decrease of 5% or more 834 −0.7 (10.1) 6.7 (7.5) 58.4 −5% to 0% 595 −1.0 (7.8) 5.8 (5.3) 60.7 0 to 5% 583 −0.4 (7.8) 5.9 (5.0) 55.8 5 to 10% 386 −0.1 (7.7) 5.7 (5.1) 57.5 10 to 15% 208 0.6 (7.5) 6.1 (4.5) 49.0 15 to 25% 247 0.3 (9.0) 6.7 (6.0) 51.8 25% and over 287 −0.2 (10.0) 7.5 (6.5) 48.4 aExcludes Kalawao County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. bDifferences are in percent. See text for formulas. Standard deviations are in parentheses. SOURCE: Data from U.S. Census Bureau.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology TABLE 8-3 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Percent Black and Other Nonwhite Population, 1990 Percent Black and Other Nonwhite, 1990 Counties (Number)a Average Proportional Algebraic Differenceb Average Proportional Absolute Differenceb Percentage of Counties with Negative Differences All 3,140 −0.4 (8.7) 6.3 (6.1) 56.2 Less than 0.5% 304 −0.7 (13.1) 7.4 (10.8) 61.6 0.5 to 1.0% 405 −2.1 (8.3) 6.1 (6.0) 67.2 1.0 to 2.0% 468 −1.6 (8.4) 6.8 (5.2) 62.4 2.0 to 5.0% 550 −1.0 (7.8) 6.2 (4.8) 58.6 5.0 to 15.0% 641 0.3 (8.2) 6.3 (5.3) 49.1 15.0 to 40.0% 546 0.8 (7.6) 5.7 (5.1) 48.7 40.0% and over 226 1.6 (8.0) 6.1 (5.5) 48.5 aExcludes Kalawao County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. bDifferences are in percent. See text for formulas. Standard deviations are in parentheses. SOURCE: Data from U.S. Census Bureau. TABLE 8-4 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Percent Hispanic Population, 1990 Percent Hispanic, 1990 Counties (Number)a Average Proportional Algebraic Differenceb Average Proportional Absolute Differenceb Percentage of Counties with Negative Differences All 3,140 −0.4 (8.7) 6.3 (6.1) 56.2 Less than 0.5% 983 0.7 (9.2) 6.1 (6.9) 52.9 0.5 to 1.0% 760 0.2 (7.0) 5.5 (4.3) 52.5 1.0 to 2.0% 485 −0.1 (8.3) 6.5 (5.2) 56.1 2.0 to 5.0% 385 −1.4 (8.8) 6.5 (6.2) 60.3 5.0 to 15.0% 291 −3.2 (9.8) 7.5 (7.0) 63.4 15.0 to 40.0% 162 −3.8 (10.4) 8.4 (7.3) 70.4 40.0% and over 74 −1.0 (8.1) 6.5 (4.9) 56.8 aExcludes Kalawao County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. bDifferences are in percent. See text for formulas. Standard deviations are in parentheses. SOURCE: Data from U.S. Census Bureau.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology TABLE 8-5 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Percent Poor Population, 1990 Percent Poor, 1990 Counties (Number)a Average Proportional Algebraic Differenceb Average Proportional Absolute Differenceb Percentage of Counties with Negative Differences All 3,140 −0.4 (8.7) 6.3 (6.1) 56.2 None 50 −1.5 (8.2) 7.0 (4.4) 58.0 Less than 5% 253 1.8 (13.9) 7.3 (11.9) 45.5 5 to 10% 1,046 −1.4 (7.7) 6.0 (5.1) 62.1 10 to 15% 929 −1.1 (8.4) 6.7 (5.2) 58.3 15 to 25% 688 0.9 (8.2) 6.1 (5.6) 50.0 25 to 40% 157 0.8 (7.0) 5.4 (4.4) 49.7 40% and over 17 3.1 (11.4) 8.9 (7.5) 35.3 aExcludes Kalawao County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. bDifferences are in percent. See text for formulas. Standard deviations are in parentheses. SOURCE: Data from U.S. Census Bureau. TABLE 8-6 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Percent Group Quarters Residents, 1990 Percent Group Quarters, 1990 Counties (Number)a Average Proportional Algebraic Differenceb Average Proportional Absolute Differenceb Percentage of Counties with Negative Differences All 3,140 −0.4 (8.7) 6.3 (6.1) 56.2 Less than 0.5% 175 1.0 (17.3) 9.9 (14.2) 50.6 0.5 to 1.0% 372 1.4 (8.1) 6.4 (5.2) 43.0 1.0 to 1.5% 6636 0.6 (7.6) 5.9 (4.7) 49.7 1.5 to 2.0% 591 −0.3 (7.4) 5.7 (4.6) 55.3 2.5 to 3.0% 535 −1.8 (8.3) 6.3 (5.7) 64.7 3.0 to 5.0% 431 −0.9 (7.0) 5.5 (4.4) 60.8 5.0% and over 400 −2.1 (9.0) 7.1 (5.9) 66.1 aExcludes Kalawao County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. bDifferences are in percent. See text for formulas. Standard deviations are in parentheses. SOURCE: Data from U.S. Census Bureau.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology TABLE 8-7 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Census Division Census Division Counties (Number)a Average Proportional Algebraic Differenceb Average Proportional Absolute Differenceb Percentage of Counties with Negative Differences All 3,140 −0.4 (8.7) 6.3 (6.1) 56.2 New England 67 −1.2 (5.3) 4.1 (3.6) 62.7 Middle Atlantic 150 0.6 (5.2) 4.1 (3.3) 54.0 East North Central 437 −1.4 (5.7) 4.7 (3.5) 64.5 West North Central 618 −3.0 (7.5) 6.4 (5.0) 72.0 South Atlantic 591 2.4 (8.3) 6.5 (5.7) 39.6 East South Central 364 2.9 (7.2) 6.0 (5.0) 37.4 West South Central 470 −0.4 (9.6) 7.0 (6.5) 50.9 Mountain 281 −2.8 (14.1) 9.0 (11.2) 68.7 Pacific 161 −2.5 (7.9) 6.5 (5.1) 68.5 aExcludes Kalawao County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. bDifferences are in percent. See text for formulas. Standard deviations are in parentheses. SOURCE: Data from U.S. Census Bureau. TABLE 8-8 Evaluation of 1990 County Population Estimates for Age Group 5-17, by Metropolitan Status, 1990 Metropolitan Status, 1990 Counties (Number)a Average Proportional Algebraic Differenceb Average Proportional Absolute Differenceb Percentage of Counties with Negative Differences All 3,140 −0.4 (8.7) 6.3 (6.1) 56.2 Nonmetropolitan 2,393 −1.2 (9.0) 6.5 (6.3) 60.0 Metropolitan 747 1.9 (7.2) 5.6 (4.9) 43.9 aExcludes Kalawao County, Hawaii, which had no persons aged 5-17 in 1980 or 1990. bDifferences are in percent. See text for formulas. Standard deviations are in parentheses. SOURCE: Data from U.S. Census Bureau.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology particular types of counties (Tables 8-1 to 8-8), except that, as one would expect, the smallest counties (those with populations under 2,500) have differences running at twice the overall average: 12.4 percent, compared with 6.3 percent overall (see Table 8-1). There may be a systematic prediction bias by county population size (Table 8-1). The average proportional algebraic difference is negative (indicating underestimates) for counties in the smaller population size groups (except for those under 2,500 with a 0.0 value) and positive (indicating overestimates) for counties in the larger population size groups. The percentage of counties with negative differences generally increases as county population size decreases. Nonmetropolitan counties also have a negative average proportional algebraic difference (see Table 8-8), with 60 percent of these counties having negative differences, which is consistent with the pattern of negative differences for smaller counties. Negative average proportional algebraic differences also characterize counties with negative or lower rates of population growth (Table 8-2); with lower percentages of black and other nonwhite population (Table 8-3); with average or higher than average percentages of Hispanic population (Table 8-4); with smaller percentages of poor population (Table 8-5); with higher percentages of group quarters residents (Table 8-6); and for counties in the Mountain, Pacific, North Central (East and West), and New England Divisions (Table 8-7). An issue in examining the average proportional algebraic differences in the 1990 county estimates of children aged 5-17 for categories of counties is whether the patterns observed—for example, the tendency for smaller (larger)-sized counties to have negative (positive) differences —are statistically significant, suggesting the possibility of a systematic bias. Tests of significance were conducted to determine whether there is evidence of possible bias with respect to the characteristics in Tables 8-1 to 8-8.8 The test results suggest the possibility of some bias associated with the estimates of children aged 5-17 for several categories of counties: county population size, percentage of black and other nonwhite population, percentage of Hispanic population, percentage of group quarters residents, metropolitan status, and census geographic division. However, the results are not conclusive given that there is only a single year—1990—for which it is possible to evaluate the estimates by comparison with figures from the census or another source. 8   Since most of these characteristics have ordered categories, a test of a linear trend was conducted using the Abelson-Tukey test procedure (Abelson and Tukey, 1963). Because the number of degrees of freedom is large, the test statistic has essentially a normal distribution under the null hypothesis of no trend. The categories for census geographic division do not have an ordering, so a one-way analysis of variance was performed for that characteristic.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology Effects on Poverty Estimates An issue in the context of Title I allocations is the extent to which errors in the population estimates for children aged 5-17 affect the estimates of the proportion of poor school-age children from log number models, or how they affect the estimates of the number of poor school-age children from log rate models. In the aggregate, the use of population estimates to convert estimated numbers from log number models to estimated proportions added about 1 percentage point to the overall average proportional absolute difference between the model estimates for 1989 and the 1990 census estimates (compare column 3 with column 2 of Table 6-3 in Chapter 6 for the two log number models). The use of population estimates to convert estimated proportions from log rate models to estimated numbers had even less effect overall (compare column 2 with column 3 of Table 6-3 for the two log rate models). In addition, although a rigorous analysis was not done, there seems to be little systematic contribution of errors in the population estimates to category differences in the model estimates of poor school-age children from the 1990 census estimates (see Appendix C). For the three single-equation rate models that were examined for 1989 in the first round of evaluations–the log rate model (under 21), the rate model, and the hybrid rate-number model (see Chapter 5)–the use of population estimates instead of 1990 census numbers to convert estimated proportions to estimated numbers of poor school-age children worsened the performance of the models for some characteristics (e.g., by increasing the spread between the largest negative and positive category differences compared with the census), improved their performance for other characteristics, and made essentially no difference for other characteristics. None of the category differences between the model estimates of poor school-age children developed with population estimates and those developed with 1990 census numbers was large. The evaluations of the effects of the population estimates on estimates of poor school-age children outlined above relate to a 10-year period: the population estimates for 1990 were developed on the basis of 1980 census data updated with other sources. The 1994 population estimates that are used to convert estimated numbers to estimated proportions of poor school-age children in 1993 from the log number (under 18) model were developed on the basis of 1990 census data. Because of the 4-year instead of 10-year period for updating, it is likely that errors in the 1994 population estimates are smaller than errors in the 1990 population estimates and that they have even smaller effects on the estimates of the number and proportion of poor school-age children. Errors in the 1996 population estimates that are used to convert estimated numbers to estimated proportions of poor school-age children in 1995 may also be somewhat smaller than errors in the 1990 population estimates.

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology EVALUATION OF SCHOOL DISTRICT ESTIMATES As it did for the school district estimates of poor school-age children, the Census Bureau evaluated its method for estimating total population and total school-age children at the district level by using the 1980-1990 evaluation file (see Chapter 7) to compare three sets of 1990 school district estimates with 1990 census numbers. The three sets of estimates were derived by: (1) applying 1980 census school district shares within counties to 1990 county population estimates; (2) applying 1980 census school district shares within counties to 1990 census county numbers; and (3) applying 1980 census school district shares within the nation as a whole to the national 1990 census number. Table 8-9 and Table 8-10 provide summary statistics for the three sets of school district estimates of 1990 total population and 1990 total school-age children, respectively, compared with the 1990 census numbers. The statistics provided are the average absolute difference between the estimates from a method and the census expressed as a percent of the average total population or total school-age children in the census, and the average proportional absolute difference between each set of estimates and the 1990 census numbers. For comparison purposes, the last row of each table provides the same statistics for county estimates of total population and total school-age children in 1990 from the Census Bureau's population estimates program. (As noted above, this program uses administrative records, such as births and deaths, to update population numbers from the previous census.) The county estimates of total population and total school-age children for 1990 differ little from the 1990 census numbers: the average absolute differences are 2 percent and 5 percent, respectively ( Table 8-9 and Table 8-10, first column); the average proportional absolute differences are 4 percent and 6 percent, respectively. The school district estimates show larger differences, although the differences are much smaller than those for school district estimates of poor school-age children (see Table 7-3 in the previous chapter). For school district estimates of total population under method (1), the average absolute difference is 10 percent of the average total population; for school district estimates of total school-age children under method (1), the average absolute difference is 12 percent of the average total school-age children. By comparison, for school district estimates of poor school-age children under method (1), the average absolute difference is 22 percent of the average number of poor school-age children. The corresponding average proportional absolute differences are 13 percent (total population), 17 percent (total school-age children), and 60 percent (poor school-age children). As noted above, evaluations of Census Bureau population estimates for states and counties have shown that the proportional differences of the estimates in comparison with census numbers are larger on average for small areas than for large ones. The proportional differences of the estimates also tend to be larger for areas in which the population is changing rapidly than for areas that are more

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology TABLE 8-9 Comparison of Within-County Shares Estimates and 1990 Census School District Numbers of Total Population in 1990 Model Average Absolute Difference, Relative to Average Total Population (in percent)a Average Proportional Absolute Difference (in percent)b 1990 School District Estimates (1) Within-county shares method using 1980 census shares applied to 1990 county model estimates 9.6 13.3 (2) Within-county shares method using 1980 census shares applied to 1990 census county numbers 9.2 12.6 (3) National stable shares method using 1980 census shares applied to 1990 census national number 13.9 18.9 1990 County Estimates from Census Bureau's Population Estimates Program 2.3 3.6 NOTES: School district estimates are based on 9,201 districts (9,243 districts in the 1980-1990 evaluation file minus 42 districts with estimated population 30 or less in 1980 or 1990). The 1990 census numbers used in the comparisons are from the complete count and are not subject to sampling error. The estimates from the three methods are controlled to the 1990 census national total population number before comparison to the 1990 census school district estimates. aThe formula, where there are n school districts or counties (i), and Y is the estimate (number) for the total population from a model (census), is ∑[( |Ymodel i − Ycensus i |) / n] / [ ∑( Ycensus i ) / n]. bThe formula is ∑ [( |Ymodel i − Ycensus i |) / Ycensus i ] / n . SOURCE: Data from U.S. Census Bureau. stable. The school district estimates of total population and total school-age children follow the same patterns. Compared with the school district estimates of poor school-age children, the estimates of total population and total school-age children benefit from two factors. First, total population and total school-age children are larger quantities to estimate. Second, the census data that are used to form within-county school district shares of total population and total school-age children, while subject to measurement error, are obtained from a complete count. Nonetheless, the estimates of total population and total school-age children for school districts are not nearly as accurate as the corresponding county estimates. The Census Bureau has

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Small-Area Estimates of School-Age Children in Poverty: Evaluation of Current Methodology TABLE 8-10 Comparison of Within-County Shares Estimates and 1990 Census School District Numbers of Total School-Age Children in 1990 Model Average Absolute Difference, Relative to Average Total School-Age Children (in percent)a Average Proportional Absolute Difference (in percent)b 1990 School District Estimates (1) Within-county shares method using 1980 census shares applied to 1990 county model estimates 12.0 16.9 (2) Within-county shares method using 1980 census shares applied to 1990 census county numbers 10.4 16.1 (3) National stable shares method using 1980 census shares applied to 1990 census national number 16.6 20.6 1990 County Estimates from Census Bureau's Population Estimates Program 4.9 6.3 NOTES: School district estimates are based on 9,201 districts (9,243 districts in the 1980-1990 evaluation file minus 42 districts with estimated population 30 or less in 1980 or 1990). The 1990 census numbers used in the comparisons are from the complete count and are not subject to sampling error. The estimates from the three methods are controlled to the 1990 census national number of total school-age children before comparison to the 1990 census school district estimates. aThe formula, where there are n school districts or counties (i), and Y is the estimate (number) of total school-age children from a model (census), is ∑[( |Ymodel i − Ycensus i |) / n] / [ ∑( Ycensus i ) / n]. bThe formula is ∑ [( |Ymodel i − Ycensus i |) / Ycensus i ] / n . SOURCE: Data from U.S. Census Bureau. begun, but has not had time to complete, an analysis of school enrollment data to determine if these data could be used to improve the school district estimates of total school-age children. Such work should be continued (see Chapter 9; see also National Research Council, 2000: Chapter 5).