APPENDIX D County Model Comparisons with 1990 Census Estimates

An external evaluation of alternative models for producing county estimates of poor school-age children can be carried out by comparing the county estimates obtained from each model for 1989 with 1900 census estimates of related children 5-17 who were poor in 1989. Although this evaluation is not ideal, it serves as a valuable tool for model assessment.

Chapter 4 reports the results of such an evaluation for four candidate models and four procedures that rely more heavily on estimates from the 1980 census. This appendix supplements the material in Chapter 4 in two ways. First, it provides additional results for the four models and four procedures examined in Chapter 4. Second, it provides evaluation results for the six single-equation models that were considered in the first round of evaluations.

EVALUATION MEASURES

Four measures are used for the evaluations in Chapter 4 and in this appendix. Two are overall measures of the differences between the county estimates from a model (or procedure) and the census, and two are measures for categories of counties. The four measures are defined as follows:

  1. Average absolute difference: the sum over all counties of the absolute (unsigned) difference between the model estimate of poor school-age children and the 1990 census estimate for each county, divided by the number of counties (3,141), or



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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations APPENDIX D County Model Comparisons with 1990 Census Estimates An external evaluation of alternative models for producing county estimates of poor school-age children can be carried out by comparing the county estimates obtained from each model for 1989 with 1900 census estimates of related children 5-17 who were poor in 1989. Although this evaluation is not ideal, it serves as a valuable tool for model assessment. Chapter 4 reports the results of such an evaluation for four candidate models and four procedures that rely more heavily on estimates from the 1980 census. This appendix supplements the material in Chapter 4 in two ways. First, it provides additional results for the four models and four procedures examined in Chapter 4. Second, it provides evaluation results for the six single-equation models that were considered in the first round of evaluations. EVALUATION MEASURES Four measures are used for the evaluations in Chapter 4 and in this appendix. Two are overall measures of the differences between the county estimates from a model (or procedure) and the census, and two are measures for categories of counties. The four measures are defined as follows: Average absolute difference: the sum over all counties of the absolute (unsigned) difference between the model estimate of poor school-age children and the 1990 census estimate for each county, divided by the number of counties (3,141), or

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations Average proportional absolute difference: the sum over all counties of the absolute difference between the model estimate of poor school-age children and the 1990 census estimate as a proportion of the census estimate for each county, divided by the number of counties,1 or Category algebraic difference: the sum for all counties (i) in a category (j) of the algebraic (signed) difference between the model estimate of poor school-age children and the 1990 census estimate for each county in the category, divided by the sum of the census estimates for the counties in the category, or Category average proportional algebraic difference: the sum for all counties (i) in a category (j) of the algebraic difference between the model estimate of poor school-age children and the 1990 census estimate as a proportion of the census estimate for each county in the category, divided by the number of counties in the category, or Measure (1) expresses overall absolute model-census differences in terms of numbers of poor school-age children; measure (2) expresses overall absolute model-census differences in terms of percentage errors for counties. Similarly, for categories of counties, measure (3) expresses model-census differences in terms of numbers of poor school-age children, while measure (4) expresses model-census differences in terms of percentage errors for counties. The two kinds of category differences are algebraic (not absolute) measures, in which positive differences offset negative differences. For measures (3) and (4), the counties are grouped into categories of the following characteristics: census division; metropolitan status of county; population size in 1990; population growth from 1980 to 1990; percent poor school-age children in the 1980 census; percent Hispanic population in 1990; percent black population in 1990; persistent poverty from 1960 to 1990 for rural counties; economic type for rural counties; percent group quarters residents in 1990; whether the county had households in the CPS sample; and percent change from 1980 to 1990 in the proportion of poor school-age children.2 Tables D-1 and D-2 show the number of counties in each category. 1   An analogous measure, shown in Table 4-2, is the average proportional absolute difference in estimated proportions of poor school-age children. 2   The characteristic of percent change in the proportion of poor school-age children from 1980 to 1990 was not included in the first round of evaluations.

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations COMPARISONS FOR CANDIDATE MODELS AND OTHER ESTIMATION PROCEDURES The four candidate models considered in Chapter 4 have the following designations: (a) log number model (under 21); (b) log number model (under 18); (c) log rate model (under 21); and (d) log rate model (under 18).3 The four other procedures (see Chapter 4) are designated as follows: (i) stable shares; (ii) stable shares within state; (iii) stable rates within state (with conversion); and (iv) average of 1980 census estimates and estimates for 1989 from the log number (under 21) model (a). Table 4-2 presents the overall measures of average absolute difference (measure 1) and average proportional absolute difference (measure 2) between the estimates from the four candidate models and four procedures and the estimates from the census. Table 4-3 presents the category algebraic differences (measure 3) for the four candidate models and procedures (i) and (iv). Table D-1 is identical to Table 4-3 except that it also includes results for procedures (ii) and (iii). Table D-2 presents the category average proportional algebraic differences for the four candidate models and the four procedures. For reasons given in Chapter 4, the 1990 census estimates used in these comparisons are ratio-adjusted by a constant factor to equal the CPS national estimate of poor school-age children in 1989. The findings from these evaluations are discussed in Chapter 4. The additional detail in Tables D-1 and D-2 is presented without commentary. 3    The estimates from the four candidate models and the models considered in the first round of evaluations, listed below, are the final estimates for all counties, after the initial estimates from the county regression model are combined in a ''shrinkage procedure'' with direct CPS estimates for those counties with households in the CPS sample and raked for consistency with the estimates from the state model; see Chapter 2.

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations TABLE D-1 Comparison of Model Estimates and Other Procedures with 1990 Census County Estimates of the Number of Poor School-Age Children in 1989: Algebraic Difference by Category of County (in percent)     Model Category Countiesa (Number) Log No. Under 21 (a) Log No. Under 18 (b) Log Rate Under 21 (c) Log Rate Under 18 (d) Census Divisionb New England 67 -2.9 -2.9 -2.9 -2.9 Middle Atlantic 150 -2.8 -2.8 -2.8 -2.8 East North Central 437 -0.2 -0.2 -0.2 -0.2 West North Central 618 1.7 1.7 1.7 1.7 South Atlantic 591 0.5 0.5 0.5 0.5 East South Central 364 -4.5 -4.5 -4.5 -4.5 West South Central 470 -2.7 -2.7 -2.7 -2.7 Mountain 281 4.3 4.3 4.3 4.3 Pacific 163 6.5 6.5 6.5 6.5 Metropolitan Status Central county of metropolitan area 493 2.4 1.6 -0.1 -0.5 Other metropolitan 254 -6.6 -5.0 5.1 6.3 Nonmetropolitan 2394 -4.2 -2.8 -0.3 0.4 1990 Population Size under 7,500 525 -9.0 -2.3 -1.9 2.3 7,500-14,999 630 -4.4 0.5 2.5 5.5 15,000-24,999 524 -5.1 -2.6 0.3 1.9 25,000-49,999 620 -4.2 -2.9 0.6 1.3 50,000-99,999 384 -3.5 -5.1 -1.2 -2.3 100,000-249,999 259 -1.8 -4.4 -1.8 -3.5 250,000 or more 199 3.3 3.2 0.5 0.5 1980 to 1990 Population Growth Decrease of more than 10.0% 444 -1.9 0.6 -3.4 -1.9 Decrease 0.1-10.0% 972 -0.6 -0.5 -1.9 -1.8 0.0-4.9% 547 -2.8 -2.8 -3.2 -3.1 5.0-14.9% 620 0.0 -1.0 0.2 -0.6 15.0-24.9% 260 7.7 5.8 5.5 4.6 25.0% or more 292 -4.0 -1.4 1.7 3.1

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Other Procedures Category  Stable Shares (i) Stable Shares in State (ii) Stable Rates in State (iii) Average of Census and (a) (iv Census Divisionb New England 35.9 -2.9 -2.9 7.8 Middle Atlantic 27.1 -2.8 -2.8 4.4 East North Central -2.8 -0.2 -0.2 -5.6 West North Central -1.8 1.7 1.7 -2.1 South Atlantic 14.8 0.5 0.5 8.1 East South Central 14.1 -4.5 -4.5 2.1 West South Central -18.1 -2.7 -2.7 -6.3 Mountain -23.2 4.3 4.3 -3.1 Pacific -21.3 6.5 6.5 0.2 Metropolitan Status Central county of metropolitan area -1.6 -0.6 -0.4 0.4 Other metropolitan 3.2 -1.6 10.1 3.4 Nonmetropolitan 3.3 1.8 -0.5 -1.4 1990 Population Size under 7,500 16.5 23.0 9.4 1.3 7,500-14,999 10.9 10.7 4.4 2.2 15,000-24,999 6.2 3.4 0.0 -0.6 25,000-49,999 2.4 -0.2 -0.3 -1.3 50,000-99,999 -2.5 -4.8 -2.5 -3.3 100,000-249,999 -4.9 -5.9 -2.9 -3.3 250,000 or more -0.6 0.8 0.8 1.8 1980 to 1990 Population Growth Decrease of more than 10.0% 9.1 9.9 -3.1 -3.4 Decrease 0.1-10.0% 7.5 0.7 -4.6 -2.7 0.0-4.9% 11.0 -2.3 -3.3 -0.2 5.0-14.9% 6.1 0.2 1.7 2.1 15.0-24.9% -12.8 4.4 3.5 2.4 25.0% or more -21.2 -6.8 7.2 1.0

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations     Model Category Countiesa (Number) Log No. Under 21 (a) Log No. Under 18 (b) Log Rate Under 21 (c) Log Rate Under 18 (d) Percent Poor School-Age Children, 1980 Less than 9.4% 516 -4.0 -4.5 0.0 0.2 9.4-11.6% 524 -0.5 -1.0 -1.6 -1.8 11.7-14.1% 530 3.6 2.3 1.8 1.0 14.2-17.2% 523 0.9 1.2 -1.2 -1.4 17.3-22.3% 519 1.8 1.7 0.3 -0.1 22.4-53.0% 523 -2.2 0.8 1.3 2.8 Percent Hispanic, 1990 0.0-0.9% 1770 -3.4 -3.3 -1.6 -1.5 1.0-4.9% 847 0.5 0.1 0.4 0.1 5.0-9.9% 193 -1.4 -0.6 -1.1 -0.8 10.0-24.9% 181 2.2 1.8 0.7 0.5 25.0-98.0% 150 3.9 4.6 2.2 2.7 Percent Black, 1990 0.0-0.9% 1446 -1.2 0.3 3.9 4.9 1.0-4.9% 615 -0.7 -2.0 1.3 0.5 5.0-9.9% 294 -2.9 -2.5 -0.7 -0.6 10.0-24.9% 381 2.0 1.2 -1.0 -1.3 25.0-87.0% 405 1.0 1.7 -1.8 -1.4 Persistent Rural Poverty, 1960-1990c Rural, not poor 1740 -4.0 -3.7 -1.2 -1.0 Rural, poor 535 -5.0 -2.1 0.7 2.1 Not classified 866 1.7 1.2 0.3 0.0 Economic Type, Rural Countiesc Farming 556 -5.5 -2.5 -1.6 0.7 Mining 146 -10.7 -5.1 -6.3 -3.6 Manufacturing 506 -6.2 -5.9 -1.7 -1.0 Government 243 2.1 -1.3 6.3 3.2 Services 323 -3.9 -3.0 -1.8 -1.2 Nonspecialized 484 -3.7 -1.0 -0.1 1.4 Not classified 883 1.7 1.2 0.3 0.0

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Other Procedures Category Stable Shares (i) Stable Shares in State (ii) Stable Rates in State (iii) Average of Census and (a) (iv) Percent Poor School-Age Children, 1980 Less than 9.4% 2.4 0.8 5.1 -1.1 9.4-11.6% -9.9 -4.0 -1.9 -3.6 11.7-14.1% -4.2 1.8 0.7 0.2 14.2-17.2% -5.0 -3.0 -5.3 -1.8 17.3-22.3% 10.7 1.9 -0.1 4.2 22.4-53.0% 12.3 4.1 1.8 4.1 Percent Hispanic, 1990 0.0-0.9% 10.7 -0.6 -1.4 0.2 1.0-4.9% 0.2 0.1 1.1 -0.4 5.0-9.9% 6.7 1.2 1.4 1.7 10.0-24.9% -5.7 1.7 1.3 0.1 25.0-87.0% -16.8 -1.2 -1.3 -0.4 Percent Black, 1990 0.0-0.9% -3.7 3.9 6.0 -0.5 1.0-4.9% -6.3 -1.6 -0.4 -2.9 5.0-9.9% -8.4 -2.3 2.2 -1.8 10.0-24.9% -2.6 -0.7 -2.1 0.2 25.0-87.0% 16.5 1.2 -2.4 3.7 Persistent Rural Poverty, 1960-1990c Rural, not poor 0.1 0.2 -1.4 -3.4 Rural, poor 9.8 5.4 0.1 1.2 Not classified -1.2 -0.7 0.4 0.7 Economic Type, Rural Countiesc Farming 13.2 18.0 7.9 1.1 Mining -8.9 -6.6 -13.1 -10.6 Manufacturing 12.1 0.8 -1.1 -0.2 Government -0.9 4.6 4.1 0.0 Services -5.8 -4.0 -3.4 -4.3 Nonspecialized 2.2 1.6 -2.0 -1.5 Not classified -1.2 -0.7 0.4 0.7

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations     Model Category Countiesa (Number) Log No. Under 21 (a) Log No. Under 18 (b) Log Rate Under 21 (c) Log Rate Under 18 (d) Percent Group Quarters Residents, 1990 Less than 1.0% 545 -6.7 -2.7 2.0 4.7 1.0-4.9% 2187 0.3 0.7 -0.3 0.1 5.0-9.9% 299 2.3 -4.4 0.5 -5.2 10.0-41.0% 110 14.2 -3.2 7.4 -7.5 Status in CPS, 1989-1991 In CPS sample 1028 1.4 1.0 -0.2 -0.5 In CPS, no poor children 5-17 246 -2.6 -1.9 7.3 7.8 Not in CPS sample 1867 -4.1 -2.8 -0.1 0.6 Change in Poverty Rate for School-Age Children, 1980-1990 Decrease of more than 3.0% 536 7.5 10.4 16.2 18.1 Decrease 0.1-3.0% 649 2.1 1.9 3.1 2.9 0.0-0.9% 272 -2.6 -0.8 -0.4 0.5 1.0-3.4% 621 3.8 2.2 3.4 2.6 3.5-6.4% 532 -1.2 -2.4 -3.8 -4.3 6.5-38.0% 523 -7.2 -5.2 -8.7 -7.8 NOTES: The census estimates are controlled to the CPS national estimate for 1989. The algebraic difference by category is the sum for all counties in a category of the algebraic (signed) difference between the model estimate of poor school-age children and the 1990 census estimate for each county, divided by the sum of the census estimates for all counties in the category. See Chapter 4 text for definitions of models. a 3,141 counties are assigned to a category for most characteristics; 3,135 counties are assigned to a category for 1980-1990 population growth and 1980 percent poor school-age children; 3,133 counties are assigned to a category for 1980-1990 percent change in poverty rate for school-age children.

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Other Procedures Category Stable Shares (i) Stable Shares in State (ii) Stable Rates in State (iii) Average of Census and (a) (iv) Percent Group Quarters Residents, 1990 Less than 1.0% -1.4 -0.9 3.7 0.3 1.0-4.9% -0.4 0.3 -0.1 0.1 5.0-9.9% 7.8 -1.4 -2.8 -0.8 10.0-41.0% 1.8 -0.9 -1.4 -2.2 Status in CPS, 1989-1991 In CPS sample -0.6 -0.7 -0.4 0.5 In CPS, no poor children 5-17 10.0 3.7 12.0 5.9 Not in CPS sample 0.6 2.3 -0.3 -2.3 Change in Poverty Rate for School-Age Children, 1980-1990 Decrease of more than 3.0% 51.6 30.1 32.8 30.0 Decrease 0.1-3.0% 29.2 8.0 9.8 12.1 0.0-0.9% 4.3 -0.9 3.3 3.1 1.0-3.4% -5.1 3.7 3.4 0.2 3.5-6.4% -14.3 -7.7 -9.5 -8.3 6.5-38.0% -25.2 -14.2 -16.5 -14.5 b Census division states: New England: Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut Middle Atlantic: New York, New Jersey, Pennsylvania East North Central: Ohio, Indiana, Illinois, Michigan, Wisconsin West North Central: Missouri, Minnesota, Iowa, North Dakota, South Dakota, Nebraska, Kansas South Atlantic: Delaware, Maryland, District of Columbia, Virginia, West Virginia, North Carolina, South Carolina, Georgia, Florida East South Central: Kentucky, Tennessee, Alabama, Mississippi West South Central: Arkansas, Louisiana, Oklahoma, Texas Mountain: Montana, Idaho, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada Pacific: Washington, Oregon, California, Alaska, Hawaii c The Economic Research Service, U.S. Department of Agriculture, classifies rural counties by 1960-1990 poverty status and economic type. Counties not classified are urban counties and rural counties for which a classification could not be made. SOURCE: Data from the Bureau of the Census.

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations TABLE D-2 Comparison of Model Estimates and Other Procedures with 1990 Census County Estimates of the Number of Poor School-Age Children in 1989: Average Proportional Algebraic Difference for Counties in Each Category (in percent)     Model Category Counties (Number) Log No. Under 21 (a) Log No. Under 18 (b) Log Rate Under 21 (c) Log Rate Under 18 (d) Census Division New England 67 4.1 4.5 6.6 7.1 Middle Atlantic 150 -5.9 -8.4 0.7 -1.0 East North Central 437 -3.6 -3.0 2.5 3.0 West North Central 618 -3.1 -0.6 0.5 2.3 South Atlantic 591 1.2 2.5 8.9 9.8 East South Central 364 -4.6 -3.0 0.5 1.3 West South Central 470 -7.6 -4.6 -4.0 -2.3 Mountain 281 0.6 5.4 7.2 10.4 Pacific 163 10.2 13.6 17.8 20.2 Metropolitan Status Central county of metropolitan area 493 0.6 -2.0 1.0 -0.6 Other metropolitan 254 -3.6 -0.8 11.6 13.7 Nonmetropolitan 2394 -2.6 0.2 2.9 4.7 1990 Population Size under 7,500 525 -5.9 1.6 2.6 7.6 7,500-14,999 630 -1.0 3.0 5.7 8.4 15,000-24,999 524 -3.2 -1.8 2.1 3.2 25,000-49,999 620 -1.5 -0.7 4.2 4.6 50,000-99,999 384 -1.4 -3.3 2.5 1.2 100,000-249,999 259 -0.7 -3.4 1.5 -0.3 250,000 or more 199 1.0 0.4 1.3 1.1 1980 to 1990 Population Growth Decrease of more than 10.0% 444 -5.2 -1.0 -1.2 2.0 Decrease 0.1-10.0% 972 -3.3 -2.2 0.1 0.9 0.0-4.9% 547 -1.3 0.4 4.0 5.0 5.0-14.9% 620 -0.7 0.0 4.7 5.0 15.0-24.9% 260 4.0 3.8 10.6 10.1 25.0% or more 292 -4.1 2.3 9.8 14.0

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Other Procedures Category Stable Shares (i) Stable Shares in State (ii) Stable Rates in State (iii) Average of Census and (a) (iv) Census Division New England 45.6 7.0 8.6 20.2 Middle Atlantic 28.8 -0.2 3.1 3.6 East North Central 0.6 3.5 5.8 -4.6 West North Central 18.7 21.0 15.9 3.7 South Atlantic 28.6 10.2 11.9 14.5 East South Central 19.5 0.4 0.3 5.0 West North Central -6.4 8.8 -0.2 -5.5 Mountain -3.4 30.5 22.6 2.6 Pacific -9.6 23.9 20.6 7.5 Metropolitan Status Central county of metropolitan area 4.2 -0.2 2.2 0.8 Other metropolitan 16.2 7.0 20.9 11.7 Nonmetropolitan 13.2 15.0 9.9 3.6 1990 Population Size under 7,500 30.3 42.0 25.9 9.2 7,500-14,999 16.3 17.5 12.2 6.1 15,000-24,999 9.0 6.8 4.5 1.1 25,000-49,999 6.0 3.1 5.3 2.2 50,000-99,999 3.1 -1.7 3.3 0.8 100,000-249,999 2.4 -2.5 2.8 0.8 250,000 or more 7.9 2.9 6.5 4.5 1980 to 1990 Population Growth Decrease of more than 10.0% 29.0 36.9 17.5 3.7 Decrease 0.1-10.0% 11.6 10.1 3.0 -0.8 0.0-4.9% 11.7 7.5 5.2 3.3 5.0-14.9% 9.9 6.1 8.7 4.8 15.0-24.9% 8.7 8.7 16.0 10.4 25.0% or more -4.0 4.3 23.8 12.6

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations       Model Category Log Rate Under 21 Rate Under 21 Log Hybrid Rate-Number Under 21   D.4 D.4a D.5 D.5a D.6 D.6a Census Divisiona New England 1.9 1.9 1.9 1.9 1.9 1.9 Middle Atlantic 2.0 2.0 2.0 2.0 2.0 2.0 East North Central 4.7 4.7 4.7 4.7 4.7 4.7 West North Central 6.8 6.8 6.8 6.8 6.8 6.8 South Atlantic 5.5 5.5 5.5 5.5 5.5 5.5 East South Central 0.3 0.3 0.3 0.3 0.3 0.3 West South Central 2.1 2.1 2.1 2.1 2.1 2.1 Mountain 9.4 9.4 9.4 9.4 9.4 9.4 Pacific 11.8 11.8 11.8 11.8 11.8 11.8 Metropolitan Status Central county of metropolitan area 4.8 4.5 4.8 4.5 7.7 7.4 Other metropolitan 10.2 7.5 9.7 7.0 2.5 -0.1 Nonmetropolitan 4.6 5.8 4.6 5.8 -0.9 0.2 1990 Population Size under 7,500 3.0 4.4 5.6 7.2 -6.6 -5.3 7,500-14,999 7.6 8.6 7.7 8.7 -0.9 0.0 15,000-24,999 5.3 6.4 5.2 6.3 -1.5 -0.4 25,000-49,999 5.6 6.1 5.5 6.0 0.3 0.7 50,000-99,999 3.6 3.9 3.8 4.0 0.3 0.6 100,000-249,999 3.0 3.1 1.7 1.8 2.1 2.2 250,000 or more 5.5 5.0 5.7 5.3 9.2 8.8 1980 to 1990 Population Growth Decrease of more than 10.0% 1.3 1.9 2.4 3.0 2.4 3.0 Decrease 0.1-10.0% 2.9 3.0 3.1 3.2 3.9 4.0 0.0-4.9% 1.6 2.3 1.2 1.9 1.3 2.0 5.0-14.9% 5.2 5.1 5.6 5.6 4.2 4.2 15.0-24.9% 10.7 9.9 10.9 10.0 12.6 11.7 25.0% or more 6.7 6.6 5.8 5.6 4.1 3.9

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Model Category Log Number Under 21 D.1 Log Number Under 18 D.2 Log Number Under 21, Fixed State Effects D.3 Percent Poor School-Age Children, 1980 Less than 9.4% 0.8 0.2 -1.0 9.4-11.6% 4.4 3.9 3.3 11.7-14.1% 8.8 7.3 7.0 14.2-17.2% 5.8 6.2 5.2 17.3-22.3% 6.8 6.7 8.5 22.4-53.0% 2.6 5.7 7.7 Percent Hispanic, 1990 0.0-0.9% 1.4 1.4 2.3 1.0-4.9% 5.5 5.0 4.7 5.0-9.9% 3.5 4.3 3.3 10.0-24.9% 7.3 6.8 7.4 25.0-98.0% 9.0 9.8 8.5 Percent Black, 1990 0.0-0.9% 3.6 5.2 5.3 1.0-4.9% 4.2 2.8 2.9 5.0-9.9% 1.9 2.4 1.5 10.0-24.9% 7.0 6.2 5.7 25.0-87.0% 6.0 6.7 7.9 Persistent Rural Poverty, 1960-1990b Rural, not poor 0.8 1.0 1.4 Rural, poor -0.3 2.7 5.2 Not classified 6.7 6.2 5.8 Economic Type, Rural Countiesb Farming -0.8 2.4 7.0 Mining -6.3 -0.4 -4.0 Manufacturing -1.6 -1.2 0.4 Government 7.2 3.6 8.7 Services 0.8 1.8 1.1 Nonspecialized 1.0 3.9 3.4 Not classified 6.7 6.2 5.8

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Model   Log Rate Under 21 Rate Under 21 Log Hybrid Rate-Number Under 21 Category D.4 D.4a D.5 D.5a D.6 D.6a Percent Poor School-Age Children, 1980 Less than 9.4% 4.9 1.7 5.6 2.3 5.6 2.3 9.4-11.6% 3.2 3.0 4.4 4.2 5.6 5.3 11.7-14.1% 6.8 6.9 6.2 6.4 7.5 7.6 14.2-17.2% 3.7 6.7 2.8 5.7 2.7 5.7 17.3-22.3% 5.3 5.8 4.4 4.8 5.0 5.6 22.4-53.0% 6.3 6.8 6.2 6.7 2.1 2.7 Percent Hispanic, 1990 0.0-0.9% 3.3 3.1 3.1 3.0 1.6 1.4 1.0-4.9% 5.4 5.1 5.1 4.8 5.6 5.3 5.0-9.9% 3.8 3.4 5.0 4.7 4.4 3.9 10.0-24.9% 5.7 5.1 7.2 6.4 8.2 7.6 25.0-98.0% 7.2 8.9 5.9 7.7 6.9 8.6 Percent Black, 1990 0.0-0.9% 9.0 9.1 8.6 8.7 4.3 4.3 1.0-4.9% 6.3 5.6 6.9 6.1 4.8 4.0 5.0-9.9% 4.2 3.6 4.1 3.6 4.3 3.6 10.0-24.9% 3.9 3.8 3.9 3.8 6.5 6.3 25.0-87.0% 3.1 4.2 2.9 4.1 4.2 5.5 Persistent Rural Poverty, 1960-1990b Rural, not poor 3.6 5.4 3.6 5.3 -1.1 0.5 Rural, poor 5.7 5.9 5.7 5.8 -1.4 -1.2 Not classified 5.2 4.8 5.2 4.8 7.2 6.9 Economic Type, Rural Countiesb Farming 3.3 5.2 5.0 6.9 -3.9 -2.1 Mining -1.7 1.5 -1.4 1.8 -6.0 -3.1 Manufacturing 3.2 3.1 3.4 3.3 -1.5 -1.7 Government 11.6 11.7 9.7 9.7 1.9 2.0 Services 3.1 4.8 3.1 4.8 -0.5 1.2 Nonspecialized 4.8 6.8 4.4 6.3 -0.4 1.4 Not classified 5.2 4.8 5.3 4.8 7.3 6.9

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Model Category Log Number Under 21 D.1 Log Number Under 18 D.2 Log Number Under 21, Fixed State Effects D.3 Percent Group Quarters Residents, 1990 Less than 1.0% -2.1 2.1 -0.5 1.0-4.9% 5.2 5.7 5.4 5.0-9.9% 7.4 0.3 5.0 10.0-41.0% 19.9 1.6 11.9 Status in CPS, 1989-1991 In CPS sample 6.4 5.9 5.8 In CPS, no poor children 5-17 2.2 3.0 0.8 Not in CPS sample 0.6 2.0 2.8 NOTES: See text for definitions of models and measures. 3,141 counties are assigned to a category for most characteristics; 3,135 counties are assigned to a category for 1980-1990 population growth and 1980 percent poor school-age children; 3,133 counties are assigned to a category for 1980-1990 percent change in poverty rate for school-age children; see Table D-1 for number of counties in each category. a Census division states: New England: Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut Middle Atlantic: New York, New Jersey, Pennsylvania East North Central: Ohio, Indiana, Illinois, Michigan, Wisconsin West North Central: Missouri, Minnesota, Iowa, North Dakota, South Dakota, Nebraska, Kansas

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Model   Log Rate Under 21 Rate Under 21 Log Hybrid Rate-Number Under 21 Category D.4 D.4a D.5 D.5a D.6 D.6a   7.0 4.9 8.9 6.7 2.7 0.6   4.6 4.6 4.7 4.7 5.7 5.7   5.5 7.3 4.0 5.8 0.3 2.0   12.7 17.4 5.0 9.3 0.6 4.7   4.7 4.4 5.3 5.0 6.8 6.6   12.6 10.2 -1.0 -2.9 5.3 3.0   4.8 6.2 5.0 6.3 -1.4 -0.1 South Atlantic: Delaware, Maryland, District of Columbia, Virginia, West Virginia, North Carolina, South Carolina, Georgia, Florida East South Central: Kentucky, Tennessee, Alabama, Mississippi West South Central: Arkansas, Louisiana, Oklahoma, Texas Mountain: Montana, Idaho, Wyoming, Colorado, New Mexico, Arizona, Utah, Nevada Pacific: Washington, Oregon, California, Alaska, Hawaii b The Economic Research Service, U.S. Department of Agriculture, classifies rural counties by 1960-1990 poverty status and economic type. Counties not classified are urban counties and rural counties for which a classification could not be made. SOURCE: Data from the Bureau of the Census.

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations TABLE D-5 Comparison of First-Round Model Estimates with 1990 Census County Estimates of the Number of Poor School-Age Children in 1989: Average Proportional Algebraic Difference for Counties in Each Category (in percent)   Model Category Log Number Under 21 D. 1 Log Number Under 18 D.2 Log Number Under 21, Fixed State Effects D.3 Census Division New England 9.3 9.7 8.1 Middle Atlantic -1.2 -3.9 -3.5 East North Central 1.2 1.8 2.2 West North Central 1.7 4.4 7.4 South Atlantic 6.2 7.6 8.1 East South Central 0.1 1.8 0.9 West South Central -3.0 0.1 0.2 Mountain 5.6 10.6 12.2 Pacific 15.6 19.2 19.2 Metropolitan Status Central county of metropolitan area 5.6 2.9 3.5 Other metropolitan 1.1 4.1 -0.1 Nonmetropolitan 2.2 5.1 6.5 1990 Population Size under 7,500 -1.3 6.6 9.9 7,500-14,999 3.9 8.1 9.3 15,000-24,999 1.6 3.0 4.2 25,000-49,999 3.4 4.2 3.7 50,000-99,999 3.4 1.5 1.0 100,000-249,999 4.2 1.4 1.4 250,000 or more 5.9 5.4 5.0 1980 to 1990 Population Growth Decrease of more than 10.0% -0.5 3.9 10.5 Decrease 0.1-10.0% 1.5 2.6 5.5 0.0-4.9% 3.6 5.3 5.1 5.0-14.9% 4.2 4.9 4.1 15.0-24.9% 9.2 9.0 7.5 25.0% or more 0.7 7.3 -0.3

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Model   Log Rate Under 21 Rate Under 21 Log Hybrid Rate-Number Under 21 Category D.4 D.4a D.5 D.5a D.6 D.6a Census Division New England 11.9 13.1 10.9 12.2 8.3 9.4 Middle Atlantic 5.7 4.1 4.2 2.8 -1.2 -2.6 East North Central 7.5 8.5 6.4 7.4 -0.1 0.7 West North Central 5.4 7.3 6.1 8.0 -0.2 1.6 South Atlantic 14.3 12.6 14.5 12.8 7.7 6.1 East South Central 5.4 4.8 5.3 4.6 0.7 0.0 West South Central 0.7 3.3 1.8 4.3 -6.7 -4.4 Mountain 12.5 14.6 17.0 19.3 3.9 5.7 Pacific 23.7 23.8 25.6 25.8 15.6 15.7 Metropolitan Status Central county of metropolitan area 6.0 4.9 5.0 4.0 6.1 4.9 Other metropolitan 17.1 13.3 16.1 12.4 6.8 3.4 Nonmetropolitan 7.9 9.4 9.0 10.5 0.3 1.6 1990 Population Size under 7,500 7.7 9.2 12.7 14.2 -3.5 -2.3 7,500-14,999 10.9 12.3 11.5 12.8 2.2 3.4 15,000-24,999 7.2 8.2 6.9 8.0 0.1 1.1 25,000-49,999 9.3 10.1 8.8 9.6 2.8 3.5 50,000-99,999 7.5 7.3 7.3 7.0 3.1 2.8 100,000-249,999 6.6 6.0 3.3 2.9 4.0 3.4 250,000 or more 6.3 4.4 7.3 5.5 8.7 6.9 1980 to 1990 Population Growth Decrease of more than 10.0% 3.7 3.9 7.9 8.0 -1.7 -1.5 Decrease 0.1-10.0% 5.0 6.4 5.4 6.8 -0.7 0.6 0.0-4.9% 9.2 9.9 8.2 8.9 2.7 3.4 5.0-14.9% 9.9 10.2 9.6 10.0 3.4 3.6 15.0-24.9% 16.0 15.6 15.6 15.2 8.0 7.6 25.0% or more 15.2 15.7 16.2 16.9 3.9 4.1

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Model Category Log Number Under 21 D.1 Log Number Under 18 D.2 Log Number Under 21, Fixed State Effects D.3 Percent Poor School-Age Children, 1980 Less than 9.4% 0.6 1.8 -1.3 9.4-11.6% 3.2 4.8 3.5 11.7-14.1% 2.9 3.6 4.3 14.2-17.2% 4.6 5.8 8.1 17.3-22.3% 2.2 3.7 6.9 22.4-53.0% 2.5 8.3 11.2 Percent Hispanic, 1990 0.0-0.9% 1.6 3.5 5.1 1.0-4.9% 6.0 8.2 6.7 5.0-9.9% 4.3 5.7 6.4 10.0-24.9% -1.1 1.8 3.1 25.0-98.0% -1.5 1.5 4.7 Percent Black, 1990 0.0-0.9% 2.4 6.5 7.3 1.0-4.9% 3.5 2.8 3.5 5.0-9.9% 2.4 2.4 1.8 10.0-24.9% 4.2 5.6 4.5 25.0-87.0% 0.9 2.1 5.6 Persistent Rural Poverty, 1960-1990 Rural, not poor 2.2 4.9 6.1 Rural, poor 1.0 5.3 7.7 Not classified 4.5 3.8 2.9 Economic Type, Rural Counties Farming -0.5 5.3 9.9 Mining -4.1 3.7 0.7 Manufacturing 1.0 2.7 3.5 Government 11.0 10.3 13.2 Services 2.7 4.5 4.3 Nonspecialized 2.0 4.9 4.8 Not classified 4.8 4.1 3.3

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Model   Log Rate Under 21 Rate Under 21 Log Hybrid Rate-Number Under 21 Category D.4 D.4a D.5 D.5a D.6 D.6a Percent Poor School-Age Children, 1980 Less than 9.4% 8.9 7.5 7.2 5.9 3.8 2.5 9.4-11.6% 7.5 9.0 8.5 10.2 2.3 3.7 11.7-14.1% 6.4 7.7 7.3 8.6 0.9 2.2 14.2-17.2% 9.1 11.1 10.2 12.3 1.4 3.2 17.3-22.3% 7.0 8.1 7.5 8.6 -0.6 0.4 22.4-53.0% 11.5 10.6 13.0 11.0 2.4 1.5 Percent Hispanic, 1990 0.0-0.9% 7.7 7.6 8.4 8.2 1.5 1.4 1.0-4.9% 12.4 12.9 12.1 12.7 5.6 6.1 5.0-9.9% 7.2 10.0 9.3 12.4 0.6 3.0 10.0-24.9% 1.9 5.4 3.3 6.9 -6.0 -2.9 25.0-98.0% 2.6 7.4 3.8 8.7 -7.7 -3.5 Percent Black, 1990 0.0-0.9% 9.2 10.4 10.4 11.7 1.5 2.6 1.0-4.9% 8.2 8.7 8.0 8.7 2.0 2.4 5.0-9.9% 7.7 6.6 7.9 6.9 3.1 2.1 10.0-24.9% 9.9 9.8 9.0 9.0 3.9 3.7 25.0-87.0% 5.0 5.4 5.9 6.2 -1.0 -0.5 Persistent Rural Poverty, 1960-1990 Rural, not poor 7.3 9.4 8.7 10.8 0.1 1.9 Rural, poor 8.6 8.3 8.4 8.1 0.0 -0.2 Not classified 10.3 8.7 9.7 8.2 6.0 4.5 Economic Type, Rural Counties Farming 5.3 7.6 9.3 11.6 -3.5 -1.3 Mining 3.1 8.6 4.5 10.3 -6.7 -2.0 Manufacturing 7.6 7.6 7.5 7.4 1.2 1.1 Government 17.3 17.2 15.0 14.8 7.2 7.0 Services 6.6 8.2 7.9 9.6 0.8 2.3 Nonspecialized 7.0 8.7 6.9 8.6 0.3 2.0 Not classified 10.6 9.0 10.1 8.6 6.3 4.8

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Model Category Log Number Under 21 D.1 Log Number Under 18 D.2 Log Number Under 21, Fixed State Effects D.3 Percent Group Quarters Residents, 1990 Less than 1.0% -1.1 7.5 3.8 1.0-4.9% 1.7 4.3 5.0 5.0-9.9% 10.4 4.3 9.5 10.0-41.0% 19.4 -0.3 12.4 Status in CPS, 1989-1991 In CPS sample 4.0 3.6 3.9 In CPS, no poor children 5-17 3.6 6.0 3.1 Not in CPS sample 1.8 5.1 6.7 NOTE: See notes to Table D-4. SOURCE: Data from the Bureau of the Census.

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Small-Area Estimates of School-Age Children in Poverty - Interim Report 2: Evaluation of Revised 1993 County Estimates for Title I Allocations   Model   Log Rate Under 21 Rate Under 21 Log Hybrid Rate-Number Under 21 Category D.4 D.4a D.5 D.5a D.6 D.6a Percent Group Quarters Residents, 1990 Less than 1.0% 11.3 10.7 13.7 13.2 1.8 1.1 1.0-4.9% 6.7 7.4 7.4 8.1 1.5 2.1 5.0-9.9% 11.9 14.2 11.3 13.5 3.3 5.3 10.0-41.0% 17.0 19.0 9.9 11.8 2.0 3.8 Status in CPS, 1989-1991 In CPS sample 7.0 6.6 8.9 8.6 4.3 3.9 In CPS, no poor children 5-17 15.4 13.9 4.6 3.5 5.8 4.5 Not in CPS sample 8.2 9.7 9.5 11.0 -0.3 1.1