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OCR for page 97
Appendix
Use of School Lunch Data in New York
State for the Estimation of School-Age
Children in Poverty: An Analysis
James H. Wyckoff and Frank Papa
This analysis uses data from the National School Lunch Program in New
York State as an alternative to census data in estimating the number of poor
children (age 5-17) for use in the allocation of Title I funds to school districts.
This analysis considers two uses of poverty estimates in the Title I allocations.
First, for the purpose of estimating the number of school-age children who are in
poor families in 1989, we compare estimates from using school lunch data for
1990 with estimates from the Census Bureau's synthetic or constant-share method
that is based on 1980 census data. Second, we examine the sensitivity of various
methods in estimating the 15 percent threshold for concentration grants. In
conclusion, we examine some of the difficulties we encountered in attempting to
use school lunch data for this purpose. Although this analysis may provide some
interesting insights to some evaluation questions, it only reflects the experience
in one state; other states may well differ in critical ways that would lead outcomes
to change as well.
The data for this analysis cover public schools and come from the New York
State Education Department Report 325 for February 1990, printed on July 10,
1992. The 325 Report is an accounting of the number of eligible applicants for
free and reduced-price school lunches by school. Our data include all public
school reports.1
1Some of the state's 3,279 public schools did not send reports to the New York State Education
Department: most of those 389 schools did not operate a school lunch program. Those observations
are treated as zeros in the analysis.
Reports from private schools are also available but they have not been included in this analysis:
804 private schools reported 42,828 free and reduced-price school lunch applicants in February
1990. This number represents about 12 percent of all school lunch applicants.
97
OCR for page 98
98
SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY
ESTIMATES OF POOR CHILDREN
The school lunch method for estimating the number of poor children in each
school district is conceptually similar to the census constant-share method.
County totals of poor children are allocated to specific school districts on the
basis of an estimate of the ratio of poor children in the district to the county total.
The school lunch ratio is computed by the ratio of free (or free and reduced-price)
school lunch applicants in a school district to those in the county. This ratio is
then multiplied by the total number of poor school-age children in the county
(from the 1990 census) to arrive at the school district estimate. When districts
cross county boundaries, the district is assigned to the county in which the school
district administrative office is located.2 In summary:
S. go
Yip'=-trio Cent,
where:
J.
1990,
(1)
yj'is the school lunch estimate of poor school-age children in school district
SLi9j0 is the number of school lunch applicants in county i, school district j in
Is the number of school lunch applicants in county i in 1990, and
CENi90iS the 1990 census estimate of poor school-age children in county i.
The evaluation below compares these estimates of poor school-age children
to those estimated using the census constant-share method, which applies the
1980 census shares of poor school-age children for school districts (or parts of
school districts) within counties to the 1990 census county estimates of poor
school-age children (synthetic method (2) in Chapter 3~. Mean algebraic and
absolute percentage errors are estimated for each method by using the 1990
census totals for school districts as "truth." Tables A-1 to A-3 summarize these
results.
Table A-1 illustrates the distribution of the algebraic percentage errors,
unweighted and when each district is weighted by the number of school-age
2We also computed estimates by employing school-level data to form county pieces when schools
of a district are located in more than one county. Roughly 35 percent of the districts cross county
boundaries. This estimation method produces estimates that are very close to the method that does
not account for the county pieces. As a result, we present only the results that assign a whole district
to the county of the district's administrative of lice.
OCR for page 99
APPENDIX
99
TABLE A-1 Distribution of Algebraic Percentage Errors for Children Age 5
17 in Families in Poverty, Various Models, Unweighted and Weighted, New
York State School Districts in Evaluation Universe, 1990 (N = 623), in percent
Census Free and
Distribution of AlgebraicConstant Reduced-Price
Percentage Errors1980 Share Free Lunch Lunch
Unweighted
Mean31.2 7.1 14.0
Less than-40.0%10.3 20.4 17.7
-40.0 to -20.0%11.4 12.4 12.8
-19.9 to-10.0%10.6 9.5 9.1
-9.9 to-0.1%9.0 9.5 10.1
0.0to 9.9%10.6 12.0 9.8
10.0to 19.9%7.7 6.6 7.5
20.0 to 39.9%11.9 11.9 10.3
40.0% and more28.6 17.8 22.6
Weighted by Related
Children Age 5-17 in
Poverty, 1990 Census
Mean0.8 1.6 1.3
Less than -40.0%5.0 8.1 6.8
-40.0 to -20.0%16.0 11.0 13.7
-19.9 to-10.0%17.0 10.0 12.1
-9.9 to-0.1%28.6 10.8 29.8
0.0 to 9.9%7.2 33.8 11.8
10.0 to 19.9%8.1 8.1 5.0
20.0to 39.9%8.1 7.9 8.9
40% and more10.1 10.3 11.9
NOTES: The census constant 1980 share estimates are calculated as described in Chapter 3 (syn-
thetic method (2)). The school lunch estimates are formed by multiplying the 1990 census estimates
of related children age 5-17 in families in poverty for the county by the school district's share of the
county's free (free and reduced-price) lunch participants. The mean unweighted algebraic percent-
age error is the sum over all school districts of the algebraic difference between the estimate of poor
school-age children from a model and the 1990 census estimate as a proportion of the census esti-
mate for each district, divided by the number of districts. The weighted mean weights each differ-
ence by the census number of poor school-age children in the district.
OCR for page 100
100
SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY
TABLE A-2 Mean Absolute and Algebraic Percentage Errors for Children
Age 5-17 in Families in Poverty, Various Methods, New York State School
Districts in Evaluation Universe, 1990, Unweighted, in percent
Census Constant 1980 Share
Percent of Mean Mean
Districts Absolute Algebraic
Category (N = 623) % Error % Error
Total 100.0 53.4 31.2
1990 School District Population
Under 2,500 11.9 66.3 34.0
2,500-4,999 14.3 41.2 15.8
5,000-7,499 17.5 57.7 32.6
7,500-9,999 10.8 58.7 28.3
10,000-14,999 12.5 61.3 45.1
15,000-19,999 9.5 43.5 29.8
20,000-29,999 10.8 67.2 55.8
30,000-39,999 5.3 36.5 11.6
40,000-49,999 2.9 42.6 25.1
50,000-99,999 3.9 24.9 10.7
100,000 or more 0.8 12.0 -12.0
1980-1990 Population Growth
Decrease of 10.0% or more 3.9 45.5 30.6
Decrease of 5.0-9.9% 12.0 54.7 34.9
Decrease of 0.1 -4.9% 24.4 48.1 27.1
Increase of 0.0-4.9% 21.8 50.6 28.1
Increase of 5.0-9.9% 15.9 58.2 35.8
Increase of 10.0% or more 22.0 59.4 33.4
Percentage Poor School-Age
Children, 1990
0.0% 2.3 0.0 0.0
0.1 %-5.9% 34.2 97.7 83.6
6.0-8.9% 16.1 42.1 20.1
9.0- 12.4% 17.0 33.1 8.7
12.5-16.4% 15.1 26.4 3.0
16.5-23.9% 11.9 23.6 -15.6
24.0% or more 3.5 24.6 -20.6
OCR for page 101
APPENDIX
10
Free Lunch
Mean
Absolute
% Error
Free and Reduced-Price Lunch
Mean
Algebraic
% Error
Mean
Absolute
% Error
Mean
Algebraic
% Error
48.77.1 52.114.0
57.44.6 59.810.1
40.1-0.4 41.94.2
65.830.4 71.238.8
47.2-12.1 45.7-10.1
53.222.1 60.431.3
39.3-6.3 43.11.3
47.314.1 54.327.8
37.2-9.0 38.3-3.3
36.7-14.4 36.9-8.0
24.2-7.0 26.5-2.9
5.15.1 4.7-0.9
23.4-0.9 31.810.0
63.07.0 67.511.0
39.3-10.3 40.4-4.9
47.920.4 51.227.7
43.012.0 47.220.1
60.611.3 64.619.4
0.00.0 0.00.0
81.422.2 90.237.6
41.92.7 44.88.9
41.06.8 41.710.6
22.6-2.0 22.00.8
24.3-10.4 23.4-12.3
24.2-16.3 24.5-21.4
OCR for page 102
102
TABLE A-2 Continued
SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY
Census Constant 1980 Share
Percent of Mean Mean
Districts Absolute Algebraic
Category (N = 623) % Error % Error
Change in Poverty Rates
for Children, 1980- 1990
Decrease of 10.0% or more 4.5 132.1 129.3
Decrease of 5.0-9.9% 11.9 95.9 93.4
Decrease of 0.1-4.9% 46.1 55.8 50.2
Increase of 0.0-4.9% 29.2 23.9 -18.7
Increase of 5.0-9.9% 7.1 37.6 -37.1
Increase of 10.0% or more 1.3 59.1 -59.1
Percent of Population
Black, 1990
0.0-0.9% 15.1 29.9 9.9
1.0-4.9% 36.9 48.6 23.9
5.0-9.9% 34.7 64.5 42.0
10.0-24.9% 13.3 64.5 47.1
Percent of Population
Hispanic, 1990
0.0-0.9%
1.0-4.9%
5.0-9.9%
22.6 38.4 16.0
49.3 48.8 28.4
28.1 73.7 48.3
NOTES: The census constant 1980 share estimates are calculated as described in Chapter 3 (syn-
thetic method (2)). The school lunch estimates are formed by multiplying the 1990 census estimates
of related children age 5-17 in families in poverty for the county by the school district's share of the
county's free (free and reduced-price) lunch participants. The mean unweighted absolute (algebraic)
children from families in poverty. Each of the methods results in estimates with
some very large errors. For example, consider the weighted results. All three
methods have at least 15 percent of the districts with errors of at least 40 percent.
This pattern is also illustrated in Table A-2, which shows unweighted estimates
broken down by various school district characteristics. Regardless of method, the
errors are very large on average and in most categories.
Weighting by the number of poor school-age children in 1990 substantially
reduces the percentage errors across all methods, as shown in Table A-3. This
approach yields results that are quite similar across all three models. Mean
OCR for page 103
APPENDIX
103
Free Lunch
Free and Reduced-Price Lunch
Mean Mean Mean Mean
Absolute Algebraic Absolute Algebraic
% Error % Error % Error % Error
101.8 48.1 103.3 51.8
64.5 47.5 73.4 57.2
53.4 11.5 57.0 20.5
33.8 -13.5 34.5 -8.6
26.4 -23.1 26.1 -21.5
44.2 -36.2 43.9 -42.0
33.3 5.3 34.8 9.8
46.7 17.2 50.0 22.0
54.0 0.2 57.5 8.2
57.8 0.9 64.2 11.7
41.3 13.8 45.3 19.2
40.8 9.9 44.1 18.4
68.5 -3.2 71.5 2.0
percentage error is the sum over all school districts of the absolute (algebraic or signed) difference
between the estimate of poor school-age children from a model and the 1990 census estimate as a
proportion of the census estimate for each district, divided by the number of districts.
algebraic percentage errors are relatively small; however, as one would expect,
mean absolute percentage errors are much larger. Most of the patterns of errors
with respect to school district attributes are as would be expected. For example,
school districts with small total population have larger errors than districts with
larger populations.
An important result of this analysis is that even after some effort in data
preparation, the school lunch method is still not meaningfully better than the
census constant-share method. At least in New York State it does not appear that
OCR for page 104
104
SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY
TABLE A-3 Mean Absolute and Algebraic Percentage Errors for Children
Age 5-17 in Families in Poverty, Various Methods, New York State School
Districts in Evaluation Universe, 1990, Weighted by Children Age 5-17 in
Poverty, 1990 Census, in percent
Census Constant 1980 Share
Category
Percent of
Districts
(N = 623)
Mean
Absolute
% Error
Mean
Algebraic
% Error
Total 100.0 23.9 0.8
1990 School District Population
Under 2,500 11.9 43.4 13.8
2,500-4,999 14.3 30.4 4.2
5,000-7,499 17.5 31.6 -0.1
7,500-9,999 10.8 32.5 -4.4
10,000-14,999 12.5 34.8 13.2
15,000-19,999 9.5 21.6 4.0
20,000-29,999 10.8 37.8 21.4
30,000-39,999 5.3 31.5 -2.0
40,000-49,999 2.9 33.6 9.4
50,000-99,999 3.9 18.3 -0.4
100,000 or more 0.8 10.4 -10.4
1980- 1990 Population Growth
Decrease of 10.0% or more 3.9 31.2 26.2
Decrease of 5.0-9.9% 12.0 13.7 -4.2
Decrease of 0.1-4.9% 24.4 20.8 -3.7
Increase of 0.0-4.9% 21.8 31.1 9.9
Increase of 5.0-9.9% 15.9 30.1 2.2
Increase of 10.0% or more 22.0 32.4 2.9
Percentage of Poor School-Age
Children, 1990
0.0% 2.3 0.0 0.0
0.1-5.9% 34.2 53.4 40.3
6.0-8.9% 16.1 34.0 9.6
9.0- 12.4% 17.0 22.2 4.5
12.5- 16.4% 15.1 22.7 -2.1
16.5-23.9% 11.9 19.0 -14.8
24.0% or more 3.5 11.3 -10.1
OCR for page 105
APPENDIX
105
Free Lunch
Mean
Absolute
% Error
Free and Reduced-Price Lunch
Mean
Algebraic
% Error
Mean Mean
Absolute Algebraic
% Error % Error
22.3
38.5
31.6
34.2
32.6
32.0
24.9
36.3
27.9
34.0
21.0
3.4
9.8
10.2
17.2
32.5
29.9
39.0
0.0
47.1
34.3
36.3
19.6
18.2
5.4
1.6
-7.4
-11.2
1.3
-4.6
6.8
0.9
13.8
3.1
-6.8
-1.5
3.4
2.2
-3.8
1.9
8.6
0.3
2.0
0.0
-5.3
2.8
19.5
-1.6
1.4
-0.6
24.2
39.2
31.8
34.9
30.0
35.6
28.7
39.7
28.1
35.6
24.0
5.3
24.2
17.0
17.1
33.1
30.6
38.0
0.0
52.1
36.7
38.5
20.0
16.2
9.1
1.3
-4.5
-7.3
3.9
-4.5
10.9
5.3
21.1
3.4
-6.3
-3.2
-3.0
7.7
9.8
1.1
11.5
3.3
4.6
0.0
8.7
8.6
23.5
-2.3
-3.3
-7.8
OCR for page 106
106
TABLE A-3 Continued
SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY
Census Constant 1980 Share
Percent of Mean Mean
Districts Absolute Algebraic
Category (N = 623) % Error % Error
Change in Poverty Rates for
Children, 1980- 1990
Decrease of 10.0% or more 4.5 79.3 75.3
Decrease of 5.0-9.9% 11.9 47.0 38.1
Decrease of 0.1-4.9% 46.1 32.1 23.1
Increase of 0.0-4.9% 29.2 19.0 -15.0
Increase of 5.0-9.9% 7.1 16.9 -15.7
Increase of 10.0% or more 1.3 10.6 -10.6
Percent of Population
Black, 1990
0.0-0.9% 15.1 21.4 -0.5
1.0-4.9% 36.9 24.4 0.5
5.0-9.9% 34.7 30.1 2.4
10.0-24.9% 13.3 16.9 -0.6
Percent of Population
Hispanic, 1990
0.0-0.9% 22.6 22.7 0.7
1.0-4.9% 49.3 20.1 -0.5
5.0-9.9% 28.1 34.8 4.1
NOTE: See notes to Table A-2.
using school lunch data results in significant gains in estimating school-age chil-
dren from poor families.
ESTIMATES OF THE CONCENTRATION GRANT THRESHOLD
Eligibility for Title I concentration grants is based on having a school-age
poverty rate of at least 15 percent or at least 6,500 poor children.3 Current Title
3Children eligible for Title I are not limited to school-age children from poor families (see Chap-
ter 1). However, for the purpose of this analysis, which is to examine the census constant-share
estimates of school-age children from poor families, eligibility is so characterized.
OCR for page 107
APPENDIX
107
Free Lunch
Free and Reduced-Price Lunch
Mean Mean Mean Mean
Absolute Algebraic Absolute Algebraic
% Error % Error % Error % Error
64.9
41.4
36.0
20.9
8.5
5.5
22.4
23.6
32.0
9.8
23.5
15.0
40.8
19.5
31.7
7.1
-4.8
-5.2
-1.2
-2.6
0.5
4.6
0.0
0.0
0.5
5.4
68.2
43.1
37.9
21.1
12.0
7.8
23.8
24.6
32.1
14.5
25.5
18.1
39.3
23.5
32.4
12.0
-3.6
-10.5
-7.7
-0.9
0.0
4.1
-0.3
0.7
0.0
5.2
I allocations employ a two-stage eligibility criterion. A district must be in a
county that meets the 15 percent (or 6,500) rule, and the district itself must meet
that criterion. Under the proposed direct allocation system, grants will be made
directly to districts and, as such, eligibility will be determined solely with regard
to district poverty rates, without regard to county poverty rates. The proposed
direct allocation method also permits states to aggregate the allocations to dis-
tricts that have total population of less than 20,000 and reallocate this total based
on alternative data, such as those from the National School Lunch Program. It is
of interest to examine eligibility for concentration grants in those districts with
less than 20,000 population under three different scenarios: the current two-stage
process, the direct allocation process to districts without controls, and direct
OCR for page 108
08
SMAL L-ARE4 ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY
allocations when school district poverty estimates must sum to the census county
totals. We examine how concentration grants eligibility differs under these cir-
cumstances when school lunch data are used rather than census constant-share
estimates, using 1990 census ratio-adjusted counts as the measure of truth.
Of the 623 districts in New York State that are in the census evaluation
universe, 476 are in districts that had less than 20,000 total population in 1990.
As shown in Table A-4, these 476 districts represent 76 percent of all districts in
the evaluation universe for New York, but they contain only 35 percent of the
poor children age 5-17 in the census evaluation universe.
Tables A-5 to A-8 examine estimates of the number of districts and percent-
age of school-age children who are in poor families under alternative estimation
methods in 1990. The census counts are the ratio-adjusted estimates of school-
age children who are in poor families from the 1990 census. Census-based
estimates (synthetic method (2) estimates) use the 1990 census counts of county
school-age children who are in poor families and allocate these totals to school
districts by the school district's share of county totals from the 1980 census. The
model-based estimates (synthetic method (1) estimates) use a similar approach,
but with the county estimates of school-age children who are in poor families in
1989 produced from the Census Bureau's county model. The school lunch esti-
mates are produced, as outlined above, by using 1990 county ratio-adjusted esti-
mates of school-age children who are in poor families from the 1990 census and
allocating them to constituent school districts by the share of that school district's
free (or free and reduced-price) school lunch eligibles relative to the county total.
Tables A-5 and A-6 provide estimates for the two-tier concentration grant
eligibility for districts with total population (from the 1990 census) of less than
20,000. That is, districts must be in counties where at least 15 percent (or 6,500)
of the school-age children are poor and in a district that also meets this criterion.4
If we take the census counts as our measure of "truth," then employing school
lunch data will likely overstate eligibility. As shown in Table A-5, roughly 50
percent more districts and school-age children are estimated to be eligible with
free school lunch data than with the census counts. This problem is further
magnified when the free and reduced-price lunch counts are employed. Table A-
6 illustrates where each method errs relative to the eligibility categorization of the
census counts: as might be expected, the school lunch estimates produce a
substantial number of false positives.
Tables A-7 and A-8 provide a similar analysis for direct allocations. Now
districts must only meet the single criterion that the district has at least 15 percent
4In Tables A-5 and A-6, county eligibility is determined by the county counts from the 1sso
census. Within each of these eligible counties, the alternative methods listed are used to determine
school district eligibility.
OCR for page 109
APPENDIX
TABLE A-4 New York State Districts in Evaluation Universe Above and
Below the 20,000 Population Threshold for Pooling Allocations (N = 623)
109
Districts
Poor Children Age 5-17
Category Number Percent Number Percent
School District Total
Population
Less than 20,000
At least 20,000
476 76.4
147 23.6
61,236 35.0
113,556 65.0
TABLE A-5 Concentration Grant Eligibility at County and School District
Level, Various Methods for New York State Districts in Evaluation Universe
with Less than 20,000 Population, 1990 (N = 476)
Districts
Method
Poor Children Age 5-17
Number
Percent
Number
Percent
Census Counts 76 16.0 16,689 27.3
Census-based Estimates 78 16.4 14,162 23.1
Model-based Estimates 76 16.0 14,134 23.1
Free Luncha 112 23.5 21,662 35.4
Free and Reduced- 136 28.6 24,515 40.0
price Luncha
NOTES: Cell entries are for school districts and poor school-age children that would be eligible for
concentration grants according to various methods (see text) under the current two-stage allocation
process (i.e., both county and school district have more than 6,500 or more than 15% poor school-age
children). The total number of poor school-age children in districts with less than 20,000 population
is 61,236.
aSome school districts (54 or 11.3%) did not report school lunch data.
OCR for page 110
110
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OCR for page 111
APPENDIX
111
TABLE A-7 Concentration Grant Eligibility at School District Level, Various
Methods for New York State Districts in Evaluation Universe with Less than
20,000 Population, 1990 (N = 476)
Districts
Method
Poor Children Age 5-17
Number
Percent
Number
Percent
Census Counts 115 24.2 25,343 41.4
Census-based Estimates 114 24.0 19,596 32.0
Model-based Estimates 109 22.9 18,285 29.9
Free Luncha 214 45.0 39,222 64.1
Free and Reduced-price 294 61.8 48,835 79.8
Luncha
Free Lunch with 124 26.1 25,024 40.9
Controlsa, b
Free and Reduced-price 127 26.7 24,045 39.3
Lunch with Controls
NOTES: Cell entries are for school districts and poor school-age children that would be eligible for
concentration grants according to various methods (see text) under a direct allocation process (i.e.,
the school district has more than 6,500 or more than 15% poor school-age children). The total
number of poor school-age children in districts with less than 20,000 population is 61,236.
aSome school districts (54 or 11.3%) did not report school lunch data.
bControls are imposed at the county level so that number of poor children and number of children
in the school district must sum to county census counts for 1990.
of its school-age children who are poor (or at least a total of 6,500~. These
estimates also show the effect of imposing county controls on the use of school
lunch estimates. (The county controls are equivalent to the estimates produced
by equation 1, above.) The school lunch estimates without controls greatly
overstate concentration grant eligibility. Imposing county controls substantially
improves the accuracy of these estimates.
Table A-9 shows mean algebraic and absolute percentage errors for the
various estimation methods. Here the school lunch estimates have either been
controlled to the statewide total of school-age children living in poor families for
the 476 districts with populations of less than 20,000 or to a similar county total.
With these controls in place, each of the methods has roughly the same algebraic
and absolute percentage errors. This result is interesting as the school lunch
estimates with county controls had the potential to be either better or worse than
the estimates with state controls. We would in general expect them to be better as
there is a tighter level of control imposed. It is possible that they are worse as a
result of lack of precision that occurs when school districts cross county bound-
aries and school lunch data are coded to the county where the district office is
located.
OCR for page 112
112
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OCR for page 114
4
SMALL-AREA ESTIMATES OF SCHOOL-AGE CHILDREN IN POVERTY
PROBLEMS WITH THIS APPROACH
Using school lunch data to estimate the number of poor children for each
school district has several potential problems, based on the experience in New
York State. As has been widely acknowledged:
· Participants in the National School Lunch Program are not the target
population of Title I:
· There are differences in eligibility between Title I and school lunch.
· There are differences in reporting geography: Title I counts resi-
dents, school lunch counts by location of the school the child attends.
· Not all eligible students apply for the school lunch program, and applica-
tion rates appear to be uneven across schools.
· Some schools choose not to participate in the school lunch program.
Other difficulties include:
· New York State has a number of regional (groups of counties) educa-
tional authorities with students, and they participate in the school lunch program;
how to allocate these students is an issue.
· In New York State, the school lunch program is administered separately
from most other programs, which can make use of the administrative data diffi-
cult (e.g., schools sometimes have separate identification numbers, which makes
matching to other data very time consuming).
Representative terms from entire chapter:
school districts
