SEELS must meet the information needs of a wide variety of audiences using a variety of data collection and analytic approaches. Accordingly, the SEELS sample must meet the following requirements in order to serve its multiple purposes:
In the remainder of this section, the approach to meeting these sample requirements is presented.
SEELS will employ a two-stage process to generate the needed sample of students in special education between the ages of 8 and 12. SEELS will draw a random sample of students in special education from a nationally representative sample of LEAs and a sample of state-supported special schools. Accordingly, the LEA is the primary sampling unit and the student with a disability is the secondary or final unit.
The SEELS sample will be generated by randomly selecting special education students from rosters of LEAs and state-supported schools that serve children of the appropriate ages in special education. The universe of eligible LEAs and special schools will be stratified by key factors to enhance representativeness; these factors are geographic region, district enrollment, and district/community wealth. Taking into account the length of the data collection period and assumptions regarding attrition from the sample, analyses of statistical power requirements suggest that an initial sample of approximately 12,075 students will yield a sample of sufficient size and representativeness to meet the analytic needs of SEELS in its final wave of data collection. This sample will be selected so as to generate 1,150 in each disability category, with the exception of 200 students who are deaf-blind and 375 with traumatic brain injuries, the least populous categories.
The following sections describe the process through which the student sample size was determined and then outline the selection procedures for the LEA and student samples.
The size of the SEELS student sample is a function of the duration of the study, desired levels of precision, and assumptions regarding attrition and response rates. The following assumptions have been used in determining the size of the student sample:
This means that approximately three students (i.e., 2.96 students) will need to be sampled for each one student who will have both a parent/guardian interview and a direct assessment in year 5 of SEELS.
The SEELS sample design emphasizes the need to estimate proportions and ratios (for example, the percentage of students in special education reading at grade level) instead of estimating the actual numbers of students in special education having specified characteristics (for example, 2,400 students reading at a particular level). However, relatively precise national estimates of the proportions or ratios of students in special education, whether analyzed as one group or considered separately by disability category, will be needed to adequately answer research questions of interest to the broad range of likely audiences for the study.
Excluding the deaf-blind, the average number of parent/guardian interviews in the NLTS was approximately 660 per disability category, resulting in a sampling efficiency of approximately 50% and standard errors for proportions of about 2.8%. This level of precision was used as a starting point for precision estimates for SEELS. To obtain the same level of precision in analyses that depend on students who have both the parent interview and the direct assessment in year 5, 1,954 students (i.e., 660 x 2.96) would need to be sampled per disability category.
This sample size is so large that it would make the study prohibitively expensive, particularly given the central importance and considerable expense of a direct assessment of students. In addition, a sample of that size would be a sizable proportion of all the students there are in some low-incidence disability categories (see Table 4-1). Students in special education account for approximately 10.6% of all students in American schools, and the number of students ages 8 through 12 in each disability category ranges from a high of approximately 1,111,000 for students with learning disabilities (approximately 4% of the elementary/middle school student population) to a low of approximately 560 for deaf-blind students (far less than 1%). The 1,954 students per category that would be needed to reach a precision level of 2.8%, as in the NLTS, would be 43% of all students in this age group with traumatic brain injury (TBI) and 16% of all students in this age group with orthopedic impairments. The SEELS sample would need to be drawn from an extremely large number of LEAs to find 1,954 students in these categories.
Table 4-1 Approximate Number of Students in special education AgeS 8 to12 in U.S. PUBLIC Schools, |
||
|
Approximate Percentage of Student Population Ages 8 to 12 |
|
Learning disabilities |
1,111,131 |
4.35 |
Speech impairments |
940,960 |
3.68 |
Mental retardation |
240,098 |
0.94 |
Serious emotional disturbance |
153,741 |
0.60 |
Other health impairments |
51,696 |
0.20 |
Multiple disabilities |
33,185 |
0.13 |
Hearing impaired |
35,650 |
0.14 |
Visual impairments |
97,680 |
0.38 |
Orthopedic impairments |
12,070 |
0.05 |
Autism |
27,323 |
0.11 |
Traumatic brain injury |
4,514 |
0.02 |
Deaf-blind |
560 |
0.002 |
Developmental delay |
1,935 |
0.01 |
Given these drawbacks to sampling sufficient numbers of students per category to reach the NLTS precision levels, the following alternative strategy was used:
Table 4-2 shows the number of students who are expected to be retained in the study for each year and for whom data are expected to be collected, based on a starting sample of 1,150 students in each category, with the exception of 375 students with traumatic brain injury and 200 who are deaf-blind.
Table 4-2 EXPECTED SAMPLE SIZE, BY YEAR AND DISABILITY CATEGORY |
||||
Deaf-Blind |
TBI |
Each Other Category |
Total |
|
Number of students |
||||
Sampled |
200 |
375 |
1,150 |
12,075 |
With location information |
180 |
338 |
1,035 |
10,868 |
Year 1 |
180 |
338 |
1,035 |
10,868 |
Year 2 |
166 |
310 |
952 |
9,998 |
Year 3 |
152 |
286 |
876 |
9,198 |
Year 4 |
140 |
263 |
806 |
8,462 |
Year 5 |
129 |
242 |
742 |
7,785 |
Number of parent/guardian interviews |
||||
Year 1 |
126 |
237 |
724 |
7,608 |
Year 3 |
106 |
200 |
613 |
6,439 |
Year 5 |
90 |
169 |
519 |
5,450 |
Number of direct assessments |
||||
Year 2 |
125 |
232 |
714 |
7,498 |
Year 3 |
114 |
214 |
657 |
6,898 |
Year 5 |
97 |
181 |
556 |
5,839 |
Number of students with parent/ guardian interviews (PGI) and direct assessments (DA) |
||||
Year 1 PGI and Year 2 DA |
87 |
163 |
500 |
5,250 |
Year 3 PGI and DA |
80 |
150 |
460 |
4,829 |
Year 5 PGI and DA |
67 |
127 |
389 |
4,088 |
The LEA Sample
The first step in developing a sample that leads to national estimates about students in special education is to select an adequate, representative sample of LEAs. Below we discuss issues related to the LEA sample including size, stratification, and fit.
There are several factors to consider in determining the number of LEAs for the sample. First, it is necessary to establish the number of LEAs that are required to generate the needed student sample. On the basis of an analysis of LEAs estimated enrollment across district size, and estimated sampling fractions for each disability category, 297 LEAs (and as many state-sponsored special schools as will participate) will be sufficient to generate the student sample. Second, the rate of LEA refusal to participate should be considered so that the required number of LEAs agree to participate within the limited recruitment period. Previous experience with the NLTS suggests that LEAs typically declined to participate because of concerns related to confidentiality of student records. Although considerable time and effort was expended in recruiting LEAs for the NLTS, approximately 55% of the LEAs invited to participate either declined, did not respond, or introduced procedures that unacceptably lengthened the recruitment process. In SEELS, both the amount of time and the funds available to recruit LEAs are less than were available in the NLTS. Efficiency can be gained if recruitment efforts focus on large LEAs, which are relatively few in number and from which a relatively large proportion of sample students will be selected. Smaller LEAs will receive less intensive recruitment effort than in the NLTS because there are many of them, yielding a large number of potential replacements for refusing districts. Although this strategy is likely to be most efficient in selecting the LEA sample quickly, there is a risk that smaller LEAs who refuse to participate differ systematically from other LEAs in terms of the types or effectiveness of programs that they offer to students. Thus, detailed tracking will be necessary to identify potential patterns that emerge with regard to LEA refusal/nonresponse. The procedural outcome of concentrating our recruitment effort on larger LEAs and being more willing to replace smaller LEAs is that a sample of 765 LEAs is expected to be enough from which to recruit 297 participating LEAs.
The initial task in selecting the SEELS sample is to define which districts should be included in and excluded from the universe of LEAs from which the sample will be selected. To meet its purposes, the SEELS sample includes only LEAs that have teachers, students, administrators and operating schoolsthat is, "operating LEAs." The SEELS sample excludes the following categories of local and state educational "districts" that appear on standard listings of educational institutions:
To create a sampling frame or master list of LEAs, two lists were considered: the public school universe maintained by Quality Education Data (QED, 1998) and the School District Name and Address File maintained by the National Center for Education Statistics in the U.S. Department of Education (1997). The two lists were compared on variables indicating LEA name and location. There were a small number of discrepancies in LEA name and contact information, probably because the data were drawn from different school years. The list with the most current information, QED, was used to construct the sampling frame. As a commercial source, it must maintain accurate data, including addresses of special education coordinators in each district, for its clients. The QED data are from the 1997-98 school year, as updated during the fall of 1998. Using the QED data, the following procedures were used to create a master list of LEAs that were eligible for the SEELS sample:
These procedures resulted in a master list of 13,426 LEAs that are expected to have at least one student in special education in the appropriate age range. These comprise the SEELS LEA sampling frame.
The SEELS LEA sample is stratified for four principal reasons: (1) to increase the precision of estimates by eliminating between-strata variance, (2) to ensure that low-frequency types of LEAs (e.g., large urban districts) are adequately represented in the sample, (3) to improve comparisons with the findings of other research, and (4) to make SEELS responsive to concerns voiced in policy debate (e.g., differential effects of federal policies in particular regions, LEAs of different sizes). The first of these reasons is especially important because of the great diversity in the universe of LEAs. Three stratifying variables are usedgeographic region, district size (student enrollment), and a measure of district/community wealth. They were selected on the basis of conceptual soundness and the likelihood of providing a gain in precision over simple random sampling. These variables and their sources are described below.
Region. This variable captures essential political differences, as well as subtle differences in the organization of schools, the economic conditions under which they operate, and the character of public concerns. Regions differ, for example, in the changes in school enrollment over time. They also differ in terms of economic health, which is linked to resources the region can target to education and other needed services. For SEELS, the regional classification variable selected is used by the Department of Commerce, the Bureau of Economic Analysis, and the National Assessment of Educational Progress (see Table 4-3).
Table 4-3 Distribution of States BY Region |
||
Northeast (N = 12) |
||
Connecticut |
Maryland |
New York |
Delaware |
Massachusetts |
Pennsylvania |
District of Columbia |
New Hampshire |
Rhode Island |
Maine |
New Jersey |
Vermont |
Southeast (N = 12) |
||
Alabama |
Kentucky |
South Carolina |
Arkansas |
Louisiana |
Tennessee |
Florida |
Mississippi |
Virginia |
Georgia |
North Carolina |
West Virginia |
Central (N = 12) |
||
Illinois |
Michigan |
North Dakota |
Indiana |
Minnesota |
Ohio |
Iowa |
Missouri |
South Dakota |
Kansas |
Nebraska |
Wisconsin |
West/Southwest (N = 15) |
||
Alaska |
Idaho |
Oregon |
Arizona |
Montana |
Texas |
California |
Nevada |
Washington |
Colorado |
New Mexico |
Wyoming |
Hawaii |
Oklahoma |
Utah |
By assigning each LEA to a region based on its state, we obtain the allocation of LEAs and proportion of total estimated elementary/middle school student population in grades 2 through 7 to region indicated in Table 4-4.
Table 4-4 Distribution of LEAs and Student Population by Region |
||||
|
Number of LEAs |
Percent of LEAs |
Number of Students |
Percent of Students |
Northeast |
2,815 |
21.0 |
4,159,121 |
19.9 |
Southeast |
1,605 |
12.0 |
5,117,654 |
24.4 |
Central |
5,049 |
37.6 |
4,870,149 |
23.2 |
West/Southwest |
3,957 |
29.4 |
6,802,643 |
32.5 |
TOTAL |
13,426 |
100.0 |
20,949,567 |
100.0 |
District size (student enrollment). LEAs vary considerably by size, the most useful available measure of which is pupil enrollment. A host of organizational and contextual variables are associated with size that exert considerable potential influence over the operations and effects of special education and related programs. These include the extent of district administrative/supportive capacity, the degree of specialization in administrative structure, the nature of citizen and interest group activity in education, and the characteristics of relationships with state and federal governance systems.
In addition, total enrollment (and the previously described estimated elementary/middle school enrollment) serves as an initial proxy for the number of students in special education served by a district. The QED database provides enrollment data from which LEAs were sorted into four categories serving approximately equal numbers of students:
The distribution of districts among these strata and proportion of students accounted for by each stratum are displayed in Table 4-5.
Table 4-5 Distribution of LEAs and Student Population by LEA Size |
||||
|
Number of LEAs |
Percent of LEAs |
Number of Students |
Percent of Students |
Very large (> 17,411) |
127 |
0.9 |
5,221,029 |
24.9 |
Large (4,707 17,411) |
644 |
4.8 |
5,253,803 |
25.1 |
Medium (1,548 4,706) |
2,050 |
15.3 |
5,237,205 |
25.0 |
Small (10 1,547) |
10,605 |
79.0 |
5,237,530 |
25.0 |
TOTAL |
13,426 |
100.0 |
20,949,567 |
100.0 |
District/community wealth. LEAs differ greatly in the resources they have available and in the demands placed on those resources by low-income students whose needs put them at risk for a variety problems, including school failure. Policies and programs may differ in LEAs that face these differential demands of disadvantaged students. Also, prior research has demonstrated that high-poverty districts also have a high proportion of students in special education. As a measure of district wealth, the Orshansky index (the proportion of the student population living below the federal definition of poverty) is a well-accepted measure. The distribution of Orshansky index scores was organized into four categories of district/community wealth, each containing approximately 25% of the student population in grades 2 through 7:
The distribution of districts among strata and proportion of students accounted for by each stratum are displayed in Table 4-6.
Table 4-6 Distribution of LEAs and Student Population by DISTRICT WEALTH |
||||
|
Number of LEAs |
Percent of LEAs |
Number of Students |
Percent of Students |
High (0% 12%) |
3,869 |
28.8 |
5,204,897 |
24.8 |
Medium (13% 34%) |
3,939 |
29.3 |
5,530,089 |
26.4 |
Low (34% 45%) |
3,095 |
23.0 |
5,065,929 |
24.2 |
Very low (> 45%) |
2,533 |
18.9 |
5,148,652 |
24.6 |
TOTAL |
13,426 |
100.0 |
20,949,567 |
100.0 |
The three variables generate a 64-strata grid into which the entire universe can be fit. Table 4-7 shows the strata and the number of LEAs in each stratum. Table 4-8 shows the number of students in all LEAs in each stratum. The next stage in the SEELS sampling process was to select the appropriate LEAs from each stratum to yield a total sample of 765 LEAs. LEAs were selected from strata so as maximize the sampling efficiency and thereby maximize the effective sample sizes.
Table 4-7 Number of LEAs in THE Universe/SAMPLE, BY STRATUM |
|||||
District Wealth (Orshansky Index) |
|||||
|
High |
Med |
Low |
Very Low |
|
Very large (>17,411) |
18/8 |
31/13 |
31/18 |
47/26 |
127/65 |
Northeast |
3/2 |
5/2 |
4/4 |
5/2 |
17/10 |
Southeast |
4/2 |
14/6 |
15/9 |
14/88 |
47/25 |
Central |
6/2 |
12/5 |
10/3 |
21/13 |
49/23 |
West/Southwest |
5/2 |
0/0 |
2/2 |
7/3 |
14/7 |
Large |
155/44 |
174/55 |
149/45 |
166/56 |
644/200 |
Northeast |
24/6 |
17/5 |
11/3 |
15/5 |
67/19 |
Southeast |
16/4 |
50/16 |
61/20 |
43/14 |
170/54 |
Central |
60/19 |
71/24 |
56/16 |
94/32 |
281/91 |
West/Southwest |
55/15 |
36/10 |
21/6 |
14/5 |
126/36 |
Medium |
720/84 |
573/71 |
397/49 |
360/46 |
2,050/250 |
Northeast |
302/34 |
133/16 |
61/8 |
30/4 |
526/62 |
Southeast |
15/2 |
143/19 |
145/18 |
180/22 |
483/61 |
Central |
85/11 |
159/20 |
138/17 |
131/17 |
513/65 |
West/Southwest |
318/37 |
138/16 |
53/6 |
19/3 |
528/62 |
Small |
2,976/84 |
3,151/74 |
2,518/52 |
1,960/40 |
10,605/250 |
Northeast |
1,016/32 |
710/19 |
386/9 |
93/2 |
2,205/62 |
Southeast |
35/2 |
196/8 |
299/10 |
375/14 |
905/34 |
Central |
386/7 |
731/15 |
913/17 |
1,084/19 |
3,114/58 |
West/Southwest |
1,539/43 |
1,514/32 |
920/16 |
408/5 |
4,381/96 |
Total |
3,869/220 |
3,929/213 |
3,095/164 |
2,533/168 |
13,426/765 |
Table 4-8 Number of STUDENTs in THE UNIVerse/SAMPLE, BY STRATUM (thousands) |
|||||
District Wealth (Orshansky Index) |
|||||
|
High |
Med |
Low |
Very Low |
|
Very large |
463/194 |
1,083/414 |
1,759/1,287 |
1,916/1,220 |
5,221/3,115 |
Northeast |
76/58 |
179/79 |
662/662 |
151/44 |
1,067/843 |
Southeast |
91/47 |
481/212 |
624/318 |
546/332 |
1,742/1,909 |
Central |
125/37 |
0/0 |
224/224 |
234/87 |
584/348 |
West/Southwest |
171/52 |
424/123 |
249/83 |
984/757 |
1,829/1,015 |
Large |
1,177/349 |
1,418/478 |
1,199/366 |
1,460/459 |
5,254/1,650 |
Northeast |
154/53 |
121/34 |
78/24 |
138/49 |
492/160 |
Southeast |
116/30 |
408/132 |
531/181 |
360/105 |
1,415/448 |
Central |
398/120 |
255/76 |
160/47 |
127/38 |
940/281 |
West/Southwest |
509/144 |
634/236 |
429/114 |
835/267 |
2,407/761 |
Medium |
1,762/216 |
1,493/183 |
1,029/128 |
953/130 |
5,237/657 |
Northeast |
707/80 |
328/41 |
161/23 |
90/13 |
1,285/157 |
Southeast |
39/6 |
399/54 |
381/49 |
462/56 |
1,282/165 |
Central |
783/98 |
345/34 |
135/14 |
51/10 |
1,314/156 |
West/Southwest |
233/32 |
421/54 |
351/42 |
350/51 |
1,356/179 |
Small |
1,802/53 |
1,536/42 |
1,079/25 |
820/19 |
5,238/139 |
Northeast |
697/24 |
400/11 |
178/4 |
40/>1 |
1,315/39 |
Southeast |
27/2 |
159/6 |
209/8 |
283/11 |
679/27 |
Central |
925/25 |
669/17 |
333/6 |
106/1 |
2,032/49 |
West/Southwest |
154/2 |
307/8 |
358/7 |
392/7 |
1,211/124 |
TOTAL |
5,205/1,520 |
5,530/2,234 |
5,066/3,612 |
5,149/3,657 |
20,950/5,700 |
LEA Sample Characteristics
Our first step in assessing the effectiveness of the sampling process was to evaluate the degree to which the selected LEA sample was comparable to the universe from which it was drawn on variables used in the sampling process. Tables 4-9, 4-10, and 4-11 depict the characteristics of the LEA sample, in weighted and unweighted form, on the sampling variables of region, LEA size, and LEA wealth. Taken together, the tables illustrate that the weighted LEA sample closely resembles the LEA universe with respect to those variables.
Table 4-9 weighted and unweighted Distribution of sampled LEAs and Student Population by Region |
||||
Region, Weighted |
Number of LEAs |
Percent of LEAs |
Number of Students |
Percent of Students |
Northeast |
2,815 |
21.0 |
4,295,394 |
20.1 |
Southeast |
1,605 |
12.0 |
5,134,032 |
24.1 |
Central |
5,049 |
37.6 |
4,969,920 |
23.3 |
West/Southwest |
3,957 |
29.5 |
6,944,088 |
32.5 |
TOTAL |
13,426 |
100.1 |
21,343,435 |
100.0 |
Region, Unweighted |
||||
Northeast |
153 |
20.0 |
1,198,504 |
21.6 |
Southeast |
174 |
22.7 |
1,549,696 |
27.9 |
Central |
201 |
26.3 |
835,056 |
15.0 |
West/Southwest |
237 |
30.0 |
1,978,082 |
35.5 |
TOTAL |
13,426 |
100.0 |
5,561,338 |
100.0 |
Table 4-10 weighted and unweighted Distribution of SAMPLed LEAs and Student Population by LEA Size |
||||
Enrollment Size Category, Weighted |
Number of LEAs |
Percent of LEAs |
Number of Students |
Percent of Students |
Very large (> 17,411) |
127 |
0.9 |
5,225,470 |
24.5 |
Large (4,707 17,411) |
644 |
4.8 |
5,288,505 |
24.8 |
Medium (1,548 4,706) |
2050 |
15.3 |
5,368,699 |
25.2 |
Small (10 1,547) |
10,605 |
79.0 |
5,460,759 |
25.6 |
TOTAL |
13,426 |
100.0 |
21,343,435 |
100.1 |
Enrollment Size Category, Unweighted |
||||
Very large (> 17,411) |
65 |
8.5 |
3,115,284 |
56.0 |
Large (4,707 17,411) |
200 |
26.1 |
1,649,463 |
29.7 |
Medium (1,548 4,706) |
250 |
32.7 |
657,823 |
11.8 |
Small (10 1,547) |
250 |
32.7 |
138,768 |
2.5 |
TOTAL |
765 |
100.0 |
5,561,338 |
100.0 |
Table 4-11 weighted and unweighted Distribution of sampled LEAs and Student Population by DISTRICT WEALTH (orshansky index) |
||||
District Wealth, Weighted |
Number of LEAs |
Percent of LEAs |
Number of Students |
Percent of Students |
High (0% 12%) |
3,869 |
28.8 |
5,323,816 |
24.9 |
Medium (13% 34%) |
3,929 |
29.3 |
5,671,446 |
26.6 |
Low (34% 45%) |
3,095 |
23.0 |
5,049,449 |
23.7 |
Very low (> 45%) |
2,533 |
18.9 |
5,298,723 |
24.8 |
TOTAL |
13,426 |
100.0 |
21,343,435 |
100.0 |
District Wealth, Unweighted |
||||
High (0%-12%) |
220 |
28.7 |
811,246 |
14.6 |
Medium (13%-34%) |
213 |
27.8 |
1,116,664 |
20.1 |
Low (34%-45%) |
164 |
21.4 |
1,805,501 |
32.5 |
Very low (>45%) |
168 |
21.9 |
1,827,927 |
32.9 |
TOTAL |
765 |
100.0 |
5,561,338 |
100.1 |
In addition to ensuring that the LEA sample matched the universe of LEAs based on variables used in the sampling, it was important to ascertain whether this stratified random sampling scheme resulted in skewed distributions on relevant variables not included in the stratification scheme. Two variables from the QED database were chosen to compare the "fit" between the first-stage sample and the population: the districts metropolitan status (Table 4-12), and the districts proportion of minority students (Table 4-13). If comparisons between the universe of LEAs and the sample revealed a poor fit, either the sample would be reweighted or a new sample would need to be selected. However, Tables 4-12 and 4-13 reveal that the fit between the weighted LEA sample and the LEA universe is quite good.
Table 4-12 weighted Distribution of sampled LEAs and universe by metropolitan status |
||||
District Type |
Number in Universe |
Percent of Universe |
Weighted Number in Sample |
Percent of Weighted Sample |
Unclassified |
766,787 |
3.7 |
842,107 |
3.9 |
Large central city |
2,819,935 |
13.5 |
2,992,281 |
14.0 |
Midsize central city |
3,632,880 |
17.3 |
3,248,397 |
15.2 |
Urban fringe of large city |
3,355,052 |
16.0 |
3,321,762 |
15.6 |
Urban fringe of midsize city |
2,200,565 |
10.5 |
2,202,556 |
10.3 |
Large town |
660,781 |
3.2 |
723,401 |
3.4 |
Small town |
4,722,488 |
22.5 |
5,216,708 |
24.4 |
Rural |
2,791,079 |
13.3 |
2,796,222 |
13.1 |
TOTAL |
20,949,567 |
100.0 |
21,343,435 |
100.0 |
Table 4-13 weighted Distribution of sampled LEAs and universe by PROPORTION OF MINORITY STUDENTS |
||||
Minority Student Population |
Number in Universe |
Percent of Universe |
Weighted Number in Sample |
Percent of Weighted Sample |
Less than 5% |
3,750,842 |
17.9 |
3,890,816 |
18.2 |
5% 10% |
2,379,978 |
11.4 |
2,549,725 |
11.9 |
10% 20% |
2,826,669 |
13.5 |
2,995,207 |
14.0 |
20% 50% |
5,655,285 |
27.0 |
5,681,479 |
26.6 |
50% 100% |
6,336,793 |
30.2 |
6,226,209 |
29.2 |
TOTAL |
20,949,567 |
100.0 |
21,343,436 |
100.0 |
Because LEAs have an unequal probability of being selected into the sample, depending on the stratum within which they fall, LEAs will need to be weighted by the inverse of the stratum sampling fraction to create population estimates. As discussed previously, approximately 1,150 students must be sampled in the higher-incidence disability categories, 375 students with traumatic brain injury, and 200 deaf-blind students to make national estimates with reasonable precision about students in each category and students in special education overall.
Student Sample Selection Procedures
During the design task, SRI will contact LEAs and obtain their agreement to participate in the study. Subsequently, in the fall of the 1999-2000 school year, the study contractor will request from participating LEAs rosters of students in special education between the ages of 8 and 12. Requests for rosters will specify that they contain the names and addresses of students in special education under the jurisdiction of the LEA, the disability category of each student, and the students birthdates or ages. As mentioned previously, some LEAs can be expected to provide only identification numbers for students, along with the corresponding birthdates and disability categories. When students are sampled in these LEAs, identification numbers of selected students are provided to the LEA, along with materials to mail to their parents/guardians (without revealing their identity to the study contractor).
After estimating the number of students enrolled in special education at the appropriate grade levels, the fraction of students in each category at each age that must be selected randomly from each district to yield a sample of 12,075 students must be determined. These sampling fractions will be calculated to maximize the effective sample efficiency while obtaining the required absolute sample sizes. Final sampling fractions cannot be calculated until the composition of the sample of participating LEAs is known; however, initial estimates are presented in Table 4-14.
Table 4-14 ESTIMATED STUDENT SAMPLING FRACTIONS BY LEA SIZE STRATUM (PERCENT) |
||||
Very Large |
Large |
Medium |
Small |
|
Specific learning disability |
12.1 |
2.4 |
0.9 |
0.6 |
Speech or language impairment |
14.3 |
2.8 |
0.9 |
0.6 |
Mental retardation |
56.0 |
11.0 |
4.3 |
2.7 |
Serious emotional disturbance |
87.0 |
17.1 |
6.7 |
4.2 |
Multiple disabilities |
100.0 |
60.0 |
24.5 |
15.0 |
Hearing impairments |
100.0 |
90.0 |
31.0 |
23.0 |
Orthopedic impairments |
100.0 |
89.0 |
37.0 |
22.5 |
Other health impairments |
100.0 |
29.0 |
11.5 |
7.26 |
Visual impairments |
100.0 |
100.0 |
100.0 |
71.2 |
Autism |
100.0 |
100.0 |
51.0 |
33.0 |
Deaf-blindness |
100.0 |
100.0 |
100.0 |
100.0 |
Traumatic brain injury |
100.0 |
100.0 |
100.0 |
100.0 |
In addition, from the state-supported special schools, 100% of students who are deaf-blind, 50% of students with visual impairments, and 15% of those with hearing impairments are expected to be sampled.
Student sampling weights are the product of the LEA sampling weights and the inverse of the student sampling fraction. The student sampling weight is the number of students in the universe represented by an individual student in the sample. Estimated sampling fractions and weights are included in Table 4-15. In addition, from the state-supported special schools, we expect sampling weights of 3.8 for the deaf-blind, 7.6 for students with visual impairments, and 25.8 for students with hearing impairments.
Table 4-15 EXPECTED STUDENT SAMPLING WEIGHTS BY LEA SIZE STRATUM |
||||
Very Large |
Large |
Medium |
Small |
|
Specific learning disability |
967 |
967 |
967 |
967 |
Speech or language impairment |
819 |
819 |
819 |
819 |
Mental retardation |
209 |
209 |
209 |
209 |
Serious emotional disturbance |
134 |
134 |
134 |
134 |
Multiple disabilities |
117 |
37 |
37 |
37 |
Hearing impairments |
117 |
26 |
26 |
26 |
Orthopedic impairments |
117 |
25 |
25 |
25 |
Other health impairments |
117 |
78 |
78 |
78 |
Visual impairments |
117 |
23 |
9 |
8 |
Autism |
117 |
23 |
17 |
17 |
Deaf-blindness |
117 |
23 |
9 |
5.6 |
Traumatic brain injury |
117 |
23 |
9 |
5.6 |
Schedule of Activities Related to LEA and Student Sample Selection
Table 4-16 contains a description of the activities required to complete the selection of the student sample.
Table 4-16 |
|
SEELS SAMPLE DESIGN ACTIVITIES AND SCHEDULE |
|
Solicit input from SEELS advisory panel |
10/23/98 and following |
Notify state education agencies (SEAs) |
12/98 |
Select sample of LEAs and state-supported schools |
12/98-1/99 |
Recruit LEAs and state-supported schools |
1/99-5/99 |
First interim sampling report |
2/24/99 |
Second interim sampling report |
3/24/99 |
Final sampling report |
6/24/99 |
Final sampling fractions |
7/26/99 |
Collect student rosters from LEAs and state-supported schools |
9/99-12/99 |
Follow up with LEAs that do not respond |
9/99-12/99 |
Select student sample |
12/99 |
Provide sample to SEELS study contractor |
1/2000 |
To minimize sample attrition over the years of data collection, the SEELS study contractor will need to use aggressive tracking mechanisms to maintain accurate and up-to-date contact information for sample members. To aid in this task, the parent questionnaire will include information that will facilitate tracking of parents/guardians, such as additional work and home telephone numbers for the respondents, location information for one or more friends or relatives who would know where the family had moved, and e-mail addresses.
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