Weighting the Youth Data

As noted in chapter 1, the percentages and means reported in the data tables throughout this report are estimates of the true values for the population of youth with disabilities in the NLTS2 age range who are able to respond to telephone interview or mail survey questions for themselves. The response for each sample member is weighted to represent the number of youth in his or her disability category in the kind of LEA (i.e., region, size, and wealth) or special school from which he or she was selected and whose parent would have indicated the youth could respond to questions for him/herself if the youth had been included in the sample.

Table A-4 illustrates the concept of sample weighting and its effect on values that are calculated for youth with disabilities as a group. In this example, 10 students are included in a sample, 1 from each of 10 disability groups, and each has a hypothetical likelihood of responding "yes" to the question "Can you find a friend when you need one?" Summing the hypothetical values for the 10 youth results in an average of 74.6 for the full group. However, this would not accurately represent the national population of youth with disabilities because many more youth are classified as having a learning disability than orthopedic or other health impairments, for example. Therefore, in calculating a population estimate, weights in the example are applied that correspond to the proportion of youth in the population who are from each disability category (actual NLTS2 weights account for disability category and several aspects of the districts from which they were chosen). The sample weights for this example appear in column C. Using these weights, the weighted population estimate is 84.8 percent. The percentages in all NLTS2 tables are similarly weighted population estimates, whereas the sample sizes are the actual number of cases on which the weighted estimates are based (similar to the 10 cases in table A-4).

The youth in LEAs and state schools with data for each survey were weighted to represent the universe of students in LEAs and state schools using the following process:

• For each of the 64 LEA sampling cells, an LEA student sampling weight was computed. This weight is the ratio of the number of students in participating LEAs in that cell divided by the number of students in all LEAs in that cell in the universe of LEAs. The weight represents the number of students in the universe who are represented by each student in the participating LEAs. For example, if participating LEAs in a particular cell served 4,000 students and the universe of LEAs in the cell served 400,000 students, then the LEA student sampling weight would be 100.

Table A-4: Example of weighted percentage calculation

• For each of the 64 LEA cells, the number of students in a disability category was estimated by multiplying the number of students with that disability on the rosters of participating LEAs in a cell by the adjusted LEA student sampling weight for that cell. For example, if 350 students with learning disabilities were served by LEAs in a cell, and the LEA student sampling weight for that cell was 100 (that is, each student in the sample of participating LEAs in that cell represented 100 students in the universe), there would be an estimated 35,000 students with learning disabilities in that cell in the universe.
  
  
• For the state schools, the number of students in each disability category was estimated by multiplying the number of students with that disability on the rosters by the inverse of the proportion of state schools that submitted rosters.
  
  
• Initial student weights were calculated for each cell by disability as the estimated number of students in that cell divided by the number of respondents in that cell.
  
  
• Weights were adjusted by disability category using a raking algorithm so that the sum of the weights by geographical region, wealth, LEA size, and ethnicity was equal to the estimated national distribution for that disability. The adjustments were typically small and essentially served as a nonresponse adjustment. However, the adjustments could become substantial when there were relatively few interviewees (as occurred in the small and medium strata for the lowest-incidence disabilities) because in these cases, there might not be any interviewees in some cells, and it was necessary to adjust the weights of other interviewees to compensate. Two constraints were imposed on the adjustments: (1) within each size stratum, the cells' weights could not vary from the average weight by more than a factor of 2, and (2) the average weight within each size strata could not be larger than 4 times the overall average weight. These constraints substantially increased the efficiency of the sample at the cost of introducing a small amount of weighting bias.
  
  
• In a final step, the weights were adjusted so that they summed to the number of students in each disability category, as reported to OSEP by the states for the 2000–01 school year (Office of Special Education Programs 2001).

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