NAEP Technical DocumentationSelf-Weighting at the Student Level

The general goal is to achieve a "self-weighting" sample at the student level; that is, as much as is possible, every eligible student should have the same probability of selection. Differences in the probability of selection among students introduce unwanted design effects, which increase the variance (reducing the marginal benefit of each added student.)

When all students are taken in each sampled school, a self-weighting sample results from setting a fixed probability of selection across schools (as each student then has a probability of selection equal to the school probability of selection, which is equal across schools). When a fixed sample size m of students (e.g., 62) is taken in each sampled school, a self-weighting sample is achieved by taking a probability-proportionate-to-size sample, with size equal to the number of students, n, within the school. Each student then has a conditional probability of selection of m/n, which, when multiplied by the school's probability of selection (which is proportional to n, i.e., b × n with b the constant of proportionality), again gives equal unconditional probabilities of selection for students across schools (equal to b × m).

This formulation leads to the setting of fixed sampling rates for smaller schools (68 or fewer students), which will have all students in the sample, and probability proportionate to student enrollment sampling rates for larger schools (69 or more students), from which a fixed sample of 62 students will be drawn. (This formulation ignores multiple-hit schools.)

There is also an added need to lower the expected number of very small schools, as the marginal cost for each assessed student in these schools is higher. These very small schools are sampled at half the rate of the larger schools, and their weights are doubled to account for the half-sampling.

Last updated 15 April 2008 (TS)

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