NAEP Technical DocumentationSelf-Weighting at the Student Level

In NAEP school sample selection, the general goal is to achieve a self-weighting, or 'epsem' sample (see for example Kish [1965]) at the student level, as much as is possible, in which every eligible student has the same probability of selection. Differences in the probability of selection between 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 is achieved by 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 of m students (e.g., 60) 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 multiplied to the school’s probability of selection which is proportional to n gives equal unconditional probabilities of selection for students across schools.

This prescription leads to the setting of fixed sampling rates for smaller schools (64 or fewer students), which will have all students in the sample, and probability proportionate to student enrollment sampling rates for larger schools (65 or more students), from which a fixed sample of 60 students will be drawn. (These sampling rates for larger schools do not include multiple hit schools.)

In NAEP assessments, sample design staff also 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 a lower rate (a half-sample rate for the very smallest schools) relative to other schools, and increase their weight by the same proportion to account for the lower sampling rate.

Last updated 09 September 2008 (RF)

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