The NAEP 2008 long-term trend (LTT) assessment sample design yielded a nationally representative sample of private school students in each age group (9, 13, and 17) through the use of a three-stage approach: selection of primary sampling units (PSUs), selection of schools within strata, and selection of students within schools. The sample of schools was selected with probability proportional to a measure of size based on the estimated age-specific enrollment in the schools. The 2008 sampling plan was designed to assess 3,250 students for each of the LTT private school age-specific samples.
The sampled students were allocated among three different tests. The operational tests were in reading and mathematics and a pilot test was conducted in mathematics.
The private school samples were drawn from a sampling frame that only included the sampled LTT primary sampling units (PSUs). From the stratified frame of private schools for each grade, a systematic random sample of age-eligible schools was drawn with probability proportional to a measure of size based on the estimated age-specific enrollment of the school. The number of age-eligible students was estimated by applying population-level percentages of age-eligible students within each grade to estimated grade enrollments for each grade, and aggregating to an age-eligible total for the school.
Each selected school was asked to provide a roster of all of its students who were age-eligible. A fixed sample of 62 students was selected from these rosters, with the exception of smaller schools with total age-eligible counts less than the sample size. The combination of using the number of age-eligible students as a measure of size and a fixed sample size of students is intended to give a self-weighting sample (each student has an equal probability of selection). In practice, differences between the estimated age-eligible enrollment for the school and the actual size of the finalized roster introduce slightly differing student probabilities across schools.