NAEP Technical DocumentationSampling of Public Schools for the 2012 Economics Assessment

In the design of each school sample, five objectives underlie the process of determining the probability of selection for each school and the number of students to be sampled from each selected school containing grade-eligible students. The five objectives are

• to meet the target student sample size;

• to select an equal-probability sample of students;

• to limit the number of students that are selected from a school;

• to ensure that the sample within a school does not include a very high percentage of the students in the school, unless all students are included; and

• to reduce the rate of sampling of small schools, in recognition of the greater cost and burden per student of conducting assessments in such schools.

The goal in determining the school's measure of size is to optimize across the last four objectives in terms of maintaining the accuracy of estimates and the cost-effectiveness of the sample design.

Therefore, to meet the target student sample size objective and achieve a reasonable compromise among the other four objectives, the following algorithm was used to assign a measure of size to each school based on its estimated grade enrollment as indicated on the sampling frame. 

The measures of size vary by enrollment size. The initial measures of size (MOS) were set as follows:

For twelfth grade

where x_js is the estimated grade enrollment for grade j in school s, and PSU_WT_s is the PSU weight for school s.

A school with more than 15 percent Black and Hispanic students and at least 10 Black or Hispanic students in the sample grade is in the high Black/Hispanic stratum for NAEP. The measures of size for schools in the high Black/Hispanic stratum are doubled to increase their chances of selection:

The next task in this development is to describe b_j, the constant of proportionality. It is a sampling parameter that, when multiplied with a school’s preliminary measure of size (M_js), yields the school’s final measure of size. It is computed in such a way that, when used with the systematic sampling procedure, the target student sample size is achieved. For public schools, b_j is 0.000096773 for twelfth grade.

The final measure of size, E_js, is defined as:

The quantity u_j (the maximum number of “hits” allowed) in this formula is designed to put an upper bound on the burden for the sampled schools. For public schools, u_j is 1.

In addition, new and newly-eligible schools were sampled from the new-school frame. The assigned measures of size for these schools:

used the b_j and u_j values from the main school samples. The variable is the probability of selection of the district  into the new-school sample.

For the NAEP 2012 samples, by design a school could not be selected, or "hit," in the sampling process more than once within a grade. In addition, an adjustment was made to the initial measures of size in the sample to attempt to reduce school burden by minimizing the number of schools selected for simultaneous administration of both the economics and long-term trend assessments. The NAEP 2012 sampling procedures used an adaptation of the Keyfitz process to compute conditional measures of size that, by their design, minimized the overlap of schools selected for both the economics and long-term trend assessments.

Schools were ordered within each jurisdiction using the serpentine sort described under the stratification of public schools. A systematic sample was then drawn using this serpentine-sorted list and the measures of size. The number of public schools selected was approximately 500 for twelfth grade. 

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