NAEP Technical DocumentationSampling of Public Schools for the 2009 Science HOT and ICT Assessments

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

• 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 and grade. The initial measures of size (MOS) were set as follows:

For fourth grade

where X_js is the estimated grade enrollment for grade j (j =  4) in school s, and PSU_WT_S is the PSU weight for school s.

For eighth and twelfth grades

where X_js is the estimated grade enrollment for grade j (j =  8, 12) in school s, and PSU_WT_S is the PSU weight for school s.

For the national HOT and ICT samples, by design a school could not be selected, or "hit," in the sampling process more than once. In addition, an adjustment was made to the initial measures of size in the national sample to attempt to reduce school burden by minimizing the number of schools selected for simultaneous administration of both the state and national studies. The 2009 NAEP studies 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 national and state 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 890 for the hands-on tasks (HOT) and interactive computer tests (ICT) assessments.

Printer-friendly Version