NAEP Assessment Sample Design → NAEP 2009 Sample Design → Sample Design for the 2009 National Assessment → Hands-On Tasks (HOT) and Interactive Computer Tests (ICT) for the 2009 Science Assessment → Private School 2009 Science HOT and ICT Assessments → Sampling of Private Schools for the 2009 Science HOT and ICT Assessments

NAEP Technical DocumentationSampling of Private 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, PSCHWT_S = the PSS area frame weight for school s, computed by the U.S. Census Bureau, and PSU_WT_S = 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, PSCHWT_S = the PSS area frame weight for school s, computed by the U.S. Census Bureau, and PSU_WT_S = the PSU weight for school s.

For the national hands-on tasks (HOT) and interactive computer tests (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 to reduce school burden by minimizing the number of schools that were selected for simultaneous administration of both the science probe assessments (that is, HOT and ICT) and the operational private school assessments (mathematics, reading, and science). 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 types of assessments.

Schools were ordered within each jurisdiction using the serpentine sort described under the stratification of private schools. A systematic sample was then drawn using this serpentine sorted list and the measures of size. The number of private schools selected was approximately 210 for the HOT and ICT assessments.

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