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NAEP Assessment Sample Design → NAEP 2006 Sample Design → 2006 Public School Sample → Sampling of Public Schools for the 2006 Assessment

Sampling of Public Schools for the 2006 Assessment

When designing each school sample, there are five objectives that 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 the respective grade:

  • to meet the target student sample size for each grade;

  • 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.

In order to meet the target student sample, and achieve a reasonable compromise among the other four objectives above, NAEP sample design staff used the following algorithm to assign a measure of size to each school based on its enrollment per grade as indicated on the sampling frame. 

The measures of size vary by grade, enrollment size, and within school target sample size. In general, very small schools will be sampled at one quarter the rate of larger "take-all-student" schools. The initial measures of size (MOS) were set as follows:

Fourth grade:


MOS subscript js = PSU_WT subscript s times bracket 4 rows. Row 1 = X subscript js, if 151 is less than or equal to X subscript js. Row 2 = 123 if 20 is less than or equal to X subscript js less than 151. Row 3 = 6.15 times X subscript js, if 5 less than or equal X subscript js less than 20. Row 4 = 30.75 if X subscript js less than 5

  

Eighth and twelfth grades:

 


MOS subscript js = PSU_WT subscript s times bracket 4 rows. Row 1 = X subscript js, if 144 is less than or equal to X subscript js. Row 2 = 95 if 20 is less than or equal to X subscript js less than 144. Row 3 = 4.75 times X subscript js, if 5 less than or equal X subscript js less than 20. Row 4 = 23.75 if X subscript js less than 5

    

where xjs is the estimated grade enrollment for grade j in school s, and PSU_WTs 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:

M subscript js equals bracket 2 rows. Row 1 equals 2 times MOS subscript js if school is in the high Black/Hispanic stratum. Row 2 equals MOS subscript js if school is not in the high Black/Hispanic stratum

The next task in this development is to describe bj, the constant of proportionality for each grade. It is a sampling parameter that, when multiplied with a school’s preliminary measure of size (Mjs), 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, bj is 0.000039192 for fourth grade, 0.000069935 for eighth grade, and 0.000132007 for twelfth grade.

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

E subscript js equals min left parenthesis b subscript j times M subscript js comma u subscript j right parenthesis      

The quantity uj (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, uj is 1.

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 numbers of schools selected were about 360, 460, and 670 for fourth, eighth, and twelfth grades, respectively.


Last updated 13 April 2010 (GF)

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