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The private school sample was drawn to cover both the national main mathematics and reading assessments and the pilot tests. This discussion focuses on the national main assessment sampling process, since the pilot test samples were embedded in the operational assessment samples for fourth and eighth grades. The twelfth-grade sample was limited to pilot testing only.
The table below indicates the target private school student sample sizes for the 2003 national main assessment. The third column in the table indicates the target student assessment yields for the national main mathematics and reading assessments. These overall targets were adjusted upwards to allow for school and student attrition from nonresponse, based on the observed attrition rates from the 2002 assessment (for each grade and private school subgroup separately). The final targets in the last column of the table were obtained by further inflation of the adjusted targets by five percent to account for ineligibility of schools, exclusion of students, and other attrition factors. The final targets in the last column were then used to determine school sample sizes and sampling rates.
Grade |
Private school stratum | National main assessment target | NAEP 2002 school yield rate | NAEP 2002 student yield rate | Attrition-adjusted target |
---|---|---|---|---|---|
All | All private | 25,800 | † | † | 40,252 |
4 | Total private | 12,600 | † | † | 18,531 |
Catholic | 6,300 | 0.90 | 0.94 | 7,820 | |
Lutheran | 1,575 | 0.86 | 0.93 | 2,068 | |
Conservative Christian | 1,575 | 0.68 | 0.93 | 2,615 | |
Other private | 3,150 | 0.59 | 0.93 | 6,028 | |
8 | Total private | 12,600 | † | † | 20,363 |
Catholic | 6,300 | 0.87 | 0.94 | 8,089 | |
Lutheran | 1,575 | 0.83 | 0.94 | 2120 | |
Conservative Christian | 1,575 | 0.60 | 0.93 | 2,964 | |
Other private | 3,150 | 0.50 | 0.92 | 7,190 | |
12 | Total private | 600 | † | † | 1,358 |
Catholic | 300 | 0.69 | 0.87 | 525 | |
Other private | 300 | 0.45 | 0.84 | 833 | |
† Not applicable; totals are calculated for counts only.
Note: The 12th grade private school stratification was limited to Catholic and all other private schools(combined into a single group) because oversampling of private schools other than Catholic was not required in the same degree of detail for 12th grade in the 2003 assessment. In addition, 12th grade schools were included for pilot testing only. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003. |
The private school sampling frame also included schools without a known affiliation (Catholic, Lutheran, Conservative Christian, or Other Private). These schools were sampled in a separate stratum to make sure that the private school samples were fully representative. The target for this group was set at 25 schools for each grade.
The procedure for setting measures of size to achieve the student sample targets was essentially the same procedure as for public schools, with each private school stratum done separately (including the affiliation-unknown stratum described in the preceding paragraph). The initial measure of size MOSjs for school s in each private school stratum j is set as follows as a function of xjs, the total number of students in school js in the fourth (eighth, twelfth) grade:
where wjs is the Private School Survey school base weight.
Multiple hits were allowed in the eighth- and twelfth-grade samples. The upper bounds uj on hits were 1 for fourth-grade private schools, 2 for eighth-grade private schools, and 3 for twelfth-grade private schools. The final bj values following the iterative process are given in the following table.
Private school stratum | Fourth grade bj value | Eighth grade bj value | Twelfth grade bj value |
---|---|---|---|
Roman Catholic | 0.000625329 | 0.000762705 | 0.000006310 |
Lutheran | 0.001823661 | 0.002518426 | 0.000119034 |
Conservative Christian | 0.000817560 | 0.001182344 | 0.000119034 |
Other private | 0.001064906 | 0.001344581 | 0.000119034 |
Affiliation unknown | 0.000280027 | 0.000280027 | 0.000119034 |
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003. |
The measures of size Ejs were calculated then as follows:
These measures were the final measures of size for the fourth- eighth- and twelfth-grade samples.