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Replicate Variance Estimates at the School Level After Nonresponse Adjustments

Every part of the school-level weighting process was replicated, i.e., the weights were recomputed for each replicate r by repeating the process with πi–1(r) replacing πi–1. This allows the final replicate weights to reflect components of variability from nonresponse adjustment, and the reductions in variability from poststratification.

As the first step in this process, for the fourth grade Westat computed replicate weights SNk(r) for each school nonresponse cell defined in Computation of School Weights. These were equal to the summation of πi–1 over all eligible sampled schools in the cell (in the original sample), divided by the summation of πi–1(r) over all cooperating original and cooperating substitute schools in the cell.

Replicate school weights wi(r), r=1,…,62, were computed as

w sub i of r equals S N sub k of r times TRIM sub i divided by pi sub i of r

Note that the trimming factors are not replicated.

The tables show national estimates and replicate estimates for the variance of the national estimates for the total number of fourth-graders using the responding school sample and the Common Core of Data (CCD) estimated grade enrollment for the school, using the wi and wi(r) weights, by NAEP region and school type.

Estimates and replicate variance estimates of enrollment based on the responding school sample and frame enrollment counts, using the school nonresponse-adjusted weights, grade 4 national main assessment: By region, 2001
Region Total Standard error of total Percent Standard error of %
Total 4,005,935 110,948 100.00
Northeast 828,643 35,603 20.69 0.93
South 1,013,319 53,576 25.30 1.16
Midwest 890,560 71,612 22.23 1.48
West 1,273,414 54,606 31.79 1.14
† Not applicable.
NOTE: Detail may not sum to totals because of rounding.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2001.
Estimates and replicate variance estimates of enrollment based on the responding school sample and frame enrollment counts, using the school nonresponse-adjusted weights, by school type, grade 4 national main assessment: 2001
School type Estimate Standard error Percentage Standard error
Total 4,005,935 110,948 100.00
Catholic 230,764 23,498 5.76 0.59
Non-religious private 54,690 14,382 1.37 0.36
Religious non-Catholic 123,662 27,272 3.09 0.67
Public 3,596,819 106,582 89.79 0.91
† Not applicable.
NOTE: Detail may not sum to totals because of rounding.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2001.
Estimates and replicate variance estimates of enrollment based on the responding school sample and frame enrollment counts, using the school nonresponse-adjusted weights, grade 8 national main assessment: By region, 2001
Region Total Standard error of total Percent Standard error of %
Total 3,810,060 113,404 100.00
Northeast 874,405 37,594 22.95 0.89
South 841,172 42,234 22.08 1.08
Midwest 928,443 80,380 24.37 1.63
West 1,166,040 42,809 30.60 1.10
† Not applicable.
NOTE: Detail may not sum to totals because of rounding.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2001.
Estimates and replicate variance estimates of enrollment based on the responding school sample and frame enrollment counts, using the school nonresponse-adjusted weights, by school type, grade 8 national main assessment: 2001
School type Estimate Standard
error
Percentage Standard
error
Total 3,810,060 113,404 100.00
Catholic 193,421 20,885 5.08 0.54
Non-religious private 32,861 8,558 0.86 0.23
Religious non-Catholic 135,270 24,434 3.55 0.59
Public 3,448,507 99,844 90.51 0.82
† Not applicable.
NOTE: Detail may not sum to totals because of rounding.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2001.
Estimates and replicate variance estimates of enrollment based on the responding school sample and frame enrollment counts, using the school nonresponse-adjusted weights, grade 12 national main assessment: By region, 2001
Region Total Standard error
of total
Percent Standard error of %
Total 3,044,940 85,864 100.00
Northeast 656,363 44,158 21.56 1.30
South 633,153 25,628 20.79 0.89
Midwest 794,710 41,170 26.10 1.12
West 960,714 55,324 31.55 1.40
† Not applicable.
NOTE: Detail may not sum to totals because of rounding.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2001.
Estimates and replicate variance estimates of enrollment based on the responding school sample and frame enrollment counts, using the school nonresponse-adjusted weights, by school type, grade 12 national main assessment: 2001
School type Estimate Standard error Percentage Standard error
Total 3,044,940 85,864 100.00
Catholic 120,080 17,568 3.94 0.57
Non-religious private 41,952 12,313 1.38 0.40
Religious non-Catholic 62,291 11,567 2.05 0.38
Public 2,820,617 84,138 92.63 0.80
† Not applicable.
NOTE: Detail may not sum to totals because of rounding.
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2001.

Last updated 26 August 2008 (FW)

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