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NAEP Weighting Procedures → Weighting Procedures and Variance Estimation for the 2001 National Main Assessment → Computation of School Weights → Replicate Weights and Variance Estimation → Replicate Variance Estimates at the School Level After Nonresponse Adjustments

NAEP Technical DocumentationReplicate 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 π_i^–1(r) replacing π_i^–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 SN_k(r) for each school nonresponse cell defined in Computation of School Weights. These were equal to the summation of π_i^–1 over all eligible sampled schools in the cell (in the original sample), divided by the summation of π_i^–1(r) over all cooperating original and cooperating substitute schools in the cell.

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

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 w_i and w_i(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.

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