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NAEP Assessment Weighting Procedures → Weighting Procedures for the 2007 Assessment → Computation of Replicate Weights for the 2007 Assessment → Computing School-Level Replicate Base Weights for the 2007 Assessment

NAEP Technical DocumentationComputing School-Level Replicate Base Weights for the 2007 Assessment

The calculation of school-level replicate base weights varied by whether a school was selected with certainty or not since replicates were formed using first-stage sample units. In certainty schools, where replicates were formed at the student-level, the school base weight for each of the 62 replicates (r = 1, ..., 62) was set equal to the full-sample school base weight. That is,

SCH_BWT_js(r) = SCH_BWT_js

For noncertainty schools, where replicate strata were formed at the school-level by grouping schools into pairs or triplets, school base weights were calculated for each of the 62 replicates based on this grouping. For schools in replicate strata comprising pairs of schools, the school-level replicate base weights, SCH_BWT_js(r), r = 1,..., 62, were calculated as follows:

                         

where

• SCH_BWT_js is the school base weight for school s in primary stratum j,

• R_jr is the set of schools within the r-th replicate stratum for primary stratum j, and

• U_js is the variance unit (1 or 2) for school s in primary stratum j.

For schools in replicate strata comprising three schools, two sets of school-level replicate base weights were computed (see replicate variance estimation for details): one for the first replicate r₁ and another for the second replicate r₂. The two sets of school-level replicate base weights SCH_BWT_js(r₁), r₁ = 1,..., 62 and SCH_BWT_js(r₂), r₂ = 1,..., 62 were calculated as described below.                          

where

• SCH_BWT_js is the school base weight for school s in primary stratum j,

• is the set of schools within the r₁-th replicate stratum for primary stratum j,

•   is the set of schools within the r₂-th replicate stratum for primary stratum j, and

• U_js is the variance unit (1, 2 or 3) for school s in primary stratum j.

In primary strata with fewer than 62 replicate strata, the replicate weights for the “unused” replicate strata (the remaining ones up to 62) for these schools were set equal to the school base weight (so that those replicates contribute nothing to the variance estimate).

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