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NAEP Weighting Procedures → 2003 Weighting Procedures and Variance Estimation → Calculation of Replicate Weights → Computing School-Level Replicate Weights

NAEP Technical DocumentationComputing School-Level Replicate Weights

The replicate school base weights w_js(r), r = 1, ., R, were computed as follows:

where

• w_js is the school base weight for school s in jurisdiction j;

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

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

Each triplet replicate stratum R_jr also has a paired replicate stratum r₂. The replicate weights assigned to schools in R_jr are as follows:

For example, consider a state with 111 noncertainty schools in which the first 54 final replicate strata contain two schools each (doublets) and replicate stratum 55 contains three schools (triplet). Replicate stratum 55 is paired with replicate stratum 23 (i.e., r₂ = 23).

In the first replicate stratum, for the first school

• the variance unit = 1;
• the replicate weight for the first replicate stratum = 2 times the school base weight; and
• the replicate weight for all other replicate strata = the school base weight.

In the first replicate stratum, for the second school

• the variance unit = 2;
• the replicate weight for the first replicate stratum = 0; and
• the replicate weight for all other replicate strata = the school base weight.

In the 55th replicate stratum, for the first school

• the variance unit = 1;
• the replicate weight for the 55th replicate stratum = 1.5 times the school base weight;
• the replicate weight for the 23rd replicate stratum = 1.5 times the school base weight; and
• the replicate weight for all other replicate strata = the school base weight.

In the 55th replicate stratum, for the second school

• the variance unit = 2;
• the replicate weight for the 55th replicate stratum = 1.5 times the school base weight;
• the replicate weight for the 23rd replicate stratum = 0; and
• the replicate weight for all other replicate strata = the school base weight.

In the 55th replicate stratum, for the third school

• the variance unit = 3;
• the replicate weight for the 55th replicate stratum = 0;
• the replicate weight for the 23rd replicate stratum = 1.5 times the school base weight; and
• the replicate weight for all other replicate strata = the school base weight.

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 zero to any replicate sum of squares).

Trimmed replicate school base weights were computed by multiplying each replicate school base weight w_js(r) by the trimming (of school base weights) factor TRIM_js.

Separate school nonresponse adjustment factors SNRADJ_js(r) were calculated for each set of replicates. Nonresponse-adjusted replicate school base weights were computed by multiplying each trimmed replicate school base weight by the school nonresponse adjustment for that replicate. Thus, the school nonresponse factors are replicated, and the resulting school nonresponse adjusted replicate weights include a component of variance due to the school nonresponse factors.

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