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

NAEP Technical DocumentationComputing Student-Level Replicate Weights

For the 2003 assessment, the first-stage sample unit in certainty schools was the student. The process of assigning students in certainty schools to replicate strata was much like that for noncertainty schools, with students replacing schools as the sampling unit. The primary strata for student replicate weighting factor assignments were the individual schools. Within each school, students were sorted by session and line number from the administration schedule before being assigned to replicate strata.

The result of this process was that within each certainty school, students were assigned as doublets or triplets in up to 62 replicate strata. The procedure for calculating replicate student base weights STUWGT_jsk(r) differs considerably between certainty and noncertainty schools. In noncertainty schools, the student base weights for replicate r = 1, ..., 62 for student k in school s in jurisdiction j is calculated as follows:

STUWGT_jsk(r) = w_js(r) × SNRADJ_js(r) × SUBADJ_js× TRIM_js × WINSCHL_js × YRRND_js× SUBJFAC_j

where

• w_js(r) is the school base weight;

• SNRADJ_js(r) is the school nonresponse factor;

• SUBADJ_js  is the substitute adjustment factor to account for the difference in size between a substitute and its corresponding original school;

• TRIM_js is the school weight trimming factor;

• WINSCHL_js is the within-school sampling interval;

• YRRND_js is the year-round factor; and

• SUBJFAC_j is the subject factor.

Note that both of the school-level weighting factors are replaced with replicate weighting factors, but none of the student-level weighting factors are replaced.

In certainty schools, students were the first stage of selection and were assigned to replicate strata as described at the beginning of this section. The replicate factors that reflect the replicate stratum assignment (e.g., 2, 0, 1.5, or 1) were given as REPFAC_jsk(r) for student k in school s in jurisdiction j. The replicate student base weight for students in certainty schools is as follows:

STUWGT_jsk(r) = w_js × REPFAC_jsk(r) × SNRADJ_js(r)  × SUBADJ_js × TRIM_js

            × WINSCHL_js × YRRND_js × SUBJFAC_j  

The school base weight w_js is a constant (equal to one) for all certainty schools. However, the school nonresponse factor SNRADJ_js(r) is replicated for the certainty schools, just as it was for noncertainty schools.

Separate student nonresponse factors were calculated for each set of replicates and incorporated in the student base weights. Thus, the student nonresponse factors are replicated, and the resulting student nonresponse adjusted replicate weights include a component of variance due to the student nonresponse factors.

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