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NAEP Weighting Procedures → Weighting Procedures and Variance Estimation for the 2000 National Main Assessment → Variance Estimation for the 2000 National Main Assessment → Sampling Variability in the 2000 National Main Assessment → Jackknife Procedure → Weights for Noncertainty Strata

NAEP Technical DocumentationWeights for Noncertainty Strata

The derivation of the 36 replicate weights reflecting the variance of the noncertainty primary sampling units (PSUs) involves defining pairs of PSUs that model the design of two PSUs drawn with replacement per stratum. PSUs are pairs that are drawn from strata within the same subuniverse and with similar stratum characteristics. The same definition of pairs is used for each of the age/grade classes in the national main assessment, since all are drawn from the same sample of noncertainty PSUs. Drawn one from each of 72 strata, the 72 noncertainty PSUs are formed into 36 pairs of PSUs. Therefore, the strata are relatively similar on socioeconomic characteristics such as proportion minority population, population change since 1980, per capita income, civilian unemployment rate, educational attainment, and unemployment rate.

For variance estimation purposes the design is regarded as calling for the selection of two PSUs with probability proportional to size with replacement from each of 36 strata. This procedure likely gives a small positive bias to estimates of sampling error.

The student replicate weight for the i^th pair of noncertainty PSUs, for the 36 pairs corresponding to values of i from 1 to 36, is computed as follows:

1. Let be the base weight of a student, which accounts for the various components of the selection probability for the student.

2. At random, one PSU in each pair is denoted as PSU number 1, while the other is denoted as PSU number 2. The i^th replicate base weight is given by:

if the student is in school number 1 or 2 of a PSU in set i if the student in school number 3 of a PSU in set i if the student does not belong to a PSU in set i

3. The i^th student replicate weight SRWT_i is obtained by applying the various school and student nonresponse adjustments, the weight trimming, and the poststratification to the i^th set of replicate base weights, using procedures identical to those used to obtain the final student weights WT from the set of base weights .

In brief, the procedure for deriving the sets of values from the values reflects the sampling of PSUs, schools, sessions, and students. By repeating the various weight adjustment procedures in each set of replicate base weights, the impact of these procedures on the sampling variance of the estimator, t, is reflected in the variance estimator .

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