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NAEP Weighting Procedures → 2002 Weighting Procedures and Variance Estimation → National Main Assessment Weights → Calculation of Replicate Weights → Defining Replicate Strata and Forming Replicates

NAEP Technical DocumentationDefining Replicate Strata and Forming Replicates

A total of 62 replicate weights r = 1,...,62 was computed for the purpose of variance estimation for the NAEP 2002 assessments. A general review of the theory that underlies the jackknife variance estimators used in NAEP assessment can be found on the page Replicate Variance Estimation. The replicate weights generated for the 2002 national main assessment school samples started with the school base weights w_s * SCHSES_s^(A).¹

In NAEP, the general procedure for assigning replicate strata A_r (for replicate stratum r ) is to order the schools by their primary strata (Census division for twelfth-grade public schools and private school stratum for private schools), with new schools in a separate stratum from the Common Core of Data (CCD) schools for twelfth-grade public schools. In 2002, schools with probability of selection equal to 1 (certainty schools) were removed from this list, and were set aside for replicate assignment at the student level.²

Within the primary strata, the noncertainty schools were sorted according to the serpentine order they had on the school frame. The twelfth-grade new public schools also were sorted according to their order on the new school frame.

The schools were then paired off into preliminary replicate strata. Within each primary stratum with an even number of sampled noncertainty schools all of the preliminary replicate strata were doublets, and within primary strata with an odd number of sampled noncertainty schools, one of the replicate strata was a triplet (the last one), and all others were doublets.

The twelfth-grade public schools contained a total of 330 preliminary replicate strata, of which three were triplets and the remainder doublets. The preliminary replicate strata were grouped into 62 final replicate strata. This grouping was used to maximize the distance in the sort order between grouped preliminary replicate strata. The first 62 preliminary replicate strata, for example, are assigned to 62 different final replicate strata in order (1 through 62), with the next 62 preliminary replicate strata then assigned to final replicate strata 1 through 62, so that the 1st preliminary replicate stratum, the 63rd preliminary replicate stratum, the 125th preliminary replicate stratum (if there were that many), etc. were all assigned to the first final replicate stratum.

For the private school "A" session school samples, grade 4 had 307 preliminary replicate strata and 1 triplet, grade 8 had 367 preliminary replicate strata and 2 triplets, and grade 12 had 259 preliminary replicate strata and 4 triplets.

¹ The weights are based on the original session assignments, not the final session assignments which may be based on a smaller number of sessions if the school is found to have fewer students than expected.
² Only one twelfth-grade public school was a certainty for the "A" session sample (the national sample). This school had replicate weights assigned to it at the student level as described for the state assessment certainty schools. No private schools were certainties.

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