​NAEP Technical DocumentationComputation of Replicate School Weights for Variance Estimation for the 2020 Assessment

			Defining Replicate Strata and Forming Replicates

In addition to the full-sample weight, a set of 62 replicate weights was provided for each school. These replicate weights are used in calculating the sampling variance of estimates obtained from the data, using the jackknife repeated replication method. The method of deriving these weights was aimed at reflecting the features of the sample design appropriately for each sample, so that when the jackknife variance estimation procedure is implemented, approximately unbiased estimates of sampling variance are obtained. This section gives the specifics for generating the replicate weights for the 2020 assessment samples.

For each sample, replicates were formed in two steps. First, each school was assigned to one or more of 62 replicate strata. In the next step, a random subset of schools in each replicate stratum was excluded. The remaining subset and all schools in the other replicate strata then constituted one of the 62 replicates.

A replicate weight was calculated for each of the 62 replicates using weighting procedures similar to those used for the full-sample weight. Each replicate base weight contains an additional component, known as a replicate factor, to account for the subsetting of the sample to form the replicate. By repeating the various weighting procedures on each set of replicate base weights, the impact of these procedures on the sampling variance of an estimate is appropriately reflected in the variance estimate.

Each of the 62 replicate weights for school \(s\) in stratum \(j\) can be expressed as follows:

\begin{equation} \begin{aligned} SCH\_WGT_{js}(r)= {} & SCH\_BWT_{js}(r) \times SCH\_NRAF_{js}(r) \times\\ &SCH\_TRIM_{js} \times SCHSESWT_{js} \times SCH\_SUBJ\_AF_{js} \end{aligned} \end{equation}

where

• \(SCH\_BWT_{js}(r)\) is the replicate school base weight for replicate \(r\);

• \(SCH\_NRAF_{js}(r)\) is the school-level nonresponse adjustment factor for replicate \(r\);

• \(SCH\_TRIM_{js}\) is the school-level weight trimming adjustment factor;

• \(SCHSESWT_{js}\) is the school-level session assignment weight; and

• \(SCH\_SUBJ\_AF_{js}\) is the small-school subject adjustment factor.
  

Specific school nonresponse adjustment factors were calculated separately for each replicate, as indicated by the index \((r)\) in the formula, and applied to the replicate school base weights. Computing separate nonresponse adjustment factors for each replicate allows resulting variances from the use of the final school replicate weights to reflect components of variance due to this weight adjustment.

School weight trimming adjustments were not replicated, that is, not calculated separately for each replicate. Instead, each replicate used the school trimming adjustment factors derived for the full sample. Statistical theory for replicating trimming adjustments under the jackknife approach has not been developed in the literature. Due to the absence of a statistical framework, and since relatively few school weights in NAEP require trimming, the weight trimming adjustments were not replicated.

In addition, the school-level session assignment weight and the small-school subject adjustment factor also used the same factors derived for the full sample.

Printer-friendly Version