## Defining Replicate Strata and Forming Replicates for the 2004 Assessment

In the 2004 NAEP assessment, replicates were formed separately for each sample [indicated by age group (9, 13, or 17) and assessment type (operational, mathematics bridge, or reading bridge)]. The first step in forming replicates was to assign each first-stage sampling unit in a primary stratum to a replicate stratum. In 2004, the formation of replicate strata varied by noncertainty and certainty PSUs. For noncertainty PSUs, the first-stage units were PSUs, and the primary stratum was the combination of NAEP region and metropolitan status (MSA, non-MSA). For certainty PSUs, the first-stage units were schools, and the primary stratum was the combination NAEP region and school type (public, private).

For noncertainty PSUs, where only one PSU was selected per PSU stratum, replicate strata were formed by pairing sampled PSUs with similar stratum characteristics within the same primary stratum (NAEP region by metropolitan status). This was accomplished by first sorting the 60 sampled PSUs by PSU stratum number and then grouping adjacent PSUs into 30 pairs. The values for a PSU stratum number reflect NAEP region, metropolitan status as well as socioeconomic characteristics such as percent Black and percent children below poverty. The formation of these 30 replicate strata in this manner models a design of selecting two PSUs with probability proportional to size with replacement from each of 30 strata. The replicate strata for the noncertainty PSUs were labeled 1 through 30.

For certainty PSUs, the first stage of sampling is at the school level, and the formation of replicate strata must reflect the sampling of schools within the certainty PSUs. Replicate strata were formed by sorting the sampled schools in the 17 certainty PSUs by their order of selection within a primary stratum (NAEP region and school type) so that the sort order reflected the implicit stratification (urbanicity stratification, minority stratification, and student enrollment size) and systematic sampling features of the sample design.

The first-stage units were then paired off into preliminary replicate strata. Within each primary stratum with an even number of first-stage units, all of the preliminary replicate strata were pairs, and within primary strata with an odd number of first-stage units, one of the replicate strata was a triplet (the last one), and all others were pairs.

If there were more than 32 preliminary replicate strata within a primary stratum, the preliminary replicate strata were grouped to form 32 replicate strata. This grouping effectively maximized the distance in the sort order between grouped preliminary replicate strata. The first 32 preliminary replicate strata, for example, were assigned to 32 different final replicate strata in order (1 through 32), with the next 32 preliminary replicate strata assigned to final replicate strata 1 through 32, so that, for example, preliminary replicate stratum 1, preliminary replicate stratum 33, preliminary replicate stratum 65 (if there were that many), etc., were all assigned to the first final replicate stratum. The final replicate strata for the schools in the certainty PSUs were labeled 31 through 62.

Within each pair preliminary replicate stratum, the first first-stage unit was assigned as the first variance unit and the second first-stage unit as the second variance unit. Within each triplet preliminary replicate stratum, the 3 schools were assigned variance units 1 through 3.

Last updated 17 April 2009 (JL)