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Defining Replicate Strata and Forming Replicates

In the 2003 assessment, schools were assigned to replicate strata separately for each sample—indicated by school type (public/private) and grade (4, 8). Schools were not assigned to replicate strata separately by subject, to capture the effect of booklet spiraling in the variance estimates. The general procedure for assigning schools to replicate strata is to order the schools by their primary strata within each sample, with new schools in a separate stratum from the non-new schools (i.e., those on the original frame). The primary strata are defined as follows for each sample:

  • Fourth- and eighth-grade public school sample primary strata were referred to as jurisdictions.

  • Fourth- and eighth-grade private school sample primary strata were referred to by affiliation (i.e., conservative Christian, Lutheran, Catholic, other private, unknown).

Within the primary strata, noncertainty schools were sorted by their order of sample selection to reflect the implicit stratification and systematic sampling features of the sample design.

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.

If there were more than 62 preliminary replicate strata within a primary stratum, the preliminary replicate strata were grouped to form 62 replicate strata. This grouping effectively maximized the distance in the sort order between grouped preliminary replicate strata. The first 62 preliminary replicate strata, for example, were assigned to 62 different final replicate strata in order (1 through 62). The next 62 preliminary replicate strata were also assigned to final replicate strata 1 through 62 in order, and so on, so that, for example, preliminary replicate stratum 1, preliminary replicate stratum 63, preliminary replicate stratum 125 (if there are that many), etc. were all assigned to the first final replicate stratum.

If, on the other hand, there were fewer than 62 preliminary replicate strata within a primary stratum, then the number of final replicate strata was set equal to the number of preliminary replicate strata.

For example, consider a state with 115 sampled schools, four certainties and 111 noncertainties.  The four certainty schools are set aside, because replicate strata will be assigned at the student level. The 111 noncertainty schools are sorted in their order on the frame. The first two schools are in the first preliminary replicate stratum, the next two schools are in the second preliminary replicate stratum, and so on, resulting in 54 preliminary replicate strata with two schools each (doublets). The last three schools are in the 55th preliminary replicate stratum (triplet). Since there are no more than 62 preliminary replicate strata, these are also the final replicate strata.

Within each doublet preliminary stratum, the first school was assigned as the first variance unit and the second school as the second variance unit. Within each triplet preliminary stratum, the three schools were assigned variance units 1 through 3.

Last updated 19 June 2008 (PE)

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