NAEP Technical DocumentationDefining Replicate Strata and Forming Replicates

			Replicate Variance Estimation

The general procedure for assigning replicate strata A_rj(for replicate stratum r and jurisdiction j) orders the schools by their primary strata within each jurisdiction, with new schools in a separate stratum from the Common Core of Data (CCD) schools. (For a description of school sampling, see School Sample Selection for the 2002 State Assessment.) Schools with a probability of selection equal to 1 (certainty schools) were removed from this list and set aside for replicate assignment at the student level.¹

Within the CCD primary strata, noncertainty schools were sorted according to their serpentine order on the CCD frame. New schools also were sorted according to their order on the new school frame. Trial Urban District Assessment (TUDA) schools were sorted by their order on the TUDA 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.

If there were more than 62 preliminary replicate strata within a jurisdiction, the preliminary replicate strata were grouped to form 62 replicate strata. This grouping 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), with the next 62 preliminary replicate strata assigned to final replicate strata 1 through 62, so, for example, the 1st preliminary replicate stratum, the 63rd preliminary replicate stratum, the 125th preliminary replicate stratum (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 the jurisdiction, the number of final replicate strata was set equal to the number of preliminary replicate strata. The remaining replicate weights for the jurisdiction were set equal to the school base weight (so that those replicates contributed zero to any replicate sum of squares).

The five TUDA district samples were dealt with in a special way within their respective states. The TUDA school samples were treated as a separate jurisdiction within their states, with replicate strata for the TUDA school utilizing the sample ordering from the TUDA sampling process. The remainder of the five states—California, Georgia, Illinois, New York, and Texas—were treated also as a separate jurisdiction, with replicate strata assigned for that part of the sample alone. Schools that were in both the TUDA and the state sample were treated as if they were only in the TUDA sample.²

¹ Schools were only set aside if they had a probability of selection of 1 of being in the school sample for the alpha sample (the operational reading and writing assessment) in particular. These were called "absolute certainty schools."
² This is a slight distortion, as the sampling process for the state took a sample from the full state frame rather than from the complement of the TUDA district, so that the replicate strata for the complement sample only approximates the true ordering used in the original state sample. In addition, there is a slight distortion for the TUDA sample, as that sample was drawn not as a direct sample from the TUDA frame, but via a special sampling process to maximize overlap with the state sample (see Assignment of Conditional Probabilities for the TUDA School Sample). Although not accounted for directly in the replicate weights, it does serves as a valid approximation.

Last updated 09 October 2008 (LH)

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