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NAEP Technical DocumentationComputing Student-Level Replicate Factors for the 2011 Assessment

The calculation of student-level replicate factors for an assessment depended on whether the variance replication procedure incorporated finite population corrections at the first stage of sampling.

Mathematics, Reading, and Science Assessments

For the mathematics, reading, and science assessments, which involved school-level finite population corrections, the student-level replication factors were calculated the same way regardless of whether or not the student was in a certainty school.

For students in student-level variance strata comprising pairs of students, the student-level replicate factors, STU_REPFAC_jsk(r), r = 1,..., 62, were calculated as follows:

where

• π_s is the probability of selection for school s,

• R_jsr is the set of students within the r-th variance stratum for school s in primary stratum j, and

• U_jsk is the variance unit (1 or 2) for student k in school s in stratum j.

For students in variance strata comprising three students, the student-level replicate factors STU_REPFAC_jsk(r), r = 1,..., 62, were calculated as follows:

while for r' = r + 31 (mod 62):

and for all other r* other than r and r':

STU_REPFAC_jsk(r*) = 1

where

• π_s is the probability of selection for school s,

• R_jsr is the set of students within the r-th replicate stratum for school s in stratum j, and

• U_jsk is the variance unit (1, 2, or 3) for student k in school s in stratum j.

Note, for students in certainty schools, where π_s = 1, the student replicate factors are 2 and 0 in the case of pairs, and 1.5, 1.5, and 0 in the case of triples.

Computer-Based Writing Assessments

For the computer-based writing assessments, which did not involve first-stage finite population corrections and there were no certainty schools, replication at the student level was not relevant. As a consequence, the replicate factors for all replicates for every student in the computer-based writing assessments were set to unity. That is, the student-level replicate factors, STU_REPFAC_jsk(r), r = 1,..., 62, were calculated as follows:

STU_REPFAC_jsk(r) = 1.

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