NAEP Technical DocumentationComputing Student-Level Replicate Base Weights for the 2009 Assessment

The calculation of the student-level replicate base weights differed by whether a student was in a school selected with certainty or not, since replicates were formed using first-stage sample units. The first-stage sample unit was the student in certainty schools and the school itself for noncertainty schools.

For students in certainty schools, where replicate strata were formed at the student-level by grouping students into pairs or triplets, student base weights were calculated for each of the 62 replicates based on this grouping. For students in replicate strata comprising pairs of students, the student-level replicate base weights, STU_BWT_jsk(r), r = 1,..., 62, were calculated as follows:

STU underscore BWT subscript s j k open paren r close paren equals open paren two times STU underscore BWT subscript j s k for s k is an element of cap r subscript j s r and cap u subscript j s k equals one close paren or equals zero for s k is an element of cap r subscript j s r and cap u subscript j s k equals two close paren or equals STU underscore BWT subscript j s k if s k is not an element of cap r subscript j s r

where

STU_BWT_jsk is the full-sample student base weight for student k in certainty school s in stratum j,
R_jsr is the set of students within the r-th replicate stratum for certainty school s in stratum j, and
U_jsk is the variance unit (1 or 2) for student k in certainty school s in stratum j.

For students in replicate strata comprising three students, two sets of student-level replicate base weights were computed (see replicate variance estimation for details): one for the first replicate r₁ and another for the second replicate r₂. The two sets of student-level replicate base weights STU_BWT_jsk(r₁), r₁ = 1,..., 62 and STU_BWT_jsk(r₂), r₂ = 1,..., 62 were calculated as described below.

STU underscore BWT subscript j s k open paren r subscript 1 close paren equals open paren one point five times STU underscore BWT subscript j s k for j s k is an element of cap r subscript j s r subsubscript 1 and cap u subscript j s k equals one close paren or equals open paren one point five times STU underscore BWT subscript j s k for j s k is an element of cap r subscript j s r subsubscript 1 and cap u subscript j s k equals two close paren or equals open paren zero for j s k is an element of cap r subscript j s r subsubscript 1 and cap u subscript j s k equals three close paren or equals STU underscore BWT subscript j s k if s k is not an element of cap r subscript s r subsubscript 1

STU underscore BWT subscript j s k open paren r subscript two close paren equals open paren one point five times STU underscore BWT subscript j s k for j s k is an element of cap r subscript j s r subsubscript two and cap u subscript j s k equals one close paren or equals open paren zero for j s k is an element of cap r subscript j s r subsubscript two and cap u subscript j s k equals two close paren or equals open paren one point five times STU underscore BWT subscript j s k for j s k is an element of cap r subscript j s r subsubscript two and cap u subscript j s k equals three close paren or equals STU underscore BWT subscript j s k if j s k is not an element of cap r subscript j s r subsubscript two

where

STU_BWT_jsk is the full-sample student base weight for student k in certainty school s in stratum j,
R_jsr1 is the set of students within the r₁-th replicate stratum for certainty school s in stratum j,
R_jsr2 is the set of students within the r₂-th replicate stratum for certainty school s in stratum j, and
U_jsk is the variance unit (1, 2 or 3) for student k in certainty school s in stratum j.

For students in noncertainty schools, where replicate strata were formed at the school-level, the student base weight for student k from school s in stratum j for each of the 62 replicates STU_BWT_jsk (r), r = 1,..., 62, were calculated as follows:

STU underscore BWT subscript j s k open paren r close paren equals SCH underscore BWT subscript j s open paren r close paren times SCHSESWT subscript j s times WINSCHWT subscript j s times STUSESWT subscript j s k times SUBJFAC subscript j s k times SUBADJ subscript j s times YRRND underscore AF subscript j s

where

SCH_BWT_js(r) is the replicate school base weight;
SCHSESWT_js is the school-level session assignment weight used in the full-sample weight;
WINSCHWT_js is the within-school student sampling weight used in the full-sample weight;
STUSESWT_jsk is the student-level session assignment weight used in the full-sample weight;
SUBJFAC_jsk is the subject factor used in the full-sample weight;
SUBADJ_js is the substitute adjustment factor used in the full-sample weight; and
YRRND_AF_js is the year-round adjustment factor used in the full-sample weight.

Last updated 09 October 2014 (GF)

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