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Computing School-Level Replicate Base Weights for the 2007 Assessment

The calculation of school-level replicate base weights varied by whether a school was selected with certainty or not since replicates were formed using first-stage sample units. In certainty schools, where replicates were formed at the student-level, the school base weight for each of the 62 replicates (r = 1, ..., 62) was set equal to the full-sample school base weight. That is,

SCH_BWTjs(r) = SCH_BWTjs

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

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

where

  • SCH_BWTjs is the school base weight for school s in primary stratum j,

  • Rjr is the set of schools within the r-th replicate stratum for primary stratum j, and

  • Ujs is the variance unit (1 or 2) for school s in primary stratum j.

For schools in replicate strata comprising three schools, two sets of school-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 school-level replicate base weights SCH_BWTjs(r1), r1 = 1,..., 62 and SCH_BWTjs(r2), r2 = 1,..., 62 were calculated as described below.                          

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

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

where

  • SCH_BWTjs is the school base weight for school s in primary stratum j,

  • cap r subscript j r subscript 1 is the set of schools within the r1-th replicate stratum for primary stratum j,

  • cap r subscript j r subscript 2  is the set of schools within the r2-th replicate stratum for primary stratum j, and

  • Ujs is the variance unit (1, 2 or 3) for school s in primary stratum j.

In primary strata with fewer than 62 replicate strata, the replicate weights for the “unused” replicate strata (the remaining ones up to 62) for these schools were set equal to the school base weight (so that those replicates contribute nothing to the variance estimate).


Last updated 26 April 2010 (GF)

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National Center for Education Statistics - http://nces.ed.gov
U.S. Department of Education