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Trimming of Student Weights for the Main Study

The nonresponse-adjusted student weights are designed to give unbiased estimates, taking into account school sampling, school nonresponse, student sampling, and student nonresponse. Student weights that are much larger than the median weight for a particular sample will generate higher variance (see, for example, Kish [1992]). The general procedure in the 2002 national assessment is to trim any weights that are greater than 4.5 times the median weight value. Although introducing some bias, the trade-off is towards lower overall mean square error given the reduction in variance.

For the fourth- and eighth-grade national public school sample (i.e., in those jurisdictions that did not participate in the State assessment), the trimming groups are the NAEP regions within each session ("B", "C", or "D"). (See NAEP 2002 Sample Design for a description of the sessions.) For twelfth-grade public schools, the trimming groups within each session ("A" or "C") are students in high minority stratum schools,1 Black or Hispanic students from low minority schools, and other students from low minority schools. This classification was utilized because of the varying sampling factors for schools and students between the two high-minority strata, and by race/ethnicity. For private schools, the trimming groups are based on the private school stratum within each session ("A", "B", "C", or "D").

The procedure computes the median of the nonresponse-adjusted student weights in the trimming group g. Any weight greater than 4.5 times the median receives a trimming factor:

TRIM subscript s k equals open left bracket 4.5 times M subscript g divided by STUWGT subscript s k times STNRADJ subscript d if STUWGT subscript s k times STNRADJ subscript d is greater than 4.5 times M subscript g or 1 if otherwise

where

  • Mg is the median of the nonresponse-adjusted student weights in trimming group g;

  • STUWGTsk is the student base weight for student k in school s; and

  • STNRADJd is the student nonresponse adjustment for adjustment cell d.

Ineligible students are not included in the calculation of a median.

1 Schools with 15 percent or more Black and Hispanic students. These were a part of the stratification for twelfth-grade public schools.


Last updated 06 November 2008 (RF)

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