Large student weights generally result from compounding nonresponse adjustments at the school and student levels with artificially low first-stage selection probabilities, which result at times from inaccurate enrollment data on the school frame used to define the school size measure. Even though measures are in place to limit the number and size of excessively large weights—such as the implementation of adjustment factor size constraints in both the school and student nonresponse procedures and the use of the school trimming procedure—large student weights can occur due to compounding effects of the various weighting components.
The student weight trimming procedure uses the multiple median rule to detect excessively large student weights. Any student weight within a given trimming group greater than a specified threshold (defined as a multiple of the median weight value of the given trimming group) has its weight scaled back to that threshold. The multiples used were 3.5 for public school trimming groups and 4.5 for private school trimming groups. Trimming groups were defined by assessment type (operational or bridge), age group (9, 13, or 17), and NAEP region for public schools; and by assessment type, age group, and private school type (Catholic, Lutheran, conservative Christian, and other private schools) for private schools.
The procedure computes the median of the nonresponse-adjusted student weights in the trimming group g. Any student k with a weight more than M times the median (where M = 3.5 for public school and 4.5 for private school trimming groups) received a trimming factor calculated as follows:
M is the trimming multiple,
MEDIANj(g) is the median of nonresponse-adjusted student weights in trimming group g, and
STUWGTjk is the weight after student nonresponse adjustment for student k in jurisdiction j.
The student trimming factor does not include a subscript s to reflect the fact that not every student in school s falls into the same trimming group.
It should be noted that excluded students are not factored into the calculation of the median, but are still eligible for student weight trimming. Using excluded students in the median calculation would lower trimming thresholds since excluded students do not experience student nonresponse and, thus, generally have smaller weights than assessed students. However, it is plausible for excluded students to have excessively large weights due to the compounding of the other weighting components.
In the 2004 assessment, relatively few students had weights considered excessively large. Out of 26,020 students included in the combined 2004 assessment samples, 40 students required student weight trimming.