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Poststratification of Student Weights

Poststratification is a weighting procedure that adjusts the weights of respondents to independent estimates of the population distribution. That is, the sums of the poststratification-adjusted weights of the respondents are equal to independent population estimates, whether for the total population or for subgroups of the population. The main purposes of poststratification are to improve the precision of survey estimates by reducing their mean square error and to enhance the comparability of survey data with other surveys, particularly when comparing estimates from the same survey over time. National NAEP utilized seven primary control cells, as follows:

  • Black non-Hispanic students;
  • Hispanic students;
  • Other race non-Hispanic students;
  • White non-Hispanic students in the Northeast Census region;
  • White non-Hispanic students in the Midwest Census region;
  • White non-Hispanic students in the Southeast Census region; and
  • White non-Hispanic students in the West Census region.

For fourth- and eighth-grade students, these seven cells were partitioned into 14 control cells h = 1,..,14, by modal-age and non modal-age students. Modal-age fourth grade students are those who were 9 years old on October 1, 20011 and the modal-age eighth grade students are those who were 13 years old on October 1, 2001.2

Twelfth-grade students had only seven control cells h = 1,..,7, which include the "younger" students only (those who were not 18 or older as of October 1, 2001).3 The complement set are not placed in any control cell, because many of the "twelfth-graders" included in the Census Bureau’s Current Population Survey (CPS) control totals were persons actually working on a high school equivalency degree, so that the CPS control set and the sampled set do not refer to the same population. These twelfth-graders received the poststratification adjustment of the younger students with the same race/region code.

The control totals for poststratification, designated as Ah, are Census-derived estimates of the total number of enrolled students in the student group.

Poststratification is done separately for the operational reading assessment students and the operational writing assessment students. In other words, both the students who did the reading assessment and the students who did the writing assessment are weighted to represent the full population.4 The subject assessment adjustment for each student is:

SUBJADJ subscript s k equals left open bracket 2 if s k is a member of A subscript h superscript left parenthesis r e right parenthesis or 2 if s k is a member of A subscript h superscript left parenthesis w r right parenthesis or 1 if s k is a member of A subscript h superscript left parenthesis e x right parenthesis

where

  • the students who did the reading assessment are indicated as Ah(re);

  • the students who did a writing assessment are indicated as Ah(wr); and

  • the excluded students are indicated as Ah(ex).

The poststratification factors PSFACh(re) and PSFACh(wr) for each cell for the reading assessment and writing assessment students, respectively, are:

PSFAC subscript h superscript left parenthesis r e right parenthesis equals A subscript h divided by left bracket the summation over s k which are members of A subscript h superscript left parenthesis r e right parenthesis of SUBJADJ subscript s k times STUWGT subscript s k times STNRADJ subscript d times TRIM subscript s k plus the summation of s k that are members of A subscript h superscript left parenthesis e x right parenthesis of SUBJADJ subscript s k times STUWGT subscript s k times TRIM subscript s k right bracket

PSFAC subscript h superscript left parenthesis w r right parenthesis equals A subscript h divided by left bracket the summation over s k which are members of A subscript h superscript left parenthesis w r right parenthesis of SUBJADJ subscript s k times STUWGT subscript s k times STNRADJ subscript d times TRIM subscript s k plus the summation of s k that are members of A subscript h superscript left parenthesis e x right parenthesis of SUBJADJ subscript s k times STUWGT subscript s k times TRIM subscript s k right bracket

where

  • the control total for poststratification cell h is Ah;
  • the subject assessment adjustment is SUBJADJsk;
  • the student base weight is STUWGTsk ;
  • the student nonresponse adjustment is STNRADJd;and
  • the student trimming adjustment is TRIMsk.

These poststratification factor calculations include all public and private school students. For fourth and eighth grades, they include all students in participating jurisdiction schools. Note that the poststratification factors used for the state assessment sample and the national sample are the same for fourth and eighth grades. Excluded students are included in both denominators, with a half weighting factor (SUBADJsk equal to 1 rather than 2), and do not have a student nonresponse adjustment.

The final student weights Wsk are equal to the following for operational reading assessment and operational writing assessment students, respectively:

For s k that are members of A subscript h superscript left parenthesis  re right parenthesis colon W subscript s k equals STUWGT subscript s k times STNRADJ subscript d times TRIM subscript s k times SUBJADJ subscript s k times PSFAC subscript h superscript left parenthesis r e right parenthesis

For s k that are members of A subscript h superscript left parenthesis w r right parenthesis colon W subscript s k equals STUWGT subscript s k times STNRADJ subscript d times TRIM subscript s k times SUBJADJ subscript s k times PSFAC subscript h superscript left parenthesis w r right parenthesis

For the twelfth-grade students, a student in the twelfth-grade complement set (18 years or older on October 1, 2001) receives the poststratification adjustment for cell h as defined by their race/ethnicity and region, even though these students were not included in the computation of the factor. For excluded students, the final weights are different depending on whether the record for the excluded student is on the operational reading assessment file or on the operational writing assessment file. The excluded student weights can be written as:

For s k that are members of A subscript h superscript left parenthesis e x right parenthesis colon W subscript s k equals STUWGT subscript s k times TRIM subscript s k times SUBJADJ subscript s k times PSFAC subscript h superscript left parenthesis o right parenthesis

where the "o" superscript for PSFAC is equal to "re" for the reading assessment file and equal to "wr" for the writing assessment file.

1 Students with birth months from October 1991 to September 1992.
2 Students with birth months from October 1987 to September 1988.
3 Students with birth months October 1983 or later.
4 With ineligible students included in both student sets.


Last updated 25 February 2009 (RF)

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National Center for Education Statistics - http://nces.ed.gov
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