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Poststratification of Student Weights

          

Poststratification Control Totals

Poststratification is a weighting procedure that adjusts the weights of respondents to reflect some known independent population distribution. That is, the poststratified-adjusted weights of the respondents sum to known population totals for certain student groups of the population, called control cells. Poststratification improves the precision of survey estimates by reducing their mean square error and enhances the comparability of survey data with other surveys, particularly when comparing estimates from the same survey over time. There were seven primary control cells, consisting of the number of enrolled students, 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.

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

The control totals for poststratification, designated as Ah, are Census-based 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 participated in the reading assessment and the students who participated in the writing assessment are weighted to represent the full population.3 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 the 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 private school students and nonparticipating jurisdiction school students with their prepoststratification weights. The control totals are for all students in public and private schools, in all jurisdictions. Excluded students are included in both denominators, with a half weighting factor (SUBJADJsk equal to 1 rather than 2). Note also that excluded students 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 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 With ineligible students included in both student sets.


Last updated 06 November 2008 (RF)

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