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NAEP Weighting Procedures → 2002 Weighting Procedures and Variance Estimation → State Assessment Weights → Poststratification of Student Weights

NAEP Technical DocumentationPoststratification 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 A_h, 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:

where

• the students who did the reading assessment are indicated as A_h^(re);
• the students who did the writing assessment are indicated as A_h^(wr); and
• the excluded students are indicated as A_h^(ex).

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

where

• the control total for poststratification cell h is A_h;
• the subject assessment adjustment is SUBJADJ_sk;
• the student base weight is STUWGT_sk;
• the student nonresponse adjustment is STNRADJ_d; and
• the student trimming adjustment is TRIM_sk

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 (SUBJADJ_sk equal to 1 rather than 2). Note also that excluded students do not have a student nonresponse adjustment.

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

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:

                                         

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.

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