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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:
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, 2001^{1} 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 A_{h}, 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:
where
the students who did the reading assessment are indicated as A_{h}^{(re)};
the students who did a 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
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 (SUBADJ_{sk} equal to 1 rather than 2), and 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 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:
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.