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

NAEP Technical DocumentationPoststratification Control Totals

Two sources of information were used to estimate the population totals for the NAEP poststratification cells:

• Census projections of population totals by age, race/ethnicity,
  and gender, for the fourth quarter of 2001.¹ These figures were obtained from the Census website.
  

• Detailed cross tabulations by age, race/ethnicity, grade, and Census Region. These tabulations were obtained from the Census website from the October Current Population Survey (CPS) Educational Supplements for October 1999 and 2000.

To estimate the size of a given cohort, the Census projections served as a starting point for refining the data using CPS data on percent in school and percent in each race/ethnicity by age and grade category. The four race/ethnicity groupings used in poststratification are as follows:

• Black non-Hispanic students;
• Hispanic students;
• other non-Hispanic students;² and
• White non-Hispanic students.

Each of these four categories were aggregated for the following age groups:

• age 9 and not age 9;
• age 13 and not age 13; and
• age 17 and not age 17.

The data listed above can be shown as X_ij, where i = 1,..,4 and j = 1,..,6, with i corresponding to the four race/ethnicity subgroups, and j corresponding to the six age categories (two age categories for each table). The primary role of the CPS student enrollment data was to partition these 2001 X_ij totals into those enrolled in the fourth, eighth, and twelfth grades, and those not enrolled, based on an averaging of 1999 and 2000 data, as well as partition the white non-Hispanic population by Census region³. The implicit assumption is that the relevant proportions are the same in 2001 as in 1999 and 2000. Combining the years 1999 and 2000 reduced the sampling variability inherent in the CPS values (i.e., trading off some bias from using the earlier year to gain greater stability by averaging across two years).

With X_ijk as the estimated number of enrolled students for the fourth (eighth, twelfth) grade within cell ij (i.e., the subset of X_ij which consists of enrolled students),

= CPS total population within the ij-th cell for year t (1999 or 2000).

= CPS total enrolled students within the ij-th cell for year t (1999 or 2000).

These were obtained from the CPS tabulations obtained from the Census website. The estimated proportion of enrolled students in cell ij (in the Census region also, for White non-Hispanic students) is derived as follows:

The poststratification control totals were calculated as:

Further details can be found in Westat (2002).

¹ These were projections for 2001 through 2010. In past NAEP assessments, monthly population estimates were used (rather than quarterly projections.) For the 2002 assessment, the monthly population estimates were not yet available, and when they were to become available they would be utilizing the new race/ethnicity definitions; therefore, NAEP opted to use the quarterly projections instead.
² In the 2002 assessment, the "other non-Hispanic students" category included American Indian, Eskimo, and Aleut non-Hispanic, and Asian and Pacific Islander non-Hispanic students.
³There are a total of 42 cells: seven cells (1-Black non-Hispanic, 2-Hispanic, 3-other non-Hispanic, 4-White non-Hispanic Northeast region, 5-White non-Hispanic South region, 6-White non-Hispanic Central region, 7-White non-Hispanic West region) crossed by six age cells.

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