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Poststratification Control Totals

To estimate the population totals for the poststratification cells, the NAEP sampling and weighting contractor obtained two sources of information:

  1. Census projections for population totals by age, race, and sex, for October of 2000. These figures were obtained from the Census website.

  2. Detailed cross tabulations by age, race, grade, and Census region. These tabulations were obtained from the Census website from the October Current Population Survey (CPS) Educational Supplement for October 1998 and 1999.

To estimate the size of a given cohort, NAEP statisticians refined the Census projections using CPS data on percent in school, percent in each race/ethnicity by age, by grade category, and so forth. The four race/ethnicity groupings used in poststratification are as follows:

  • black non-Hispanic,

  • Hispanic,

  • other non-Hispanic,1 and

  • White non-Hispanic.

Within each of these four categories, Westat produced aggregations for the following age groups:

  • age 9 and not age 9,

  • age 13 and not age 13, and

  • age 17 or younger2 .

In this process, Census totals were written as Xij, where i = 1,…,4 and j = 1,…,5, with i corresponding to the four race/ethnicity subgroups, and j corresponding to the five age categories. The primary role of the 1998 and 1999 CPS student enrollment data was to partition these 2000 Xij totals into those enrolled in the fourth, eighth, and twelfth grades, and those not enrolled, based on an averaging of 1998 and 1999 data, as well as partition the white non-Hispanic population into Census regions. The implicit assumption was that the relevant proportions were the same in 2000 as in 1998 and 1999. Westat combined two years (1998 and 1999) to reduce 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).

Xijk is the estimated number of enrolled students for the fourth (eighth, twelfth) grade within cell ij (i.e., the subset of Xij which consists of enrolled students).

Y hat superscript open paren t closed paren sub i jCPS total population within the ijth cell for year t (1998 or 1999)
Y hat superscript open paren t closed paren sub i j k= CPS total enrolled students within the ijkth cell for year t (1998 or 1999)2

These were obtained from the Census website's CPS tabulations. Westat computed the estimated proportion of enrolled students in cell ij (in the Census region also, for White non-Hispanics) from the estimates as follows:

pi hat sub i j k equals open paren summation over t from 1998 to 1999 of Y hat superscript open paren t closed paren sub i j k closed paren divided by summation over t from 1998 to 1999 of Y hat superscript open paren t closed paren sub i j

The poststratification control totals were calculated then as:

X hat sub i j k equals X sub i j times pi hat sub i j k

1 Other non-Hispanic classifications include American Indian, Eskimo, and Aleut non-Hispanic, and Asian and Pacific Islander non-Hispanic.

2 Westat only poststratifies the sampled twelfth-graders who were 17 or younger to the corresponding CPS control totals (with the older twelfth-graders not included in computing the adjustment). The CPS totals for 'twelfth-graders' who are 18 or older includes adults who are working on receiving a high-school diploma equivalent, which would not be an appropriate control total in this context. The older twelfth-graders receive the poststratification adjustment from the younger twelfth-graders in the final calculation of their weights.

Last updated 07 July 2008 (EH)

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