NAEP Technical DocumentationAge Distribution Fractions for Ages 9 and 13

The computation of the age distribution fractions for the age 9 and age 13 assessments starts with estimates derived from the NAEP 2005 reading and mathematics assessments. For grades 4 and 8, estimates of the percentages of students who were born in the years 1991, 1992, 1993, etc., were computed separately for public and private schools by Census region.

These estimates were determined by first computing the weighted percentages of assessed and excluded students for the NAEP 2005 reading and mathematics assessments. The nonresponse-adjusted trimmed final weights for the students, not including the poststratification adjustment, were used for this purpose. The weighted aggregations are estimates of the total number of students in each birth-year group for grade 4 or grade 8 in the school year 2004-05.

Next, the weighted percentages from the reading and mathematics assessments were averaged, generating a composite estimator for each birth-year for fourth- and eighth-graders. As the two operational studies produce unbiased estimators with approximately the same variance, the composite estimators of the totals also will be unbiased and with a lower variance. The tables below present these estimates by Census region for fourth grade, first for public schools and then for private schools.

The composite percentages are the best estimates of the percentages of fourth-graders in school year 2004-05 who were born in 1991, 1992, 1993, etc. The objective is to get the percentages of those born in a particular year (e.g., 1995) who are in grades 2, 3, 4, and 5. Since direct estimates are not available, an indirect estimate can be obtained by assuming that the other grades have the identical distribution as fourth grade, but moved back or moved forward by 1 year. This effectively assumes a stationary distribution of age and grade, which is only a rough approximation of reality, but it suffices to give good measures of size. The derived percentages by age and grade using this stationarity approximation are illustrated for the northeast Census region in the table below.

In distribution, the third-graders are exactly 1 year younger, the second-graders exactly 2 years younger, etc. If we read across the grade distribution for those born in 1995, we see that the percentages for second through sixth grades are equal to the percentages for 1993 through 1997 for fourth grade. The same logic was applied to all eight tables provided above, yielding the percentages found in the sampling of public schools and private schools for grade distribution for youths born January 1998 through December 1998 (who were nine-years-old on January 1, 2008: the 2007-08 school year).

A similar logic applied to the age 13 sample. For the age 13 long-term trend sample, the starting point was the NAEP 2005 grade 8 reading and mathematics assessments. Composite estimates were computed in the same way as for the age 9 sample. The eight tables below provide these estimates by Census region.

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