NAEP Technical DocumentationAge Distribution Fractions for Ages 9 and 13 for the the 2012 Long-Term Trend (LTT) Assessment

The computation of the age distribution fractions for the age 9 and age 13 assessments starts with estimates derived from the NAEP 2009 reading, mathematics and science assessments. For grades 4 and 8, estimates of the percentages of students who were born in the years 1995, 1996, 1997, 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 2009 reading, mathematics and science assessments and then combined together. The nonresponse-adjusted trimmed final weights for the students 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 2008-09.The tables below present these estimates by Census region for fourth grade, first for public schools and then for private schools.

The combined percentages of the reading, mathematics and science operational assessments are the best estimates of the percentages of fourth-graders in school year 2008-09 who were born in 1995, 1996, 1997, etc. The objective is to get the percentages of those born in a particular year (e.g., 1999) 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 one 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 one year younger, the second-graders exactly two years younger, etc. If we read across the grade distribution for those born in 1999, we see that the percentages for second through sixth grades are equal to the percentages for 1997 through 2001 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 2002 through December 2002 (who were nine-years-old on January 1, 2012: the 2011-12 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 2009 grade 8 reading, mathematics and science 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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