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NAEP Technical DocumentationAge Distribution Fractions for the 2020 Private School Long-Term Trend Assessment
Age distribution fractions are estimated proportions of students in each grade that are age-eligible for sampling. The fractions are components in the school measure of size. For ages 9 and 13, a breakout by every year of birth cohort represented in the relevant grades was fully carried out. The computation of the age distribution fractions for the age 9 and age 13 assessments starts with estimates derived from the NAEP 2017 reading and mathematics assessments. For grades 4 and 8, estimates of the percentages of students by year of birth were computed separately for public and private schools by census region.
These estimates were determined by first computing the weighted percentages of assessed, absent, and excluded students for the NAEP 2017 reading and mathematics assessments and then aggregating them. The student base weights were used for this purpose. The weighted aggregations are estimates of the total number of students by year of birth for grade 4 or grade 8 in the school year 2016-17. The tables below present these estimates by region for fourth grade for private schools.
| Year of birth | Weighted aggregations | Weighted proportions |
|---|---|---|
| Total | 59,000 | 1.00 |
| 2003 | 33 | # |
| 2004 | 33 | # |
| 2005 | 293 | # |
| 2006 | 16,000 | 0.26 |
| 2007 | 43,000 | 0.73 |
| 2008 | 335 | 0.01 |
| 2009 | 100 | # |
| # Rounds to zero. NOTE: Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2020 Long-Term Trend Assessment. | ||
| Year of birth | Weighted aggregations | Weighted proportions |
|---|---|---|
| Total | 85,000 | 1.00 |
| 2005 | 785 | 0.01 |
| 2006 | 37,000 | 0.43 |
| 2007 | 48,000 | 0.56 |
| 2008 | 192 | # |
| # Rounds to zero. NOTE: Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2020 Long-Term Trend Assessment. | ||
| Year of birth | Weighted aggregations | Weighted proportions |
|---|---|---|
| Total | 108,000 | 1.00 |
| 2005 | 2,000 | 0.02 |
| 2006 | 42,000 | 0.39 |
| 2007 | 63,000 | 0.58 |
| 2008 | 524 | # |
| # Rounds to zero. NOTE: Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2020 Long-Term Trend Assessment. | ||
| Year of birth | Weighted aggregations | Weighted proportions |
|---|---|---|
| Total | 60,000 | 1.00 |
| 2005 | 640 | 0.01 |
| 2006 | 20,000 | 0.34 |
| 2007 | 39,000 | 0.65 |
| 2008 | 263 | # |
| # Rounds to zero. NOTE: Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2020 Long-Term Trend Assessment. | ||
The combined percentages of the reading and mathematics assessments are the best estimates of the percentages of fourth-graders in school year 2016-17 by year of birth. The objective is to get the percentages of those born in a particular year (e.g., 2007) 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 region in the table below.
| Year of birth | Second grade | Third grade | Fourth grade | Fifth grade | Sixth grade |
|---|---|---|---|---|---|
| Total | 1.00 | 1.00 | 1.00 | 1.00 | 1.00 |
| 2003 | # | # | # | # | # |
| 2004 | # | # | # | # | 0.26 |
| 2005 | # | # | # | 0.26 | 0.73 |
| 2006 | # | # | 0.26 | 0.73 | 0.01 |
| 2007 | # | 0.26 | 0.73 | 0.01 | # |
| 2008 | 0.26 | 0.73 | 0.01 | # | # |
| 2009 | 0.73 | 0.01 | # | # | # |
| # Rounds to zero. NOTE: Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2020 Long-Term Trend Assessment. | |||||
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 2007, we see that the percentages for second through sixth grades are equal to the percentages for 2005 through 2009 for fourth grade. The same logic was applied to all four tables provided above, yielding estimates of the percentages of nine year olds by grade that were used to compute school measures of size during the sampling of private schools.
A similar logic applied to the age 13 sample. For the age 13 sample, the starting point was the NAEP 2017 grade 8 reading and mathematics assessments. Aggregated estimates were computed in the same way as for the age 9 sample. The four tables below provide these estimates by region for eighth grade for private schools.
| Year of birth | Weighted aggregations | Weighted proportions |
|---|---|---|
| Total | 63,000 | 1.00 |
| 2000 | 156 | # |
| 2001 | 621 | 0.01 |
| 2002 | 19,000 | 0.31 |
| 2003 | 42,000 | 0.67 |
| 2004 | 675 | 0.01 |
| # Rounds to zero. NOTE: Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2020 Long-Term Trend Assessment. | ||
| Year of birth | Weighted aggregations | Weighted proportions |
|---|---|---|
| Total | 78,000 | 1.00 |
| 2001 | 992 | 0.01 |
| 2002 | 31,000 | 0.40 |
| 2003 | 45,000 | 0.58 |
| 2004 | 173 | # |
| # Rounds to zero. NOTE: Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2020 Long-Term Trend Assessment. | ||
| Year of birth | Weighted aggregations | Weighted proportions |
|---|---|---|
| Total | 111,000 | 1.00 |
| 2000 | 75 | # |
| 2001 | 2,000 | 0.02 |
| 2002 | 46,000 | 0.41 |
| 2003 | 63,000 | 0.57 |
| 2004 | 418 | # |
| # Rounds to zero. NOTE: Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2020 Long-Term Trend Assessment. | ||
| Year of birth | Weighted aggregations | Weighted proportions |
|---|---|---|
| Total | 52,000 | 1.00 |
| 2000 | 29 | # |
| 2001 | 503 | 0.01 |
| 2002 | 15,000 | 0.28 |
| 2003 | 37,000 | 0.70 |
| 2004 | 272 | 0.01 |
| # Rounds to zero. NOTE: Detail may not sum to totals because of rounding. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2020 Long-Term Trend Assessment. | ||
Last updated 07 March 2024 (SK)