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NAEP Assessment Sample Design → NAEP 2004 Long-Term Trend Sample Design → Sampling of Schools and Students → Long-Term Trend School Sample Selection → Long-Term Trend School Sample Measures of Size → Long-Term Trend Age Distribution Fractions → Long-Term Trend Age Distribution Fractions for Ages 9 and 13

NAEP Technical DocumentationLong-Term Trend Age Distribution Fractions for the Age 9 and 13 Studies

The computation of the age distribution fractions for the age 9 and age 13 studies starts with estimates derived from the NAEP 2002 reading and writing operational studies. For grades 4 and 8, estimates of the percentages of students who were born in the years 1988, 1989, 1990, etc., were computed separately for public and private schools, by NAEP region. These estimates were computed by first computing the weighted percentages of assessed and excluded students for the NAEP 2002 reading operational study, and the weighted percentages of assessed and excluded students for the NAEP 2002 writing operational study. 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 2001–02.

Next, the weighted percentages from the reading operational study and writing operational study were averaged, generating a composite estimator for each birth-year for fourth (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 for the eight school-type/NAEP region student groups for fourth grade.

Weighted percentages from the NAEP Grade 4 reading and writing operational studies, public schools Northeast region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentages
Total	730,900	100.00	740,500	100.00	100.00
1988	700	0.1	1,100	0.2	0.1
1989	830	0.1	770	0.1	0.1
1990	14,000	1.9	14,700	2.0	2.0
1991	202,200	27.7	202,900	27.4	27.5
1992	509,900	69.8	518,700	70.1	69.9
1993	3,100	0.4	2,200	0.3	0.4
1994	100	0.0	50	0.0	0.0
1995	70	0.0	100	0.0	0.0
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2002.

Weighted percentages from the NAEP Grade 4 reading and writing operational studies, public schools Southeast region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentages
Total	850,200	100.00	949,500	100.00	100.00
1988	380	0.0	280	0.0	0.0
1989	4,000	0.5	4,300	0.5	0.5
1990	47,400	5.6	65,800	6.9	6.3
1991	336,800	39.6	410,600	43.3	41.4
1992	459,000	54.0	464,200	48.9	51.4
1993	2,100	0.3	3,900	0.4	0.3
1994	330	0.0	240	0.0	0.0
1995	160	0.0	70	0.0	0.0
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

Weighted percentages from the NAEP Grade 4 reading and writing operational studies, public schools Central region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentages
Total	791,000	100.00	811,000	100.00	100.00
1988	40	0.0	20	0.0	0.0
1989	990	0.1	1,400	0.2	0.2
1990	20,500	2.6	24,600	3.0	2.8
1991	334,800	42.3	346,600	42.7	42.5
1992	432,600	54.7	436,500	53.8	54.3
1993	2,000	0.3	1,600	0.2	0.2
1994	150	0.0	240	0.0	0.0
1995	3	0.0	0	0.0	0.0
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

Weighted percentages from the NAEP Grade 4 reading and writing operational studies, public schools West region by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentages
Total	1,130,200	100.00	1,151,900	100.00	100.00
1988	120	0.0	30	0.0	0.0
1989	710	0.1	1,100	0.1	0.1
1990	22,000	2.0	22,000	1.9	1.9
1991	363,900	32.2	373,500	32.4	32.3
1992	740,000	65.5	752,200	65.3	65.4
1993	3,000	0.3	2,700	0.2	0.3
1994	220	0.0	380	0.0	0.0
1995	210	0.0	10	0.0	0.0
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

Weighted percentages from the NAEP Grade 4 and writing operational studies, private schools Northeast region by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentages
Total	100,300	100.00	105,800	100.00	100.00
1989	190	0.2	60	0.1	0.1
1990	660	0.7	1,100	1.0	0.9
1991	23,700	23.6	25,900	24.5	24.1
1992	74,100	73.9	76,900	72.7	73.3
1993	1,600	1.6	1,800	1.7	1.7
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

Weighted percentages from the NAEP Grade 4 reading and writing operational studies, private schools Southeast region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentages
Total	64,600	100.00	68,600	100.00	100.00
1989	0	0.0	330	0.5	0.2
1990	460	0.7	1,000	1.5	1.1
1991	26,000	40.3	24,600	35.9	38.1
1992	37,800	58.6	42,200	61.5	60.1
1993	220	0.3	450	0.7	0.5
1994	50	0.1	0	0.0	0.0
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

Weighted percentages from the NAEP Grade 4 reading and writing operational studies, private schools Central region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentages
Total	107,300	100.00	112,400	100.00	100.00
1989	210	0.2	20	0.0	0.1
1990	460	0.4	1,100	1.0	0.7
1991	45,600	42.5	46,000	40.9	41.7
1992	60,600	56.5	64,600	57.5	57.0
1993	370	0.4	730	0.7	0.5
1995	0	0.0	20	0.0	0.0
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

Weighted percentages from the NAEP Grade 4 reading and writing operational studies, private schools West region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentages
Total	91,800	100.00	95,800	100.00	100.00
1990	650	0.7	650	0.7	0.7
1991	29,300	31.9	31,000	32.4	32.1
1992	60,700	66.2	63,100	65.9	66.0
1993	1,000	1.1	940	1.0	1.1
1994	0	0.0	80	0.1	0.0
1995	60	0.1	0	0.0	0.0
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

The composite percentages are the best estimates of the percentages of fourth-graders in school year 2001–02 who were born in 1989, 1990, 1991, etc. The objective is to get the percentages of those born in a particular year (e.g., 1992) who are in second grade, third grade, fourth grade, and fifth grade. 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 NAEP Northeast region in the table below.

Age and grade distribution for public schools, Northeast region, 2001-02 school year, assuming stationarity, by year of birth: 2002

Year of birth	Second Grade	Third Grade	Fourth Grade	Fifth Grade	Sixth Grade
Total	100.00	100.00	100.00	100.00	100.00
1986	0.00	0.00	0.00	0.00	0.10
1987	0.00	0.00	0.00	0.10	0.10
1988	0.00	0.00	0.10	0.10	1.90
1989	0.00	0.10	0.10	1.90	27.50
1990	0.10	0.10	1.90	27.50	69.90
1991	0.10	1.90	27.50	69.90	0.40
1992	1.90	27.50	69.90	0.40	0.01
1993	27.50	69.90	0.40	0.01	0.01
1994	69.90	0.40	0.01	0.01	0.00
1995	0.40	0.01	0.01	0.00	0.00
1996	0.01	0.01	0.00	0.00	0.00
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

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 1992, we see that the percentages for second through sixth grade are equal to the percentages for 1990 through 1994 for fourth grade. The same logic was applied to all eight tables given above, yielding the percentages found in School Measures of Size for grade distribution for youths born January 1994 through December 1994 (who will be nine-years old on January 1, 2004: the 2003–04 school year¹).

A similar logic applied to the Age 13 sample. For the Age 13 long-term trend sample, the starting point was the NAEP 2002 Grade 8 reading and writing operational studies. Composite estimates were computed in the same way as for the Age 9 sample. The eight tables below provide these estimates by NAEP region.

Weighted percentages from the NAEP Grade 8 reading and writing operational studies, public schools Northeast region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentage
Total	713,500	100.0	718,000	100.0	100.0
1984	420	0.1	120	0.0	0.0
1985	1,400	0.2	1,300	0.2	0.2
1986	16,500	2.3	20,100	2.8	2.6
1987	193,300	27.1	210,100	29.3	28.2
1988	495,200	69.4	481,800	67.1	68.3
1989	6,700	0.9	4,400	0.6	0.8
1990	40	0.0	70	0.0	0.0
1991	0	0.0	20	0.0	0.0
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004 Long-Term Trend Assessment.

Weighted percentages from the NAEP Grade 8 reading and writing operational studies, public schools Southeast region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentage
Total	810,800	100.0	823,700	100.0	100.0
1984	430	0.1	390	0.1	0.1
1985	5,100	0.6	5,600	0.7	0.7
1986	47,300	5.8	52,800	6.4	6.1
1987	307,300	37.9	309,100	37.5	37.7
1988	446,600	55.1	451,600	54.8	55.0
1989	3,600	0.5	3,700	0.5	0.5
1990	260	0.0	130	0.0	0.0
1991	310	0.0	260	0.0	0.0
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004 Long-Term Trend Assessment.

Weighted percentages from the NAEP Grade 8 reading and writing operational studies, public schools Central region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentage
Total	853,700	100.0	860,100	100.0	100.0
1985	860	0.1	1,000	0.1	0.1
1986	27,900	3.3	24,500	2.9	3.1
1987	365,600	42.8	373,600	43.4	43.1
1988	456,900	53.5	459,100	53.4	53.5
1989	2,300	0.3	1,800	0.2	0.2
1990	170	0.0	90	0.0	0.0
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004 Long-Term Trend Assessment.

Weighted percentages from the NAEP Grade 8 reading and writing operational studies, public schools West region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentage
Total	1,055,000	100.0	1,058,000	100.0	100.0
1984	20	0.0	170	0.0	0.0
1985	2,100	0.2	1,800	0.2	0.2
1986	28,500	2.7	25,200	2.4	2.5
1987	353,200	33.5	349,800	33.1	33.3
1988	666,600	63.2	676,100	63.9	63.5
1989	4,500	0.4	4,900	0.5	0.4
1990	60	0.0	60	0.0	0.0
1991	8	0.0	0	0.0	0.0
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004 Long-Term Trend Assessment.

Weighted percentages from the NAEP Grade 8 reading and writing operational studies, private schools Northeast region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentage
Total	88,700	100.0	91,800	100.0	100.0
1986	700	0.8	1,400	1.5	1.2
1987	21,900	24.7	20,400	22.2	23.4
1988	65,400	73.7	68,800	75.0	74.3
1989	700	0.8	1,200	1.3	1.1
1990	40	0.1	0	0.0	0.0
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004 Long-Term Trend Assessment.

Weighted percentages from the NAEP Grade 8 reading and writing operational studies, private schools Southeast region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentage
Total	70,400	100.0	72,200	100.0	100.0
1985	150	0.2	40	0.1	0.1
1986	1,200	1.8	960	1.3	1.6
1987	26,800	38.1	26,200	36.3	37.2
1988	41,800	59.3	44,500	61.6	60.5
1989	410	0.6	480	0.7	0.6
1991	0	0.0	80	0.1	0.1
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004 Long-Term Trend Assessment.

Weighted percentages from NAEP Grade 8 reading and writing operational studies, private schools Central region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentage
Total	87,100	100.0	90,200	100.0	100.0
1985	0	0.0	100	0.1	0.1
1986	1,200	1.3	1,300	1.4	1.4
1987	32,800	37.7	35,600	39.5	38.6
1988	52,900	60.8	52,700	58.5	59.6
1989	190	0.2	530	0.6	0.4
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004 Long-Term Trend Assessment.

Weighted percentages from the NAEP Grade 8 reading and writing operational studies, private schools West region, by year of birth: 2002

Year of birth	Reading operational aggregate weight	Reading operational weighted percent	Writing operational aggregate weight	Writing operational weighted percent	Composite percentage
Total	76,500	100.0	79,800	100.0	100.0
1985	390	0.5	160	0.2	0.4
1986	1,500	2.0	1,200	1.5	1.8
1987	26,400	34.5	26,200	32.8	33.6
1988	47,600	62.2	51,400	64.4	63.3
1989	620	0.8	850	1.1	0.9
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004 Long-Term Trend Assessment.

¹ Note that this school year is two years later than the 2001–02 school year represented in the tables above: what was true for the 1992 birth-year group in that school year is true of the 1994 birth-year group in the 2003–04 school year.

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