NAEP Technical DocumentationLong-Term Trend School Sample Measures of Size

			Age Distribution Fractions

For 9-year-olds, the frame contained schools in the PSUs with a second, third, fourth, or fifth grade. M_ij(2), M_ij(3), M_ij(4), and M_ij(5) denote the estimated enrollments for four grades respectively within each school j within each PSU i, and F_i(2), F_i(3), F_i(4), and F_i(5) denote the global percentage of students who were 9 years old (birth months January 1994 through December 1994) within each grade, NAEP region, and within public and private schools separately. These values are shown in the table below for public and private schools respectively. Age Distribution Fractions for Nine and Thirteen-Year Olds describes how the NAEP sample design staff computed these percentages (as well as those for 13- and 17-year-old students given below). The totals are less than 100 percent as a small number of nine-year olds are distributed outside of the grade range second through fifth.

Age distribution percentages for 9-year old students, long-term trend assessment: By school type and NAEP region, 2004
School type	NAEP region	Fi(2)	Fi(3)	Fi(4)	Fi(5)	Total
Public schools	Northeast	2.0	27.5	69.9	0.4	99.7
	Southeast	6.3	41.4	51.4	0.3	99.5
	Central	2.8	42.5	54.3	0.2	99.8
	West	1.9	32.3	65.4	0.2	99.9
Private schools	Northeast	0.9	24.0	73.3	1.7	99.9
	Southeast	1.1	38.1	60.1	0.5	99.7
	Central	0.7	41.7	57.0	0.5	99.9
	West	0.7	32.1	66.0	1.0	99.9
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.

The measure of size for the 9-year-olds component of the long-term trend study for each school was computed as follows:

For 13-year-olds, the frame contained schools in the PSUs with a fifth, sixth, seventh, or eighth grade. M_ij(6), M_ij(7), M_ij(8), and M_ij(9) denote the estimated enrollments for the four grades respectively within each school j within each PSU i, and G_i(6), G_i(7), G_i(8), and G_i(9) denote the global percentage of students who were 13 years old (birth months January 1990 through December 1990) within each grade, NAEP region, and within public and private schools separately. These values are shown in the table below for public and private schools respectively. Age Distribution Fractions for Nine and Thirteen-Year Olds describes how sample design staff computed these percentages . The totals are less than 100 percent as a small number of 13-year-olds are distributed outside of the grade range 6 through 9.

Age distribution percentages for 13-year-olds, long-term trend assessment: By school type and NAEP region, 2004
School type	NAEP region	Gi(6)	Gi(7)	Gi(8)	Gi(9)	Total
Public schools	Northeast	2.6	28.2	68.3	0.8	99.8
	Southeast	6.1	37.7	55.0	0.4	99.2
	Central	3.1	43.1	53.4	0.2	99.9
	West	2.5	33.3	63.5	0.4	99.8
Private schools	Northeast	1.2	23.4	74.3	1.1	99.9
	Southeast	1.5	37.2	60.4	0.6	99.8
	Central	1.4	38.5	59.6	0.4	99.9
	West	1.8	33.6	63.3	0.9	99.6
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.

The measure of size for the 13-year-olds component of the long-term trend study for each school was computed as follows:

For 17-year-olds, the frame contained schools in the PSUs with a ninth, tenth, eleventh, or twelfth grade. M_ij(9), M_ij(10), M_ij(11), and M_ij(12) denote the estimated enrollments for the four grades respectively within each school j within each PSU i, and J_i(9), J_i(10), J_i(11), and J_i(12) denote the global percentage of students who were 17 years old (birth months October 1986 through September 1987) within each grade and NAEP region. These values are shown in the table below for all schools, public and private, together (a breakout by public/private status was not done as for ages 9 and 13 because of the small percentage of private school students in the twelfth grade). Age Distribution Fractions for Age 17 describes how sample design staff computed these percentages . The totals are less than 100 percent as a small number of 17-year-olds are distributed outside of the grade range ninth through twelfth.

Age distribution percentages for 17-year-olds, long-term trend assessment: By school type and NAEP region, 2004
School type and NAEP region	Ji(9)	Ji(10)	Ji(11)	Ji(12)	Total
Northeast	3.9	22.6	65.4	8.0	100
Southeast	5.9	24.3	66.2	3.7	100
Central	3.7	30.6	63.7	2.0	100
West	5.4	23.1	64.7	6.7	100
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.

The measure of size for the 17-year-olds component of the long-term trend study for each school was computed as follows:

The within-school sample size for 9-year-olds and 13-year-olds for each school, y_ij, is as follows :

For 17-year-olds the within-school sample size is as follows:

The school measure of size for 9- and 13-year-olds is:

MOS subscript ij equals open left brace S subscript ij divided by 128 if 129 is less than or equal to S subscript ij or 1 if 20 less than or equal to S subscript ij less than or equal to 128 if S subscript ij divided by 20 if 6 is less than or equal to S subscript ij less than or equal to 19 or 0.25 if S subscript ij less than or equal to 5

For 17-year-olds the school measure of size is:

MOS subscript ij equals open left brace S subscript ij divided by 121 if 122 is less than or equal to S subscript ij or 1 if 20 less than or equal to S subscript ij less than or equal to 121 if S subscript ij divided by 20 if 6 is less than or equal to S subscript ij less than or equal to 19 or 0.25 if S subscript ij less than or equal to 5

The school probability of selection for all three ages is as follows:

PSCijis equal to 1, except for private schools identified in the area probability component of the Private School Survey (PSS). For these schools, PSCij is the reciprocal of the probability of selection into the PSS area probability component. Adding this component to the measure of size allows us to correctly represent the full universe of private schools in this area probability component. R is computed so that the expected yield within the sampled schools equals the overall target of sampled students in each age group. These targets and the calculated values for R are given in the table below.

Sampling targets and factors, long-term trend assessment: By school type and age, 2004
School type	Age sample	Student target	Computed factor R
Public	9-year-old	30,200	0.00822
Private	9-year-old	7,600	0.02040
Public	13-year-old	31,700	0.00872
Private	13-year-old	8,000	0.02258
Public	17-year-old	39,300	0.01216
Private	17-year-old	10,200	0.03647
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.

Last updated 22 October 2009 (GF)

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