Assigning Measure of Size and Selecting School Samples for the 2000 National Main Assessment

			Grade 4 and 12 Public School Samples Grade 8 Public School Samples Private School Samples

To increase cost efficiency in sampling, the 2000 national main samples were designed to include schools with a relatively high number of students and more public schools with higher percentages of minority students. A measure of size was assigned to each school based on two factors—school type (public and private) and grade:

In the table above, S_i is the estimated number of grade-eligible students in a given school i; L is the target within-school student sample size for a given grade and school type; and k_i is the i^th school's oversampling factor; where

		100,	for grade 4 and 12 public schools
L =
		60,	for grade 8 public schools and all private schools

		2,	for high-minority public schools
ki =
		1,	for low-minority schools and all private schools

This procedure was used to obtain approximately self-weighting samples of students (i.e., students selected with approximately equal overall probabilities) at each grade and school type within oversampling domains. Two aspects of the school-level measure-of-size cause the resulting student weights to vary:

• Schools with fewer than 20 estimated grade-eligible students were assigned somewhat lower measures of size and thus lower probabilities of selection. This was designed to increase cost efficiency.

• Each public school designated as high-minority was given double the measure of size of a public school not designated high minority of similar size. Such high-minority schools were oversampled to enlarge the sample of Black and Hispanic students, which enhanced the reliability of estimates for these groups.

For each grade and public/private school sample, schools were selected (without replacement) within the appropriate sample areas systematically from a sorted list with probabilities proportional to assigned measures of size. Schools were ordered to achieve an implicit stratification on school characteristics related to school achievement and to ensure that the sampled schools represented a variety of population student groups. To meet specific sample requirements, the school sampling procedures differed by

• grade 4 and 12 public schools;

• grade 8 public schools; and

• grades 4, 8, and 12 private schools.

Last updated 19 March 2008 (GF)

Printer-friendly Version