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In addition to the following questions about TIMSS, more FAQs about international assessments are available at: http://nces.ed.gov/surveys/international/faqs.asp.

How does TIMSS select a representative sample of students?

To provide valid estimates of student achievement and characteristics, TIMSS selects a random sample of students that represents the full population of students in the target grades. This population is defined internationally as the following:

Fourth-grade: all students enrolled in the grade that represents four years of formal schooling, counting from the first year of the International Standard Classification of Education (ISCED), Level 1, providing the mean age at the time of testing is at least 9.5 years. 

Eighth-grade: all students enrolled in the grade that represents eight years of formal schooling, counting from the first year of ISCED Level 1, providing the mean age at the time of testing is at least 13.5 years.

Twelfth-grade: All students in the final year of secondary schooling who are taking or have taken advanced mathematics or physics courses.

TIMSS guidelines call for a minimum of 150 schools to be sampled per grade, with a minimum of 4,000 students assessed per grade. The school response rate target is 85 percent for all countries. A minimum participation rate of 50 percent of schools from the original sample of schools is required for a country's data to be included in the international database. The response rate target for classrooms is 95 percent, and the target student response rate is set at 85 percent, from both original and substitute schools.

Countries are allowed to use substitute schools (selected during the sampling process) to increase the response rate once the 50 percent minimum participation rate of original school sampling is reached. In accordance with TIMSS guidelines, substitute schools are identified by assigning the two schools neighboring the sampled school in the frame as substitutes to be used in instances where an original sampled school refuses to participate. Substitute schools are required to be in the same implicit stratum (i.e., have similar demographic characteristics) as the sampled school.

U.S. sampling frame
The TIMSS U.S. sample is drawn from the Common Core of Data (CCD) listing of public schools supplemented with the Private School Universe Survey (PSS) listing of private schools. The combination of these national listings has proven to be close to 100 percent complete.

U.S. sampling design
The U.S. TIMSS sample uses a stratified two-stage cluster sampling design. The U.S. sampling frame, or list of schools from which the sample is selected, is both explicitly and implicitly stratified (that is, sorted for sampling).

The U.S. sampling frame is explicitly stratified by three categorical stratification variables: (1) the percentage of students eligible for free or reduced-price lunch, (2) school control (public or private), and (3) region of the country (Northeast, Central, West, Southeast).  Explicit stratification controls completely the sample size for a specific variable or variables so that the proportion of schools in the specific variable's subgroups exactly matches that of the population.

The U.S. sampling frame is implicitly stratified by two categorical stratification variables:  community type (city, suburb, town, or rural) and minority status (i.e., above or below 15 percent of the student population). Implicit stratification controls the sample size for a specific variable or variables, but it does not do so completely because it does not rely on independent random draws within each stratum, as occurs with explicit stratification.  Instead, implicit stratification entails sorting the list of all schools by the implicit stratification variable(s), and taking a systematic sample. The sample's proportion of schools in the specific variable's subgroups will then be close to that of the population. The variability of the sample sizes in the subgroups will be reduced considerably by systematic sampling, but it will not be reduced to zero as in explicit stratification.

Once the sampling frame has been stratified, the first stage of the sampling design makes use of a systematic "probabilities proportional to size" technique to select schools for the original sample that are representative of the U.S. as a whole. The second stage of the sampling design consists of selecting intact mathematics classes within each participating school. All students in sampled classrooms are selected for assessment. In this way, the overall sample design for the United States is intended to approximate a self-weighting sample of students as much as possible, with each fourth- or eighth-grade student having an equal probability of selection.

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National Center for Education Statistics - http://nces.ed.gov
U.S. Department of Education