Selecting the Sample for the Mathematics AssessmentSamples for Grades 4 and 8The national results presented for grades 4 and 8 are based on nationally representative probability samples of students. The NAEP national sample was obtained by aggregating the samples of public school students from each jurisdiction participating in the state assessments, and then supplementing the aggregate sample with a nationally representative sample of students from nonpublic schools. This integrated sample design has been used in NAEP assessments since 2002. Prior to 2002, separate samples were drawn for the NAEP national and state assessments. Beginning in 2002, the NAEP national sample was obtained by aggregating the samples from each state, rather than by obtaining an independently selected national sample. As a result, the size of the national sample increased, and smaller differences between years or between types of students were found to be statistically significant than would have been detected in assessments before 2002. Prior to 2005, Department of Defense Education Activity (DoDEA) overseas and domestic schools were reported separately. In the 2005 assessments, all DoDEA schools, both domestic and international, were combined as one jurisdiction. Data shown for years prior to 2005 for DoDEA were recalculated to combine the domestic and international results to make them comparable to those for 2005. In addition, the definition of the national sample changed in 2005; it now includes all of the international DoDEA schools. Sample for Grade 12The 2005 national results presented for grade 12 are based on a nationally representative probability sample that was chosen using a complex multistage design that involved sampling students for selected schools within selected geographic areas across the country. The sample design had the following stages:
WeightingEach selected school that participated in the assessment and each student assessed represents a portion of the population of interest. Sampling weights are needed to make valid inferences from the student samples to the representative populations from which they were drawn. Sampling weights account for disproportionate representation of students from different states and for students who attend nonpublic schools. Sampling weights also account for lower sampling rates for very small schools and are used to adjust for school and student nonresponse. AccommodationsAccommodations for students with disabilities (SD) and English language learners (ELL) have been permitted for a representative sample of students beginning with the 1996 mathematics assessment. (English language learners were previously referred to as limited English proficient (LEP).) View a summary of the national and state sample sizes and target populations for grades 4 and 8. View a summary of the district sample sizes and target populations for grades 4 and 8. View a summary of the national, state, and district school and student participation rates for the NAEP 2007 mathematics assessment.
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