NAEP Technical DocumentationWeighted Enrollment from the 2002 Main Study School Samples

The 2002 national main sample is a probability sample, drawn from a complete school sampling frame, with separate samples of public and private schools. The summation of the probability-weighted estimated grade enrollment aggregations (estimated grade enrollment divided by the school probability of selection) provides unbiased estimates of the corresponding frame grade enrollment figures. NAEP sampling staff compiled these aggregations for the student groups of Black, Hispanic, Asian/Pacific Islander, and American Indian students; type of location; region for public schools; and private schools as a group. (Private schools were not separated into school type groups because of the considerable number of schools both on the frame and in the sample with unknown status.) The mean across schools, weighted by enrollment, of the median household income of the area where the school is located, was also computed.

The differences between the sample totals and the frame totals were calculated and tested for statistical significance. The test is a two-sided t-test (a test on a difference of means) with an alpha level of 0.05 of the null hypothesis that the difference between sample and frame is zero (on the characteristic being checked, such as percent Black students). Assuming that the null hypothesis is correct, namely that all of the expectations of differences are zero, the p-values for the two-sided t-test should have a uniform distribution in the interval [0,1]^1.

For the fourth-grade national samples, no patterns of deviation were found between the sample estimates and the frame. For the eighth-grade national samples, the sampling and weighting contractor found that the national sample-estimated percentage of Black students in public schools was significantly lower than the frame value (15.2 percent sample versus 16.2 percent frame). The other minorities in public schools did not show deviations, and median income and type of location did not show deviations. In private schools there were no significant deviations.

For twelfth-grade public schools, the sample has fewer Black and Hispanic students than the frame. The public school sample percentage of Black students was 13.7 versus a frame percentage of 16.2. The public school sample percentage of Hispanic students was 11.1 versus a frame percentage of 14.5. Private schools showed no such difference between the sample and frame.

¹ See for example Efron, B. (2007), Correlation and large-scale simultaneous significance testing, Journal of the American Statistical Association 102, p. 103

Last updated 10 December 2008 (EH)

Printer-friendly Version