For the arts assessment, a sample of 105 primary sampling units (PSUs) was drawn from a frame of PSUs based on current Census information. For the long-term trend (LTT) assessment, a sample of 67 PSUs was selected.
After the PSU frame was created, certainty PSUs (those with large measures of size that make it efficient to take them with probability of selection equal to 1) were identified and set aside. This set of 29 certainty PSUs was the same for arts and LTT.
Stratification of the noncertainty PSUs (those with probabilities of selection strictly less than 1) was carried out after analysis of Census 2000 data and NAEP 2000 achievement scores identified the stratification variables. This analysis identified the set of PSU-level, Census-based variables that had as much association with mathematics and science assessment scores as possible. The intent is that the results of this analysis and stratification were to be used for multiple design years and subject matter. They were used previously in 2006. Periodically, this analysis and stratification will be conducted according to the availability of Census data and key assessment scores. Measures of size and probabilities of selection were defined, and a systematic sample of PSUs was drawn. For arts and LTT, 76 and 38 noncertainty PSUs were selected, respectively. Efforts were made to minimize the overlap of sampled noncertainty PSUs between the arts and LTT.
The PSUs satisfied the following criteria:
The PSU sampling frame included all U.S. states and the District of Columbia, but excluded the U.S. territories and Puerto Rico;
PSUs consisted of one county or contiguous multiple counties;
Metropolitan Statistical Areas (MSAs) were designated as separate PSUs even with their large size, as they were sufficiently compact in terms of their travel costs (due to higher levels of transportation infrastructure);
PSUs did not cross Census region boundaries;
PSUs did not cross state boundaries, in general;
Non-MSA PSUs in the Northeast and South Census regions had a minimum population of 15,000 youths (age 0 to 17 inclusive), and in the Midwest and West Census regions had a minimum population of 10,000 youths, in general, according to the 2003 U.S. Census Bureau's Population Estimates Program; and
Non-MSA PSUs were to be of minimum size (defined in terms of square miles or maximum distance between points—a rough proxy for travel time) while still satisfying the minimum population constraints.