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Table of Contents | Search Technical Documentation | References
NAEP Technical DocumentationSelection of PSUs in the 2000 National Main Assessment
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A sample of 94 primary sampling units (PSUs) was drawn for each of the survey years 1994, 1996, 1998, and 2000. Of these 94 PSUs, 22 were selected with certainty because they had the largest populations in the PSU universe. These 22 certainty PSUs appeared in the set of 94 sample PSUs for each of the survey years. Within each of the 72 noncertainty strata, one PSU was selected with probability proportionate to its 1990 population for each survey year (i.e., within each stratum, a PSU's probability of being selected was proportional to its population). The PSUs were selected with probability proportional to size (PPS) with the twin aims of obtaining approximately self-weighting samples of students and having approximately equal workloads in each PSU.
PSUs were drawn to minimize overlap of the PSUs from one assessment to the next, except that certainty PSUs were retained in each assessment year and some of the larger noncertainty PSUs are in the sample for more than one of these years. Each sample of 94 PSUs was drawn from the 1,027 PSUs on the frame. Primarily because of the use of MSAs as PSUs, PSUs varied considerably as to their probability of selection, because they varied greatly in size. In 2000, the 36 selected noncertainty MSA PSUs had probabilities of selection ranging from .03 to .58, while the 36 selected non-MSA PSUs had probabilities from .03 to .11. Parts of 42 states were included in the sample PSUs. Because one PSU was selected from each noncertainty stratum, the distribution of the noncertainty PSUs is the same as the noncertainty strata.
The order of the PSUs was randomized within each stratum. Selection of PSUs within a stratum was not independent among the survey years. Ordering the PSUs within a stratum by size, geography, or other variables could have resulted in unintended and possibly detrimental correlations between survey estimates across years. The PSU ordering has no effect on sampling variance because only one PSU is selected for a given year.
For each PSU within a stratum, a normalized measure of size was calculated by dividing the PSU's 1990 population by the aggregate 1990 population of all PSUs in the stratum. Next, a cumulative count of normalized measures of size was calculated for each PSU within a stratum. Where k is the PSU and i is the stratum, the cumulative count Cik is calculated as
where NMij is the normalizing measure for the jth PSU in the ith stratum.
A random number between zero and one was generated for each stratum. With the use of this random number, denoted r, the following sequence of sample designation numbers was generated for the 5 survey years.
| Statistic | 1994 | 1996 | 1998 | 2000 |
|---|---|---|---|---|
| Sample designation number | r | r + 0.4 | r + 0.8 | r + 0.2 |
| SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2000. | ||||
Only the noninteger part of any number in the sequence that exceeded 1.0000 was retained. For example, if r was equal to 0.326743, then r + 0.8 was equal to 1.126743 and 0.126743 became the sample designation number for 1998.
The first PSU in the stratum whose cumulative count was equal to or greater than r was designated the 1994 sample PSU. Similarly, the first PSUs in the stratum whose cumulative counts were equal to or greater than the noninteger portions of r + 0.4, r + 0.8, and r + 0.2 were designated the 1996, 1998, and 2000 main sample PSUs, respectively.
The sample designation numbers for 1996, 1998, and 2000 were functions of r to minimize the overlap among the sets of main sample PSUs chosen for the various survey years. In strata with smaller numbers of PSUs, some PSUs had large enough normalized measures of size so that they were drawn for two and sometimes even three survey years. As the spacing between the sample designation numbers for any two consecutive survey years was 0.4, selecting the same PSU in two consecutive survey years was rare. For example, only one noncertainty PSU was selected for both the 1998 and the 2000 assessments.
Last updated 17 June 2008 (MH)