NAEP Technical DocumentationPrimary Sampling Unit (PSU) Frame: Stratification for the 2008 Assessment

			Stepwise Regression Analysis Results for PSU Stratification Final PSU Strata

The primary sampling unit (PSU) strata were determined by Census region and metropolitan status (metropolitan or non-metropolitan)—a total of eight "primary" strata. Measures of size were defined for each of these strata, determined by the relative share of the eventual PSU sample (the sample size is designed to be proportional to the number of youths). The PSU stratum measure of size then is the total number of youths in the stratum. The table below presents these counts for each of the eight primary strata. The relative share of the PSU sample size for each stratum is the number of youths in the stratum divided by the total number of youths, multiplied by 76 (the total noncertainty PSU sample size for the Arts assessment). The resulting number is then rounded to the nearest even integer (the integer needs to be even to facilitate variance estimation), except for the Midwest metropolitan PSU stratum, which is rounded down. The results of these calculations are given in the table below.

Noncertainty primary sampling unit frame size statistics, by primary stratum: 2008
Primary stratum	PSUs	Counties	Youths	Target number of PSU strata	Set number of PSU strata	Youth per PSU stratum
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2008.
Total noncertainty PSUs	1,040	2,938	42,965,727	76.0	76	565,339
Northeast region metropolitan	46	83	4,687,427	8.3	8	585,928
Northeast region non-metropolitan	50	94	1,149,764	2.0	2	574,882
Midwest region metropolitan	100	246	7,328,445	13.0	12	610,704
Midwest region non-metropolitan	249	769	3,588,803	6.3	6	598,134
South region metropolitan	153	458	12,754,676	22.6	22	579,758
South region non-metropolitan	269	872	5,187,996	9.2	10	518,800
West region metropolitan	71	101	6,579,302	11.6	12	548,275
West region non-metropolitan	102	315	1,689,314	3.0	4	422,329

The division of the primary strata into the final strata was done on a stratum-by-stratum basis. The criteria for good PSU strata were 1) the strata should have as equal measures of size as possible (this reduces sampling variance), and 2) the strata should be as heterogeneous in measured achievement as possible (i.e., there should be strata with low mean achievement, strata with mid-level mean achievement, and strata with high mean achievement). This second criterion will also ultimately reduce the variance of the assessment estimates since the final PSU sample will be balanced in terms of assessment means.

PSU assessment means from the current year cannot be used as assessments are only conducted after sampling is completed. Information is available about PSU sociodemographic characteristics in advance however. An analysis was done within each primary stratum to find sociodemographic variables that were good predictors of the NAEP 2000 mathematics and science assessment results. Using these sociodemographic variables to define strata should increase the chance of having efficient strata definitions. Stepwise Regression Analysis Results for PSU Stratification describes this analysis for each primary stratum.

The final step in stratification was to define the desired number of strata using the selected stratifiers, while constructing strata that were as close to equal size as possible (with size defined by number of youths). The objective was to establish strata that had a high between-stratum variance for the stratifiers (i.e., which "spread out" the stratifiers as much as possible). This was accomplished through the use of proprietary software developed for this purpose. Adjustments were then done manually. These strata are given in Final PSU Strata.

Last updated 10 January 2011 (JL)

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