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Primary Sampling Unit Frame: Stratification


Stepwise Regression Analysis Results for PSU Stratification

Final PSU Strata


The primary sampling unit (PSU) strata were determined by NAEP 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 major strata. The relative share of the PSU sample size for each primary stratum is the number of youths in the stratum divided by the total number of youths, multiplied by 60 (the total noncertainty PSU sample size). This is then rounded to the nearest even integer (the integer needs to be even to facilitate variance estimation), except for the Central 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, 2004
Primary stratum PSUs Counties Youths Target number of PSU strata Set number of PSU strata Youths per PSU stratum
Total noncertainty PSUs 1,065 3,004 47,114,000 60 60 785,000
Northeast Region Metropolitan 40 87 4,924,000 6.27 6 821,000
Northeast Region Non-Metropolitan 60 107 1,457,000 1.85 2 728,000
Southeast Region Metropolitan 103 291 10,226,000 13.02 14 730,000
Southeast Region Non-Metropolitan 223 752 4,859,000 6.19 6 810,000
Central Region Metropolitan 82 195 8,649,000 11.01 10 865,000
Central Region Non-Metropolitan 281 840 4,305,000 5.48 6 717,000
West Region Metropolitan 74 123 9,246,000 11.07 12 770,000
West Region Non-Metropolitan 202 609 3,450,000 4.39 4 862,000
SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

The division of the primary strata into the final strata was done on a primary stratum by primary 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 middling mean achievement, and strata with high mean achievement). This second criterion will also ultimately reduce the variance of the assessment estimates, as the final PSU sample will be guaranteed to be balanced in terms of mean assessment.

PSU assessment means from the current year cannot be used as that is only collected during the field period 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 predicted well mathematics and science assessment results in the NAEP 2000 study. Using these sociodemographic variables to define strata should increase the chance of having efficient strata definitions. Stepwise Regression Analysis Results for PSU Stratification describes the analysis for each primary stratum.

The final step in stratification defined 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 22 October 2009 (GF)

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