NAEP TechnicaL DocumentationStepwise Regression Analysis Results for Primary Sampling Unit (PSU) Stratification for the 2016 Assessments

The objective was to find the optimum set of primary sampling unit (PSU)-level sociodemographic characteristics in terms of strength of relationship to achievement. The PSU-level values of these characteristics were derived from the 2010 Decennial Census summary files and the 2006-2010 American Community Survey (ACS) estimates, computed by combining the county-level data (using county youth estimates as the relative weighting factor for each county within the PSU). The characteristics used and their abbreviations as used in the tables, were as follows:

• aggregate minority group percentages (percentage of Black, Hispanic, American Indian, or Native Hawaiian/Other Pacific Islander students);

• income levels (per capita household income, percentage of children below the poverty line);

• education levels in the population (i.e., percentage of persons aged 25+ who completed high school, percentage of persons aged 25+ with a college degree);

• percentage of renters (i.e., percentage of householders who rent rather than own their place of residence); and

• percentage of female-headed households. 

These PSU-level census characteristics were analyzed with the eighth-grade reading assessment scores from five previous NAEP cycles (2002, 2003, 2005, 2007, and 2009). The criterion was that good strata should be heterogeneous for each of the five characteristics (i.e., within-stratum variance for each assessment value should be low and between-stratum variance high).

The analysis was done separately within each of the eight primary strata (census region by metro status), using a forward stepwise regression approach, with a p-value cutoff of 20 percent.  The results of the regression model were used to generate the final PSU strata.

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