NAEP Technical DocumentationRegression Analysis Results for PSU Stratification

The object was to find the optimum set of PSU-level sociodemographic characteristics in terms of strength of relationship to achievement. The PSU-level values of these characteristics were derived from the 2000 Census Summary File I (SF 1) and Summary File 3 (SF 3) files for each county, 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 were

race/ethnicity percentages in schools (percent Black, Hispanic, or American Indian—Pct BHI below; percent Black; percent Hispanic—Hsp below; percent Asian),
income levels (median household income—med income below, percent children below the poverty line—Cld Pov below),
education levels in population (i.e., percent of persons age 25 and over who completed high school with no college degree, percent of persons age 25 and over with college degrees—CG grd below), and
percent of renters.

These PSU-level Census characteristics were examined within each of the four NAEP 2000 assessment values: fourth-grade mathematics achievement, fourth-grade science achievement, eighth grade mathematics achievement, and eighth grade science achievement. These PSU-level values for achievement were computed using the State NAEP 2000 database. The criterion was that good strata should be heterogeneous for each of the four characteristics (i.e., within-stratum variance for each assessment value should be low and between-stratum variance high), so that strata are defined that do a good job for both mathematics and science, in both grades, not just the best possible job for one subject and one grade. This will prevent overfitting to some extent. The analysis was done separately within each of the eight primary strata, using a forward stepwise regression approach, with a p-value cutoff of 20 percent. The results are given in the tables below. The order of the regressors is the order of entry in the stepwise procedure. The p-value is for an F-test for entry of the regressor into the forward stepwise model. The minus or plus sign indicates the direction of effect (negative indicates that increase in the regressor is related to reduced achievement; positive indicates that increase in the regressor is related to increased achievement). The regressor is in italics if the direction of the effect is in an unexpected direction (i.e., negative when we generally expect a positive effect or vice versa). The stratifiers that were chosen to generate the final PSU strata are indicated in a note below the regression analysis result tables (these were chosen by the statisticians after study of the results).

Northeast Metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject and grade, long-term trend assessment: 2004
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Cld pov - (p=0.004)	Cld pov - (p=0.017)	Black - (p=0.044)	HS grd + (p=0.011)
Second variable	Black - (p=0.137)	†	†	Black - (p=0.105)
† Not applicable. NOTE: Stratifiers chosen were percent child poverty and percent Black. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

Northeast Non-Metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject and grade, long-term trend assessment: 2004
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Renters + (p=0.036)	HS grd + (p=0.0006)	Cld pov - p=0.0007	CG grd + (p=0.066)
Second variable	†	Black - (p=0.101)	Renters - (p=0.125)	Black - (p=0.012)
Third variable	†	Pct BHI + (p=0.106)	Med Inc - (p=0.174)	Hsp + (p=0.064)
Fourth variable	†	†	Black + (p=0.087)	†
† Not applicable. NOTE: Stratifier chosen was percent child poverty. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

Southeast Metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject and grade, long-term trend assessment: 2004
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Med Inc + (p=0.004)	Cld pov - (p=0.010)	Black - (p=0.0008)	Cld pov - (p=0.031)
Second variable	Hsp + (p=0.096)	†	†	†
Third variable	Renters - (p=0.028)	†	†	†
† Not applicable. NOTE: Stratifiers chosen were percent child poverty and percent Black. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

Southeast Non-Metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject and grade, long-term trend assessment: 2004
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Black - (p=0.002)	Med Inc + (p=0.009)	Black - (p=0.003)	Black - (p<0.0001)
Second variable	Asian + (p=0.046)	Black - (p=0.057)	Pct BHI + (p=0.130)	Hsp + (p=0.005)
NOTE: Stratifier chosen was percent Black. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

Central Metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject and grade, long-term trend assessment: 2004
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Cld pov - (p=0.069)	Asian + (p=0.004)	Hsp - (p=0.029)	†
Second variable	Med Inc - (p=0.148)	Med Inc - (p=0.029)	†	†
Third variable	Pct BHI + (p=0.135)	Cld pov - (p=0.081)	†	†
Fourth variable	†	Black + (p=0.094)	†	†
Fifth variable	†	HS grd - (p=0.098)	†	†
Sixth variable	†	CG grd + (p=0.051)	†	†
† Not applicable. NOTE: Stratifiers chosen were percent child poverty, percent Asian, and percent college graduates. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

Central Non-Metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject and grade, long-term trend assessment: 2004
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Cld pov - (p=0.002)	Med Inc + (p=0.004)	Black + (p=0.147)	Cld pov - (p=0.076)
Second variable	Black + (p=0.065)	Renters - (p=0.085)	†	†
† Not applicable. NOTE: Stratifiers chosen were percent child poverty and median household income. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

West Metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject and grade, long-term trend assessment: 2004
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Asian - (p=0.087)	†	CG grd + (p=0.002)	Renters - (p=0.005)
Second variable	Renters + (p=0.051)	†	Asian - (p=0.101)	CG grd + (p=0.023)
Third variable	†	†	HS grd + (p=0.174)	Blacks - (p=0.058)
Fourth variable	†	†	†	Asian - (p=0.078)
† Not applicable. NOTE: Stratifiers chosen were percent college graduates and percent renters. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

West Non-Metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject and grade, long-term trend assessment: 2004
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Asian - (p=0.033)	CG grd + (p=0.086)	HS grd + (p=0.0001)	CG grd + (p=0.084)
Second variable	Cld pov - (p=0.047)	HS grd - (p=0.111)	Asian - (p=0.0007)	Med Inc - (p=0.053)
Third variable	HS grd - (p=0.019)	Cld pov - (p=0.017)	Hsp - (p=0.135)	Cld pov - (p=0.112)
Fourth variable	†	Pct BHI - (p=0.13)	Cld pov + (p=0.197)	Hsp + (p=0.064)
† Not applicable. NOTE: Stratifiers chosen were percent child poverty and percent high school graduates. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2004.

Last updated 14 July 2009 (JL)

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