NAEP Technical DocumentationStepwise Regression Analysis Results for PSU Stratification

The object 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 2000 Census Summary Files and the 2003 county population 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:

race/ethnicity percentages in schools (percent Black, Hispanic, or American Indian – "Pct BHI" below; percent Black; percent Hispanic – "Hsp" below; percent Asian; percent American Indian; percent two or more races);
income levels (median household income – "Med Inc" 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 – "HS grd," percent of persons age 25 and over with college degrees – "CG grd" below);
percent of renters; and
percent of female householders living alone.

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 2000 state NAEP 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 prevents overfitting to some extent.

The analysis was done separately within each of the eight mega strata (census region by metro status), 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 unexpected (i.e., negative when we generally expect a positive effect, or vice versa). The stratifiers chosen by the statisticians to generate the final PSU strata are indicated in a note below the regression analysis result tables.

Northeast metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject grade and variable: 2009
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Cld pov - (p=0.084)	Cld pov - (p=0.174)	Black - (p=0.068)	HS grd + (p=0.026)
Second variable	Black - (p=0.159)	†	†	Black - (p=0.193)
† Not applicable. NOTE: Stratifiers chosen were percent child poverty (Cld pov) and percent Black. HS grd = high school graduate with no college degree. Black includes African American SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.

Northeast non-metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject grade and variable: 2009
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Renters + (p=0.092)	CG grd + (p=0.010)	Cld pov - (p=0.085)	Black(p=0.005)
Second variable	†	Black + (p=0.176)	Med Inc - (p=0.002)	HS grd + (p=0.030)
Third variable	†	†	Renters - (p=0.085)	†
† Not applicable. NOTE: Stratifier chosen was percent child poverty (Cld pov). Renters = individuals who do not own their homes; CG grad = college graduate; Med Inc = median household income; HS grad = high school graduate with no college degree. Black includes African American. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.

Midwest metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject grade and variable: 2009
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Cld pov - (p=0.003)	Asian + (p=0.004)	Cld pov - (p<0.001)	†
Second variable	Med Inc - (p=0.200)	Med Inc - (p=0.055)	Med Inc - (p=0.001)	†
Third variable	Pct BHI + (p=0.100)	†	Black + (p=0.006)	†
Fourth variable	†	†	HS grd - (p=0.050)	†
† Not applicable. NOTE: Stratifiers chosen were percent child poverty (Cld pov), median household income (Med Inc), and percent Asian. Pct BHI = percent Black, Hispanic, or American Indian; HS grd = high school graduate with no college degree. Black includes African American and Hispanic includes Latino; Asian includes native Hawaiian and other Pacific Islander. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.

Midwest non-metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject grade and variable: 2009
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Cld pov - (p=0.012)	Cld pov - (p=0.002)	†	CG grd + (p=0.005)
Second variable	Pct BHI + (p=0.128)	Asian + (p=0.124)	†	Pct BHI - (p=0.079)
† Not applicable. NOTE: Stratifiers chosen were percent child poverty (Cld pov), percent college graduates (CG grd), and percent Black, Hispanic, or American Indian (BHI). Black includes African American and Hispanic includes Latino; Asian includes native Hawaiian and other Pacific Islander. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.

South metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject grade and variable: 2009
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Hsp + (p=0.001)	Asian + (p=0.014)	Black - Hsp - (p=0.005)	Cld pov - (p=0.011)
Second variable	Cld pov - (p=0.001)	Black - (p=0.038)	†	Black - (p=0.127)
† Not applicable. NOTE: Stratifiers chosen were percent child poverty (Cld pov), percent Black, and percent Hispanic (Hsp). Black includes African American and Hispanic includes Latino; Asian includes native Hawaiian and other Pacific Islander. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.

South non-metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject grade and variable: 2009
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Black - (p<0.001)	Black - (p=0.005)	Black - (p=0.014)	Black - (p<0.001)
Second variable	Asian + (p=0.037)	Med Inc + (p=0.037)	Asian + (p=0.036)	Med Inc + (p=0.045)
Third variable	†	Black-Hisp + (p=0.176)	Cld Pov - (p=0.068)	†
Fourth Variable	†	†	CG grd - (p=0.127)	†
† Not applicable. NOTE: Stratifiers chosen were percent Black, median household income (Med Inc), and percent Asian. Cld Pov = children below the poverty line; CG grd = college graduate. Black includes African American and Hispanic includes Latino; Asian includes native Hawaiian and other Pacific Islander. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.

West metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject grade and variable: 2009
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	CG grd + (p=0.094)	Pct BHI - (p=0.049)	HS grd + (p<0.001)	HS grd - (p=0.160)
Second variable	HS grd + (p=0.191)	†	Asian + (p=0.007)	Med Inc - (p=0.001)
Third variable	†	†	Black - (p=0.080)	CG grd + (p=0.003)
Fourth variable	†	†	†	Asian + (p=0.009)
Fifth variable	†	†	†	Cld pov - (p=0.037)
Sixth variable	†	†	†	Renters - (p=0.087)
† Not applicable. NOTE: Stratifiers chosen were percent high school graduates (HS grd) and percent college graduates (CG grd). Pct BHI = percent Black, Hispanic, or American Indian; Med Inc = median household income; Cld pov = children below the poverty line; Renters = individuals who do not own their homes. Black includes African American and Hispanic includes Latino Asian includes native Hawaiian and other Pacific Islander. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.

West non-metropolitan stepwise regression analysis on NAEP 2000 achievement scores, by subject grade and variable: 2009
Variable	Mathematics 4	Mathematics 8	Science 4	Science 8
First variable	Renter - (p=0.013)	CG grd + (p=0.006)	HS grd + (p<0.001)	CG grd + (p=0.220)
Second variable	Black + (p=0.040)	†	Cld pov + (p=0.008)	Med Inc - (p=0.038)
Third variable	Cld pov - (p=0.005)	†	Asian - (p=0.017)	Cld pov - (p=0.135)
Fourth variable	HS grd - (p=0.092)	†	†	†
† Not applicable. NOTE: Stratifiers chosen were percent college graduates (CG grd), percent child poverty (Cld pov), and percent high school graduates (HS grd). Renter = individuals who do not own their homes; Med Inc = median household income. Black includes African American; Asian includes native Hawaiian and other Pacific Islander. SOURCE: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2009 Assessment.

Last updated 25 February 2016 (GF)

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