The purpose of this study is to quantitatively investigate one of many possible reasons for gaps in grade 8 students' mathematics test scores between students of different ethnicities or economic levels. Recent advances in multi-level structural equation modeling, together with increased sample sizes available from the National Assessment of Educational Progress (NAEP, also known as The Nation's Report Card) allow for a renewed investigation of the factors that explain ethnic or economic test score gaps in the United States. Using preliminary and confirmatory samples from the 2003 grade 8 NAEP mathematics assessment and survey results, the current study estimates a basic two-level model of ethnic and economic predictors of mathematics test scores and explores one possible mediator of ethnic and economic composition effects.

Within schools, the study confirms previous studies documenting that White, Asian, or higher income students tend to score higher than lower-income, Black, Hispanic, or American Indian students. Between schools, the model suggests that schools with higher percentages of lower-income students are less effective for all of their students than schools with higher percentages of higher-income students. No such composition effects are confirmed based on ethnic composition, that is, the percentages of Black, Asian, or American Indian students in a school. Unexpected composition effects are found suggesting that schools with higher percentages of Hispanic students and schools with higher percentages of Title I students are more effective for all of their students than schools with lower percentages in these categories. Effective Title I funding, social capital in the Hispanic community, and effective school response to large numbers of Spanish-speaking students are suggested as explanations.

A successful confirmatory factor analysis is performed on one potential mediator of composition effects—a second-order construct called Full-School Engagement (FSE). FSE is shown to be a partial mediator of the effect of school economic composition on grade eight adjusted mean mathematics test scores. No other composition effects are consistently mediated by FSE. This study demonstrates a successful application of two-level structural equation modeling using the rich, but complex, NAEP database.