The quantitative methods of regression and factor analysis were used to study the equity of educational outcome and the effectiveness of schools in 30 sixth-grade classrooms in western New York State. Equity of educational outcome refers to a situation in which educational achievement is fairly and justly distributed across racial and socioeconomic boundaries. The reading scores of the participating students (N=744) on the New York State Pupil Evaluation Program (PEP) test of May 1987 were used to define the relationship between student achievement and background. To study the relationship between equity of educational outcomes and school effectiveness, the dependent variable was the value that described the association between achievement and background. School effectiveness was studied using a set of school input variables often associated with educational achievement. The strength of the relationship between student achievement and background varied considerably from one classroom to another. Findings on school effectiveness suggest that some variables conventionally used in effectiveness studies may not be positively related to the equity of educational outcomes. Implications for reducing inequities are discussed. Factor analysis and multiple regression techniques appeared appropriate for studies of educational equity. Six tables present study data. (SLD)