Multiple regression studies of schools are capable of detecting only "average" effect. A basic assumption of such studies is that all schools are functioning within the parameters of a given educational technology and that differences in output can be attributed to different levels of input. With decentralized decision making characteristics of public elementary and secondary education, it is entirely possible that some schools are functioning within totally different parameters than are the bulk of schools. If these "different" schools are small in number, their effect would be lost in a multiple regression analysis. Using data of the public elementary schools in New York State, regression analysis was used to identify outlier schools, socioeconomic characteristics being the independent variables and average pupil achievement being the dependent variable. Schools with an unusually large residual score were considered outliers, and were compared with other schools using analysis of variance. Both positive and negative outliers tended to be small innovative schools, but the positive achievers were different with respect to resource applications in a direction which supports conventional wisdom about quality schools. The paper concludes by discussing the implications for future research. (BW)