Purpose: The purpose of this paper is to examine what factors affect student achievement in reading and mathematics. The research questions addressed the perceptions of school principals and background characteristics related to student achievement in Korea and the USA with respect to differences among students in low, middle and high quantiles. Design/methodology/approach: Data were taken from the Program for International Student Assessment 2012. Scores in the reading and mathematics were analyzed in conjunction with a principal survey. The Quantile Regression method was used for data analysis with three quantile points. T-statistics were used to test for significance. The predictor set consisted of seven school-leadership variables, and four to six additional covariates. Findings: The most important finding for the USA was a relationship between organizational hindrance (HND) and low student achievement for the middle and upper quantiles in mathematics and for all quantiles in reading. The (HND) variable included poor teacher-student relations, low expectation of students, overly strict enforcement of rules, lack of attention to student needs, resistance to change, lateness to class, and lack of preparation. The most important finding for Korea was that there were significant associations across all groups between teacher attitude (TCHATT) and student reading achievement and with the low group in mathematics. Research limitations/implications: This study adds to knowledge about school capacity and suggests that the leadership role of the principal is to overcome negative environmental factors and create a positive organization. Originality/value: The non-Gaussian approach of regression analysis allowed us to identify significant differences that we otherwise might not have found.