Québec's students at the secondary level have always been considered as a relatively performing group on the basis of their mean scores in international skills tests (reading, math, sciences) such as PISA, and TIMSS. It is less known that students' performance in private schools, where a significant proportion are enrolled at the secondary level, raise substantially the reported mean scores. Nonetheless, a school with high standardized scores may be an institution where students come from a much advantaged background or are selected on the basis of their abilities or social class. The impact of non-randomness for the estimation of a treatment effect poses analytical challenges like bias related to selection, causality, or recruitment that must be reduced or neutralized. There are many categories of estimators that can be implemented to assess a non-random policy/intervention based on models for both the outcome variable and the treatment assignment, while taking into consideration the selection bias. We use rich student-level micro data from five (2000, 2003, 2006, 2009, 2012) Programme for International Student Assessment (PISA) and four types of estimators to estimate the impact of private schools on student performance in reading, math, and sciences. The analysis also conducts a falsification exercise with students from Ontario as a control group relative to Québec's students in the private or public sector. Results suggest that the large minority of students attending private schools at the secondary level largely explains the higher PISA scores of Québec over the years, as well as the scores in the public sector (due to external effects from school competition). According to the more conservative treatment effects, private schools add approximately one year of study in reading and math scores. Results highlight the major importance of increased 'knowledge capital' by the private sector, that is proficiency scales in cognitive skills. The characteristics of schools and teachers in the private sector, and the socio-economic status of students and their parents, are also important factors of achievement gaps between the two systems of education.