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Driven by the focus on standardised assessment and performance-driven accountability, a considerable body of literature has documented differences in students' academic achievement across school sectors, both internationally and in Australia. However, few studies have to date explored the potential mechanisms underlying such differences, particularly through the lens of school climate and student engagement. And despite extensive literature on school climate and student engagement, including their relationships with achievement, the differences in these patterns across school sectors remain under-studied. In this paper, we leverage nationally representative data from a large-scale longitudinal survey in Australia with linked administrative data on student achievement to reveal different patterns of school climate and student engagement across government, Catholic and independent sectors. Employing multivariable regression analyses, we identify unique school climate and student engagement facets that are associated with improved achievement in each of these sectors, offering important pointers for educational policies. [ABSTRACT FROM AUTHOR]