Outcome-based education and student learning in probability and statistics: the mediating roles of engagement and self-efficacy in a new liberal arts context

In the context of pursuing quality education empirical evidence for Outcome-Based Education (OBE) in foundational mathematics is limited, particularly regarding the psychological mechanisms through which it affects learning. This gap is acute within China's New Liberal Arts initiative, a national higher-education reform integrating quantitative reasoning with humanistic and interdisciplinary competencies. This study investigated the association between OBE and three learning outcomes, namely knowledge mastery (KM), statistical application ability (SAA), and cross-disciplinary thinking (CDT), with student engagement (ENG) and self-efficacy (SE) as mediators. A quasi-experimental design was conducted with 321 undergraduates (OBE: n = 148; traditional: n = 173) at a private university in Eastern China. Analyses included ANCOVA and hierarchical linear modeling for objective examination scores, and partial least-squares structural equation modeling (PLS-SEM, 5,000 bootstraps) for psychological mechanisms. After adjusting for prior mathematics achievement, the OBE group scored significantly higher than the traditional group on the final examination (adjusted mean difference = 6.89, p < 0.001), with the advantage confirmed by propensity-score matching (d = 0.36, p = 0.005). OBE was positively associated with ENG (β = 0.265, p < 0.001) and SE (β = 0.276, p < 0.001). ENG was identified as a significant statistical mediator in the OBE–KM and OBE–SAA pathways (VAF = 45.7% and 49.5%, respectively), while SE served as a statistical mediator in the OBE–CDT pathway (VAF = 74.0%). Sensitivity analysis supported result robustness (E-value = 3.27). The findings are consistent with a dual-pathway model in which OBE is associated with student learning through a behavioral pathway via ENG to KM and SAA, and a motivational pathway via SE to CDT. A behavioral pathway via ENG to KM and SAA, and a motivational pathway via SE to CDT. Given the quasi-experimental, cross-sectional design, findings should be interpreted as conditional associations pending longitudinal replication.