Relationship between Entrance Exam Scores, Academic Performance, and Student Dropout Rates: A Longitudinal Case Study

This study investigates the relationship between entrance exam scores and academic performance, as well as their implications for student retention, at the Jorge Basadre Grohmann National University (UNJBG). Using data from 1,526 students admitted in 2017 and tracked through 2024, the analysis explores entrance scores by subject area, average academic performance, and dropout rates across four study tracks. Results reveal that Verbal Reasoning (VR) and Language (LA) consistently exhibit moderate positive correlations with academic performance, while discipline-specific subjects such as Biology (BI) and Mathematical Reasoning (MR) show varying levels of influence depending on the study track. A strong negative relationship between entrance scores and dropout rates was identified, supported by Spearman correlations of -0.8 (average scores) and -0.77 (minimum scores). Based on these findings, a data-driven admission policy is proposed, introducing track-specific minimum score thresholds designed to reduce dropout rates while maintaining accessibility. The proposed threshold for Health and Biomedical Sciences would result in eliminate 24.29% of dropouts by reducing admissions by only 16.56%. The study underscores the value of aligning admission criteria with program-specific academic demands and highlights the potential of advanced data science techniques to refine predictive models and identify more nuanced patterns. These insights contribute to the development of evidence-based admission policies that optimize retention and support long-term academic success in the Peruvian higher education context.