Evaluation of college admissions: a decision tree guide to provide information for improvement

To alleviate pressures of further education, facilitate students' adaptive development, balance urban and rural education, and improve academic training, Taiwan implemented a 12-year basic national education program. This program, based on multiple intelligence theory, uses an adaptive admissions system affirming learners' rights and equal opportunities (Ministry of Education, 2009). The 5-year junior college program assesses learning abilities through various admission systems, focusing on diversified student development while creating a fair admissions system. The exam-free admissions system, implemented since 2011, allows applicants to choose colleges and departments based on their interests and conditions, while colleges recruit talent based on their standards. Applicants can also forgo enrollment opportunities. However, when enrollment exceeds available seats, many students fail to meet entrance requirements, and preferential choices for specific colleges lead to underenrollment in others. This necessitates exploring whether the exam-free system maintains educational objectives or exacerbates advantages for popular colleges, potentially marginalizing rural and suburban colleges leading to insufficient enrollment or weak competition.

Data mining, combining statistics, algorithms, artificial intelligence, and machine learning, analyzes large datasets to discover rules or models (Fayyad et al., 1996). Decision trees, a common data mining method, are simple classifiers for supervised learning, prediction, and variable reduction (Kingsford and Salzberg, 2008). Previous research has applied decision trees to various educational contexts, including identifying variables describing student achievement (Kirby and Dempster, 2014), predicting student evaluation of teaching (Park and Dooris, 2020), analyzing student learning behavior (Križanić, 2020), providing early warnings for underachieving students (Asif et al., 2017), and predicting academic behavior stability (Singer et al., 2020). Studies have also used decision trees in higher education for predicting GPA (Amburgey and Yi, 2011), building personalized learning systems (Lin et al., 2013), and developing early warning systems (Howard et al., 2018). However, Lynch (2017) highlights ethical considerations and potential drawbacks of big data analytics in education. Regarding college admissions, data mining has been used to predict enrollment (Tanna, 2012; Zeng et al., 2014; Ragab et al., 2012; Maltz et al., 2007), while the theory of multiple intelligences (Gardner, 2011) advocates for diverse learning approaches, although its empirical support is debated (Waterhouse, 2006). Chou (2009) questions the fairness of resource allocation in Taiwan's education system.

This study analyzes 2016 enrollment data from Taiwan's 5-year junior colleges, five years after the 2011 education reform. Data (6013 applicants: 2294 enrolled, 3719 failed) were obtained from the joint admissions committee. The data include 21 candidate-based independent variables and 1 dependent variable (enrollment results). Decision tree classification, specifically the CHAID (chi-square automatic interaction detector) algorithm, was used to build an assessment model. CHAID uses chi-square distribution for categorical variables; continuous variables were transformed into categorical ones. The algorithm automatically selects variables with the strongest interaction with the dependent variable, merging categories with no significant difference. The study also performed descriptive statistics, chi-square tests of independence, and t-tests, Mann-Whitney U-tests, and Kolmogorov-Smirnov Z-tests to analyze categorical and continuous variables. The dataset was divided into training (80%, 4809 applicants) and testing (20%, 1204 applicants) sets to evaluate the model's performance. The CHAID tree's growth condition was set with a maximum depth of 6, minimum observations in parent node at 100, and minimum in child node at 50, using the Bonferroni method to adjust for significance level of 0.05. The study generated a decision tree and analyzed its structure to identify key factors influencing enrollment success and failure.

Descriptive statistics revealed that School A (metropolitan area) had the highest applicant-to-enrollment ratio (4.01), while School D (agricultural county) had the lowest (1.8). Metropolitan area schools had full enrollment, while agricultural county schools were underenrolled. Most applicants (35.6%) were local. The registration threshold significantly influenced enrollment, with 70.2% of those who failed to enroll reaching it. Chi-square tests showed significant relationships between enrollment results and college location, metropolitan status, distance to college, registration threshold, type of junior high school, and origin from remote areas. T-tests, Mann-Whitney U-tests, and Kolmogorov-Smirnov Z-tests revealed that enrollment failures showed significantly higher average scores in size of junior high school graduation, competition, service-learning effectiveness, daily life performance, multiple learning performances, comprehensive assessment program, and writing test. Conversely, they scored significantly lower in technically and artistically gifted, balanced learning performance, and other factors. The CHAID model had a sensitivity rate of 81.9%/80.6% for detecting enrollment failures, with an overall accuracy of 76.9%/74.8% for training/test sets. Key variables included college location (metropolitan vs. agricultural county), other factors (English test scores), registration threshold, technically and artistically gifted, comprehensive assessment program, disadvantaged status, distance to college, type of junior high school, and writing test. The decision tree revealed that metropolitan area colleges had significantly higher failure rates (77.0%/78.3%) compared to agricultural county colleges (51.4%/52.6%). In metropolitan colleges, English test scores and registration threshold were crucial factors. For agricultural county colleges, distance to college was a major factor, with local applicants having higher success rates. A reverse selection of talent was observed in agricultural county colleges, where higher-performing students might forgo enrollment.

The findings highlight the disparity between metropolitan and agricultural county colleges in Taiwan's exam-free admissions system. Metropolitan colleges retain a significant advantage in selecting students, leading to high competition and a high failure rate. The high failure rate even when students meet the threshold suggests a competitive pressure beyond academic performance. The inverse selection in agricultural counties suggests that better-performing students opt for other colleges, leading to underenrollment and a less competitive environment. This challenges the intended educational goals of the system, emphasizing the need to address regional disparities. The decision tree model provides actionable insights for both applicants and institutions, facilitating better informed decisions and potentially reducing the negative consequences of the existing system.

This study demonstrates the effectiveness of decision tree analysis in revealing factors contributing to enrollment success and failure in Taiwan's exam-free college admissions system. The findings highlight regional disparities and the occurrence of inverse selection of talent, particularly in agricultural county colleges. Future research could explore interventions to address these issues, such as targeted support for students in rural areas or modified admissions policies to better achieve the intended educational goals. The decision tree model offers a valuable tool for improving college admissions processes and promoting equitable access to higher education.

The study's findings are based on 2016 data and might not reflect current trends. The reliance on self-reported data may introduce biases. The study focuses on Taiwan's specific context and may not be generalizable to other education systems. Further research with larger datasets and longitudinal studies could enhance the robustness of the findings.