Beyond Mean Comparison: Assessing the Proportional Diostribution of Critical Thinking Mastery in Problem Based Learning on Pressure Concepts Using Chi-Square Analysis

Abstrak

Purpose of the study: The study evaluates the effectiveness of Problem-Based Learning (PBL) in improving students’ critical thinking mastery of pressure concepts by analyzing the proportional distribution of mastery rather than relying solely on mean score comparisons. Methodology: A quasi-experimental pretest-posttest nonequivalent control group design was employed with 60 eighth-grade students selected through purposive sampling from intact classes. Students were assigned to a PBL group (n=30) or a conventional instruction group (n=30). Critical thinking was measured using a validated 10-item multiple-choice test adapted from Ennis’s indicators. Baseline equivalence was tested with the Mann–Whitney U test, within-group mastery shifts with McNemar’s test, and between-group distributional differences with the Chi-square test of independence. Reliability was confirmed (Cronbach’s α = 0.86). Main Findings: The PBL group achieved a significantly higher mastery rate (83%) compared to the conventional group (60%), χ²(1) = 4.02, p = 0.045, with a moderate effect size (Cramer’s V = 0.26). McNemar’s test confirmed a statistically significant mastery transition within the PBL class (p < 0.05). The strongest gains occurred in analytical explanation and inferential reasoning dimensions. Novelty/Originality of this study: Analyzing mastery distribution reveals equitable learning outcomes that mean comparisons obscure. The findings demonstrate that PBL systematically shifts categorical achievement toward competency thresholds, particularly in higher-order cognitive dimensions. In practice, this supports the adoption of distributional analysis in classroom assessment. The study’s novelty lies in its methodological shift from continuous mean scoring to categorical mastery distribution, offering a more pedagogically relevant framework for evaluating instructional equity.