DEVELOPMENT AND VALIDATION OF A SENIOR HIGH SCHOOL STATISTICS AND PROBABILITY ACHIEVEMENT TEST USING ITEM RESPONSE THEORY

Tóm tắt

This study addressed the critical need for sophisticated diagnostic tools in Philippine mathematics education by developing and validating the Senior High School Statistics and Probability Achievement Test (SHSTAT). Validation in this study refers to established internal structural evidence and psychometric calibration, assessed through unidimensionality, local independence, and item-model fit. Utilizing a descriptive-developmental research design grounded in Item Response Theory (IRT), the study transcended the limitations of Classical Test Theory to provide precise measurement across the ability continuum. The instrument was administered to 1,703 Grade 11 students from public and private schools in Cavite. Results from a Modified Parallel Analysis (MPA) confirmed the instrument's unidimensionality, with all item factor loadings (λ ≥ 0.90) substantially exceeding the 0.30 criterion. Comparative model fitting identified the Three-Parameter Logistic (3PL) model as the superior fit for multiple-choice data, effectively accounting for item discrimination (a), difficulty (b), and pseudo-guessing (c). Iterative refinement resulted in a 30-item scale that satisfied the assumption of local independence (|Q3| < 0.20) and exhibited excellent item-fit indices (RMSEA < 0.05). Distinct from traditional procedural assessments, item- and test-level IRT analyses indicate that the SHSTAT demonstrates high conditional measurement precision, with the Test Information Function (TIF) peaking at 17.5 around θ ≈ 1.3, indicating optimal precision at moderately high proficiency levels. This precision is driven by highly discriminating items, whose Item Characteristic Curves (ICCs) exhibit steep slopes and whose Item Information Functions (IIFs) show concentrated information between 0.8 < θ < 1.8. Consistently, the Test Characteristic Curve (TCC) displays a pronounced slope within this same range, confirming strong differentiation among higher-ability examinees. This study contributes a psychometrically robust instrument for competitive academic placement and offers educators a reliable and accurate means of assessing students’ cognitive skills in Statistics and Probability, supporting data-driven instruction and curriculum refinement.