Mathematical Model of Distractor Non-uniformity in Multiple-Choice Items

Abstract

This study developed and evaluated the Distractor Non-Uniformity Index (DNUI), a mathematical model designed to quantify the imbalance in distractor selection for multiple-choice test items. Employing both developmental and quantitative research designs, the DNUI was formulated during the model development phase. Its relationship to and influence on traditional indices were examined using secondary data gathered from the midterm and final examinations in the course GE 4: Mathematics in the Modern World, administered during the first semester of Academic Year 2024–2025. The dataset consisted of the responses of 193 students enrolled in the course. Content validation by six experts yielded a high Scale Content Validity Index (S-CVI/Ave) of 0.95, indicating strong agreement on the model’s clarity and practical utility. Reliability analysis demonstrated a strong positive correlation (r = 0.76, p < 0.01) in DNUI values across two distinct student groups answering identical items, confirming the index’s consistency across comparable testing conditions. Significant weak correlations were observed between DNUI and traditional item analysis metrics: a positive correlation with the Difficulty Index (ρ = 0.33, p < 0.01) and a negative correlation with the Discrimination Index (ρ = –0.29, p < 0.01). Regression analyses further confirmed that DNUI significantly predicts both traditional indices (p < 0.01), though it accounts for only a limited portion of the variance. These findings establish DNUI as a valid and reliable diagnostic tool for evaluating distractor quality in multiple-choice items. It is recommended that DNUI be applied as a complementary index, used along with traditional item analysis metrics such as item difficulty and discrimination to ensure a more comprehensive evaluation of test item quality.