Mathematics · Psychometrics and Statistics

In test development, analyzing how well an item and its options perform is essential. Distractor analysis in multiple-choice testing evaluates incorrect options to ensure they are plausible enough to differentiate between knowledgeable and unknowledgeable test-takers. This differentiation capability is mathematically quantified using specific item analysis metrics. A psychometrician evaluates a multiple-choice item administered to 200 test-takers to ensure it effectively differentiates between ability levels. Based on the 27% rule, the test-takers are divided into an upper group (54 students) and a lower group (54 students). If 45 students in the upper group answered the item correctly and 18 students in the lower group answered it correctly, what is the Discrimination Index (D) for this item?