Item Analysis: Difficulty and Discrimination Index
Item analysis tells you which test questions worked: how hard each one was (difficulty index) and whether it separated learners who know the lesson from those who don't (discrimination index).
Step 1: Form the upper and lower groups
Rank the learners from highest to lowest total score. Take the top third as the upper group and the bottom third as the lower group. Each group has n learners.
Step 2: Count correct answers per item
For each item, count how many in the upper group got it right (U) and how many in the lower group got it right (L).
Step 3: Compute the two indexes
Discrimination index D = (U − L) ÷ n
Step 4: Interpret them
| P | Difficulty |
|---|---|
| 0.00 – 0.14 | Very difficult |
| 0.15 – 0.39 | Difficult |
| 0.40 – 0.70 | Moderate |
| 0.71 – 0.85 | Easy |
| 0.86 – 1.00 | Very easy |
| D | Discrimination |
|---|---|
| 0.19 and below | Poor, reject |
| 0.20 – 0.29 | Marginal, needs improvement |
| 0.30 – 0.39 | Reasonably good, may improve |
| 0.40 and above | Very good |
Combine the two to decide. A moderate, very good item is kept as it is. An item with poor or marginal discrimination is discarded when it is also easy or difficult, and revised (mostly its choices) when it is moderate. Items with reasonably good or very good discrimination are kept, revised as needed.
Worked example
45 learners took the test, so each group has n = 45 ÷ 3 = 15 learners. On item 7, 12 in the upper group and 6 in the lower group got it right.
- P = (12 + 6) ÷ (2 × 15) = 18 ÷ 30 = 0.60 → moderate
- D = (12 − 6) ÷ 15 = 6 ÷ 15 = 0.40 → very good
- Decision: accept the item as it is. It's a good item to reuse.
Tips
- A negative D (the lower group did better) usually means a wrong answer key or a confusing question. Check it first.
- Item analysis is most reliable with at least 20–30 learners.
Let ClassToolsPH compute this for you
ClassToolsPH runs the full item analysis (P, D, interpretation and decision for every item) right after the exam, and lets you save your best items to a reusable item bank.