Item Analysis Calculator
Paste your students' answers and the answer key — or a sheet already scored 0/1 — and get every item's difficulty, its discrimination index from the top and bottom 27%, the corrected point-biserial, and a distractor analysis, plus the test's KR-20 reliability and standard error of measurement. Items that are too easy, too hard or backwards are flagged. Free, no sign-up, and the answers stay in your browser.
Paste from a spreadsheet, or type answers separated by commas or spaces. A row typed as one run of letters (BDACAB) is split into one answer per item. Blank cells count as omitted.
One letter per item, in column order — separated by spaces or commas, or typed as one run.
Results
Paste at least two students' answers, or load the example, to analyze the items.
How to Use the Item Analysis Calculator
- 1. Choose your data. Pick Answer letters and a key to score a multiple-choice test here, or Already scored 0/1 if your sheet holds 1 for correct and 0 for wrong.
- 2. Paste the answers. One row per student and one column per item, straight from a spreadsheet. A row typed as one run of letters (BDACAB) is split for you, and a blank cell counts as omitted.
- 3. Enter the key. One letter per item in column order — B D A C A B, B,D,A,C,A,B and BDACAB all work.
- 4. Choose the groups. Kelley's 27% is the default for the upper and lower groups; 25%, 33% and a 50% split are there if your course uses them.
- 5. Read the flags, then the distractors. Start with the flagged items, then pick an item in the distractor analysis to see which wrong answers did their job.
The Statistics and How They Are Calculated
| Statistic | Calculation | What it tells you |
|---|---|---|
| Difficulty p | Students correct ÷ all students | The share who got it right — higher means easier. A blank counts as wrong. |
| Discrimination D | p in the upper group − p in the lower group | How much better the strongest students did than the weakest, from −1 to 1. |
| Corrected point-biserial r | Pearson r between the item (0/1) and the total of the other items | Whether the item agrees with the rest of the test, using every student rather than the extremes. |
| KR-20 | k ÷ (k − 1) × (1 − Σpq ÷ σ²) | Internal consistency of a right/wrong test (Kuder & Richardson, 1937); identical to Cronbach's alpha on 0/1 data. |
| SEM | σ × √(1 − KR-20) | The typical error in a student's total score, in raw points. |
k = number of items; pq = p × (1 − p) for each item; σ² = variance of total scores.
Two conventions are worth stating in a report. The upper and lower groups are the top and bottom 27% of students by total score (Kelley, 1939), rounded to the nearest whole student, with students tied at a cut-off split by row order — in a small class, change the group size and see whether D moves. And σ² divides by N, so it matches the pq item variances; computing it with N − 1 (Excel's VAR.S) while keeping pq gives a slightly higher figure, 0.50 instead of 0.44 in the example below.
Worked Example: A Six-Question Quiz
Press Load example: twelve students, six four-option questions, the key B D A C A B, and one blank (S12 skipped Q5). With 27% groups, the upper group is S01, S04 and S07, who scored 5 out of 6, and the lower group is S06, S09 and S12.
| Item | p | D | r (corrected) | Flag |
|---|---|---|---|---|
| Q1 | 0.58 | 1.00 | 0.43 | — |
| Q2 | 0.92 | 0.33 | 0.34 | Very easy |
| Q3 | 0.58 | −0.33 | −0.47 | Negative — check the key |
| Q4 | 0.58 | 1.00 | 0.63 | — |
| Q5 | 0.17 | 0.67 | 0.31 | Very hard |
| Q6 | 0.50 | 1.00 | 0.47 | — |
Q3 needs attention first. Two of the three strongest students chose C, while two of the three weakest chose the keyed answer A, so the distractor analysis flags C as drawing more upper than lower students: either C is defensible, the key is wrong, or the question is ambiguous. Q4's option D was chosen by nobody, which makes it a three-option question in practice, and Q2's A and C went unused too — normal for an item 92% of the class answered correctly. KR-20 is 0.44 (mean 3.33, σ = 1.37, SEM = 1.03), about what six items can deliver.
Interpreting Difficulty, Discrimination and Reliability
| Discrimination index D | Ebel's reading |
|---|---|
| 0.40 and above | Very good item |
| 0.30 to 0.39 | Reasonably good; may be improved |
| 0.20 to 0.29 | Marginal; usually needs revision |
| Below 0.20 | Poor; revise or discard |
| Below zero | Working backwards — check the key and the wording |
Guidelines from Ebel and Frisbie (1991). The calculator flags D below 0.20 as weak and D or r below zero as negative.
There is no single ideal difficulty, but an item nearly everyone gets right or wrong cannot separate students: D cannot be large when p is close to 0 or 1. The calculator flags p above 0.90 as very easy and below 0.20 as very hard; on a four-option item, a p near 0.25 means the class did no better than blind guessing. For reliability, many testing offices look for a KR-20 of 0.70 or more on a classroom test and 0.90 for high-stakes decisions. KR-20 rises with the number of items, so judge a short quiz gently and a final exam strictly.
A good distractor is chosen by at least 5% of students and by more weak students than strong ones (Haladyna & Downing, 1993). One that nobody picks can be rewritten around a common misconception; one that attracts the upper group usually means the stem is unclear or a second answer is arguably right.
Frequently Asked Questions
- What is a good item discrimination index?
- By Ebel's widely used guidelines, 0.40 or above is very good, 0.30 to 0.39 reasonably good, 0.20 to 0.29 marginal, and below 0.20 poor. A negative value means weaker students outperformed stronger ones on that item, which usually points to a wrong key or a misleading question.
- What is item difficulty in item analysis?
- Item difficulty, often written p, is the proportion of students who answered the item correctly, so a higher value means an easier item. An item with p = 0.92 was answered correctly by 92% of the class. It is also called the difficulty index or facility index.
- Why are the upper and lower groups 27%?
- Kelley (1939) showed that, when scores are roughly normal, taking the top and bottom 27% makes the groups extreme enough to differ clearly while still large enough to estimate reliably. Many courses use 25% or 33% instead, and with small classes a 50% split keeps more students in each group; the calculator offers all four.
- What is the difference between the discrimination index and the point-biserial correlation?
- The discrimination index D compares only the top and bottom groups, so it is easy to compute by hand and to explain. The corrected point-biserial correlates the item with the total of the other items across every student, which uses all the data and is usually more stable. The two normally agree in sign; when they disagree, look at the item closely.
- What does a negative discrimination index mean?
- It means the lower group answered the item correctly more often than the upper group. The most common causes are a key error, a question with two defensible answers, or a distractor that is more attractive to students who know the material. Check the distractor analysis to see which option drew the strong students.
- What is a good KR-20 value?
- For classroom tests, 0.70 or higher is a common target, and high-stakes exams usually aim for 0.90 or more. KR-20 depends heavily on test length and on how much students differ, so a short quiz given to a similar group will score low even when its items are sound.