How to Do Item Analysis on an MCQ Test: Difficulty, Discrimination and Distractors

By Pooja Goenka · Published 2026-10-21

Item analysis is a way of checking each question in a multiple-choice test against how the whole group performed. For every question you work out three things: what share of students got it right (difficulty, sometimes called facility), whether stronger students got it right more often than weaker ones (discrimination), and which wrong options were actually chosen (distractor analysis). Together they show which questions to keep, which to fix, and which have a wrong answer key.

Here is the short version:

• Difficulty is the share who answered correctly. Very low or very high values say the question separates almost no one.
• Discrimination compares the top and bottom groups. Rule of thumb: below 0.2 is weak, below 0 means something is wrong.
• A negative value usually points at the answer key, the wording, or a trap that catches careful students.
• Distractor counts show which wrong options draw students and which are never picked.
• You need a reasonable group size. With fewer than about ten students the numbers are noise.

This is old, well-understood assessment practice (it comes from classical test theory), and it needs no software beyond a spreadsheet. I will use one small example throughout.

Why a score list is not enough

A results sheet ranks students. It says nothing about whether a bad score came from the student or from question 14. A key typed wrongly, an ambiguous stem, or an option that is arguably correct all lower scores without any student having learned less. Item analysis is the step that separates those cases, and it is the cheapest quality check an institute can run on a paper it will reuse.

Number 1: difficulty (facility)

Difficulty is the number who answered correctly divided by the number who answered. If 19 of 30 students got a question right, its difficulty is 19 / 30, which is 0.63, or 63%. Despite the name, a higher number means an easier question.

How to read it:

• Above about 0.9: almost everyone got it. It tells you the topic was understood, and little about who understood it best.
• Below about 0.2: very few got it. That is either a topic nobody learned, a question beyond the syllabus, or a wrong key.
• In between: most questions in a ranking test should sit here.

These cutoffs are conventions, not laws. A diagnostic quiz that checks a basic fact can reasonably be 95% easy. A paper meant to rank applicants for a few places wants plenty of mid-range items.

Number 2: discrimination

Discrimination asks whether a question does its job of telling stronger students from weaker ones. The simple version works like this.

1. Rank students by total score.
2. Take the top 27% and the bottom 27%. The 27% is a long-standing convention for this calculation.
3. For the question, work out the share correct in each group.
4. Subtract the bottom group's share from the top group's.

The result runs from -1 to 1. Here is a 30-student example, so each group has 8 students.

Q5 is working well. Stronger students got it right far more often. Q9 is weak, because nearly the same share of top and bottom students got it. That does not make it a bad question: if it is an easy one, nearly everyone gets it, and it will not separate anyone. Q14 is the one to chase. More of the weak students got it right than the strong ones.

A common rule of thumb is that below 0.2 is weak and negative values need a look. Discrimination is also a statistical measure, so with a small group a difference of one student moves it a lot. That is why a cohort of ten or fewer should not drive decisions.

Number 3: distractors

Distractors are the wrong options. For each question, count how many students chose each option. Take Q14, where the key says C:

Now the problem is visible. More students chose B than the keyed answer, and in this example the stronger students were among them. Open the question and read B with fresh eyes. In practice one of three things turns up:

• The key is wrong, and B is the correct answer. Fix the key and re-score.
• The wording is ambiguous, so B is also defensible. Rewrite the question or accept both.
• B is a deliberate trap that careful students fall into. That is a teaching signal about a misconception worth reviewing in class, though it may also mean the item is unfair.

The reverse case matters too. A distractor that nobody picks is doing no work. If only two of four options are ever chosen, the question is effectively a coin flip between two, and you can replace the dead options with more plausible wrong answers.

A review routine for every paper

1. Run the numbers after each test with at least ten students.
2. Sort by discrimination, lowest first.
3. Open any question with negative discrimination and read the options chosen before anything else.
4. Check the key. Then the wording. Only then call it a hard question.
5. Decide per question: keep, rewrite, replace, or re-score the paper.
6. Record the change against the question in your bank, so the next batch gets the better version.

If you re-score after changing a key, tell students what changed and why. That costs a paragraph and prevents a lot of arguments. A way for students to challenge an answer key also catches errors before they reach the analysis.

Limits worth knowing

Item analysis cannot tell you whether a question is a good one in the sense of testing the right skill. It only tells you how it behaved with this group. A well-written question can show weak discrimination on a group that all studied the same material. It also works on objective items. Essay and handwritten answers need a different check, such as moderation between markers.

Where LogicWiz fits

LogicWiz Exams has this analysis built into the results page for a test. For each question it shows the share who got it right, a separation value, and the percentage who chose each option, with the keyed answer marked and the most-chosen wrong option highlighted when it drew at least as many as the right one. The separation value is the top-27%-minus-bottom-27% calculation above, for multiple-choice questions, and it appears from ten finished candidates. Questions get a plain note when stronger candidates did worse, when separation is below 0.2, or when fewer than 20% or more than 90% got it right. Pricing is not listed publicly, so get in touch if you want to see it on your own paper. For the surrounding workflow, see how to mark handwritten answers online and reduce cheating in online tests.

Common questions

What is item analysis in an MCQ test?

It is a check on each question using the results of the whole group. You calculate how many got it right, whether stronger students did better than weaker ones, and which wrong options were chosen, to decide whether to keep, fix or drop the question.

What is a good discrimination index for a multiple-choice question?

Common guidance treats 0.2 and above as acceptable, higher as better, and below 0.2 as weak. A negative value means weaker students did better than stronger ones, which is a reason to check the answer key and wording.

What is the difficulty index?

It is the proportion of students who answered a question correctly. A value of 0.63 means 63% got it right. Higher means easier.

How many students do you need for item analysis?

Enough that one student does not swing the result. Around ten is a practical minimum for rough flags, and larger groups give steadier numbers.

Why use the top and bottom 27%?

It is a long-established convention for comparing the strongest and weakest groups while leaving out the middle, where small score differences are mostly noise. Some tools use other splits or correlation measures instead.