Item difficulty and discrimination calculator

Interactive tool

Calculate item statistics

Use equal-sized upper and lower groups for the discrimination calculation.

Reset example

Total attempts Total correct Upper-group size Upper-group correct Lower-group size Lower-group correct

Difficulty index0.72

72% answered correctly in this administration.

Discrimination index0.40

Useful positive separation for this administration.

These values describe one administration. They do not prove validity and should not decide an item’s fate without content review.

Item difficulty formula

For a one-mark item, the difficulty index is the proportion of attempts answered correctly:

Difficulty index = total correct ÷ total attempts

A result of 0.72 means 72% of the learners who attempted the item answered correctly. A higher number means the item was easier for that group. This is sometimes called the facility value because the word difficulty can feel backward.

Upper-lower discrimination formula

A simple classroom method compares equal-sized groups with stronger and weaker total assessment performance:

Discrimination index = upper-group proportion correct − lower-group proportion correct

If 18 of 20 learners in the upper group and 10 of 20 in the lower group answered correctly, the result is 0.90 minus 0.50, which equals 0.40. This is a useful positive result for that administration.

How to interpret the results responsibly

Pattern	Possible meaning	Review action
Very easy with positive discrimination	An essential outcome may be widely mastered	Keep it if the blueprint requires that coverage
Very hard with positive discrimination	A demanding item may still be functioning	Confirm alignment and that the content was taught
Moderate difficulty with weak discrimination	Ambiguity, guessing or mixed skills may be involved	Inspect the stem, key, options and scoring
Negative discrimination	The key, wording or an alternative answer may be wrong	Review promptly with a subject expert

Do not apply one threshold to every assessment. Small groups produce unstable estimates, and broad tests can behave differently from narrow tests. Read the statistics with the question, answer key, curriculum alignment, distractor choices and test blueprint.

What the calculator does not measure

• It does not establish that a question or test is valid.
• It does not calculate a point-biserial correlation from student-level data.
• It does not diagnose why an item behaved unexpectedly.
• It does not replace fairness, accessibility, curriculum and subject review.

For the complete workflow, examples and distractor review, read Item Analysis in Education.

Frequently asked questions

What is a good difficulty index?

There is no universal ideal. The appropriate value depends on the learning outcome and assessment purpose. A diagnostic check can intentionally include accessible items, while a selection assessment may need more separation.

What does a negative discrimination index mean?

It means the lower group answered correctly more often than the upper group in this administration. Check the key first, then inspect ambiguity, alternative answers, scoring, curriculum alignment and group size.

Can I use this calculator with a small class?

Yes, as a prompt for review, but do not treat a small-group result as a stable property of the item. Retain the evidence and compare it with future administrations.

Is student-level data sent to Examiar?

No. This page calculates from the counts entered in your browser. Do not enter names, IDs or other personal information.