Test Analysis
Focused calculation
Item Difficulty Index Calculator
Find the proportion of valid attempts answered correctly and retain incorrect and omitted counts.
Enter one item's response counts
Difficulty depends on the tested group
The same item can be easy for one cohort and difficult for another.
Interpret the rate with instruction, opportunity to learn, and test purpose.
The estimate becomes easier to schedule when you check whether the item separates upper and lower groups.
Calculation basis
Assumption: Higher facility means more respondents answered correctly; the statistic is often called item difficulty despite that direction.
One item across a hundred responses
Among 100 responses, 68 correct gives 68.0% facility; 25% were incorrect and 7% were omitted.
Omissions deserve their own review
A high omission rate may reflect time pressure, layout, unclear instructions, or lack of knowledge.
Combining omissions with chosen incorrect answers can hide a usability problem.
After the first result is recorded, inspect how incorrect options function.
Reconcile the response categories
- Confirm the keyed answer.
- Reconcile correct, incorrect, and omitted responses.
- Calculate from one administration.
- Inspect the item before revising it.
Questions that affect interpretation
Does a high percentage mean a difficult item?
No. In the conventional facility index, a higher value means more respondents were correct.
Should omitted responses be excluded?
Follow the analysis plan; this page keeps them in the full administered-response denominator.
What is a good item difficulty?
It depends on the assessment purpose and score use.
Review the item in context
Store the item identifier, key, administration, population, response counts, and any scoring correction. A revised key changes the classification of every affected response.
For multi-point items, a dichotomous facility rate may discard meaningful partial-credit information.
Compare versions only when wording, answer options, placement, and time conditions remain sufficiently stable.
Never remove an item solely because its index looks unusual; content importance and evidence of ambiguity also matter.
Facility should be interpreted differently for a mastery check, screening item, diagnostic probe, and speeded test. A very high value may be desirable for essential prerequisite knowledge rather than evidence that an item is unnecessary.
Inspect subgroup counts carefully before comparing facility. Differences can reflect opportunity to learn, language demands, accommodations, or sampling, and they require more than an aggregate percentage to understand.
A facility index should be calculated after resolving invalid responses, duplicate attempts, and scoring appeals. If an item is removed from the test, retain its diagnostic analysis separately but do not leave its responses in a denominator described as the final scored form.