Question Difficulty Index Calculator
Calculate item difficulty from proportion correct or mean score divided by maximum score for partial-credit questions.
Calculate item difficulty index
Measure how easy or difficult a test question was using the proportion of students who answered correctly, or use mean score ÷ maximum score for partial-credit items.
What is a question difficulty index?
In classical test item analysis, the difficulty index is commonly the proportion of examinees who answer an item correctly. For a right/wrong question, p = number correct ÷ number who answered. A p-value of 0.70 means 70% of the group answered correctly.
Why a higher difficulty index means an easier question
The name can be counterintuitive: as the difficulty index rises, the observed success rate rises. An item with p = 0.90 was answered correctly by 90% of the group and was therefore easy for that group. An item with p = 0.20 was answered correctly by only 20% and was more difficult for that group.
Partial-credit item difficulty
For an item that can earn multiple points, this calculator can use mean item score ÷ maximum possible item score. That produces the average proportion of available points earned and keeps the index on a 0-to-1 scale.
Difficulty is group-dependent
An item does not have one permanent difficulty value. The index depends on the students who took the test, instruction, wording, administration conditions and scoring method. Difficulty should also be reviewed alongside discrimination, distractor performance, content coverage and learning objectives before revising an assessment.