Item Analysis Calculator (Difficulty & Discrimination Index)

How it works

p = correct ÷ total; D = p_upper − p_lower (upper and lower 27% groups); ideal p ≈ (1 + 1/options) ÷ 2; max D = 2p (p ≤ 0.5) or 2(1 − p); point-biserial ≈ correlation of item score with total

Classical item analysis judges each question by two numbers. Difficulty is simply the proportion who got it right — misnamed, since higher means easier — and the most informative items sit midway between the guessing rate and perfection, around 0.6 for four-option questions. Discrimination asks whether the item separates strong from weak students: the difference between the pass rates of the top and bottom 27% (Kelley showed 27% is the best trade-off between group size and separation), or equivalently the correlation between the item and the total score. Items with D above 0.3 are doing their job; near zero they add noise; negative values almost always mean a mis-keyed or ambiguous question, and a quick look at which distractors the top students chose usually reveals why.

Worked example

39 of 60 students answered correctly (p = 0.65, moderate, close to the 0.63 ideal for four options); 14 of the top 16 and 6 of the bottom 16 did — D = 0.875 − 0.375 = 0.50, very good, reaching 71% of the maximum 0.70 possible at that difficulty. Keep the item.

Frequently asked questions