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Item Discrimination Index Calculator

Work out item discrimination index instantly with clear inputs, formula shown and shareable results.

About Item Discrimination Index Calculator

Discrimination index D is the difference in success rate between the top and bottom performing groups, usually the upper and lower 27%. With 24 of 30 correct in the top group and 9 of 30 in the bottom, D is 0.50 - excellent. A negative D means stronger candidates did worse, which almost always signals a mis-keyed or ambiguous item.

Formulas

Discrimination index

D = (upper correct - lower correct) / group size

Group definition

conventionally the top and bottom 27% of candidates by total score

Worked example

With the default values below, Item Discrimination Index Calculator returns Discrimination Index D of 0.5000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Correct answers in the top groupminimum 0
24
Correct answers in the bottom groupminimum 0
9
Candidates in each groupminimum 1
30

Results

Discrimination Index D
0.5000
Proportion Correct In The Top Group
0.800
Proportion Correct In The Bottom Group
0.300
Interpretation
Excellent discrimination

Step by step

  1. 1Values used
  2. 2Discrimination index
  3. 3Group definition
  4. 4Discrimination Index D= 0.5000
  5. 5Proportion Correct In The Top Group= 0.800
  6. 6Proportion Correct In The Bottom Group= 0.300
  7. 7Interpretation= Excellent discrimination

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why use 27% for the groups?

Kelley showed it maximises the reliability of the difference for a normally distributed trait, balancing group extremity against group size.

What does a negative index mean?

Usually a wrong answer key, a misleading distractor or an ambiguous stem. Such items should be removed before scoring.

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