What item difficulty is optimal for a test?

For maximum score variance and reliability, average item difficulty should be around p = 0.50–0.60 on a multiple-choice test (accounting for guessing). Items with p 0.90 are too easy; 0.30–0.80 is the acceptable range. For classroom mastery tests, p = 0.70–0.85 is appropriate.

What discrimination index is acceptable?

Discrimination index D: < 0.20 marginal item (should be revised or removed); 0.20–0.29 acceptable; 0.30–0.39 good; ≥ 0.40 excellent. A negative D indicates the item is answered correctly more often by low scorers than high scorers — almost certainly a flawed item that should be reviewed.

Item Analysis: Difficulty and Discrimination Index

Formula Definitions

The Item Analysis: Difficulty and Discrimination Index works by applying a well-defined formula to the values you enter. Understanding the formula behind the calculation helps you interpret the result and check that your inputs are correct. Below we break down the key components that drive the Item Difficulty Index.

The core formula used by this calculator is:

Result = f(inputs, settings)

Each variable in the formula has a specific meaning:

inputs — Values entered into the Item Difficulty Index.
settings — Options, units, or parameters that adjust how the calculation is performed.
Result — Computed output for the chosen inputs and settings.

How to Use This Calculator

Enter the required values. Enter the required values into the Item Analysis: Difficulty and Discrimination Index input fields.
Adjust settings. Adjust any settings, select applicable options, or choose units as needed.
Calculate the result. Press Calculate to compute the result using the underlying formula.
Interpret the output. Review and interpret your result using the provided context, reference ranges, or explanatory notes.

Glossary and Definitions

Input: A value entered into the calculator to be processed.
Output: The computed result returned by the calculator for the given inputs.
Setting: An option that adjusts how the calculation is performed, such as unit selection or mode.
Item analysis: A key concept referenced by the Item Difficulty Index: Calculate item difficulty index p = proportion answering correctly and item discrimination D = (upper 27% correct – lower 27% correct) / n for test items. Identify items that are too easy (p > 0.90), too hard (p < 0.20), or poorly discriminating (D < 0.20).
Item difficulty: A key concept referenced by the Item Difficulty Index: Calculate item difficulty index p = proportion answering correctly and item discrimination D = (upper 27% correct – lower 27% correct) / n for test items. Identify items that are too easy (p > 0.90), too hard (p < 0.20), or poorly discriminating (D < 0.20).
Discrimination index: A key concept referenced by the Item Difficulty Index: Calculate item difficulty index p = proportion answering correctly and item discrimination D = (upper 27% correct – lower 27% correct) / n for test items. Identify items that are too easy (p > 0.90), too hard (p < 0.20), or poorly discriminating (D < 0.20).
Test development: A key concept referenced by the Item Difficulty Index: Calculate item difficulty index p = proportion answering correctly and item discrimination D = (upper 27% correct – lower 27% correct) / n for test items. Identify items that are too easy (p > 0.90), too hard (p < 0.20), or poorly discriminating (D < 0.20).
Classical test theory: A key concept referenced by the Item Difficulty Index: Calculate item difficulty index p = proportion answering correctly and item discrimination D = (upper 27% correct – lower 27% correct) / n for test items. Identify items that are too easy (p > 0.90), too hard (p < 0.20), or poorly discriminating (D < 0.20).
Item statistics: A key concept referenced by the Item Difficulty Index: Calculate item difficulty index p = proportion answering correctly and item discrimination D = (upper 27% correct – lower 27% correct) / n for test items. Identify items that are too easy (p > 0.90), too hard (p < 0.20), or poorly discriminating (D < 0.20).