Item Analysis (Difficulty & Discrimination) Calculator
Analyze test item difficulty index (P) and discrimination index (D) using Kelly’s 27% rule, with automatic Retain, Revise, or Discard evaluation decision badges for teachers.
How to Perform Test Item Analysis in 3 Simple Steps
Enter your Upper Group (Nu) and Lower Group (Nl) sizes, or use the Kelly's 27% quick calculator.
Input the number of correct responses from the Upper Group (Ru) and Lower Group (Rl) per item.
Review instant Difficulty (P) & Discrimination (D) indices alongside automatic Retain, Revise, or Discard badges. Copy the table for Chapter 4.
Item Analysis Sample Groups
Define the size of your Upper (Nu) and Lower (Nl) achievement groups.
Analyzed Test Questions
Good quality questions
Needs minor stem/option edit
Poor or negative discrimination
Test Item Response Matrix & Evaluation
Input correct answers (Ru and Rl) per question to compute live indices.
| Item | Question / Competency | Upper (Ru) | Lower (Rl) | Difficulty (P) | Diff. Interpretation | Discrimination (D) | Disc. Interpretation | Item Decision | Actions |
|---|---|---|---|---|---|---|---|---|---|
| Mean | Overall Assessment Averages | — |
Formula Substitution Breakdown & Diagnosis
Select any test item to inspect the exact algebraic substitution for your thesis defense.
This indicates that of the combined upper and lower groups correctly answered this question.
🎯 Difficulty Index (P) Reference Scale
| Range | Verbal Interpretation | Assessment Implication |
|---|---|---|
| 0.00 – 0.20 | Very Difficult | Too hard; few examinees got it right |
| 0.21 – 0.40 | Difficult | Challenging item |
| 0.41 – 0.60 | Average / Moderate | Ideal difficulty for discrimination |
| 0.61 – 0.80 | Easy | Accessible to most students |
| 0.81 – 1.00 | Very Easy | Too easy; provides little differentiation |
⚡ Discrimination Index (D) Scale (Ebel & Frisbie)
| Range | Quality Level | Action Decision |
|---|---|---|
| 0.40 and above | Very Good Item | Retain |
| 0.30 – 0.39 | Good Item | Retain |
| 0.20 – 0.29 | Reasonably Good | Revise |
| 0.00 – 0.19 | Poor Item | Reject |
| Below 0.00 | Defective (Negative) | Discard |
How to Compute Index of Difficulty and Index of Discrimination in Test Item Analysis
A definitive measurement and evaluation guide for classroom teachers, psychometricians, and educational researchers.
1. What is Test Item Analysis?
Item analysis is a systematic statistical procedure used in educational measurement, psychometrics, and curriculum evaluation to evaluate the quality of individual test questions. Whether designing diagnostic, formative, or summative assessments, educators analyze student responses to ensure that each item accurately gauges student mastery, possesses an optimal challenge level, and functions reliably.
Two complementary metrics form the cornerstone of classical test theory (CTT):
- Index of Difficulty (P): Determines how easy or difficult an item was for the examinees.
- Index of Discrimination (D): Measures how effectively the question separates high-achieving examinees from low-achieving examinees.
2. Truman Lee Kelly’s 27% Rule Explained
To conduct an item analysis without scoring every individual script by hand, psychometricians rely on Kelly’s 27% Rule (established by Truman Lee Kelly in 1939). In this method:
- All exam answer sheets are ranked from highest overall score to lowest overall score.
- The top 27% of students are selected as the Upper Group (Nu).
- The bottom 27% of students are selected as the Lower Group (Nl).
- The middle 46% of test scripts are set aside, as Kelly demonstrated that 27% provides the optimal mathematical balance between sample size sensitivity and contrast between high and low achievement.
3. Mathematical Formulas and Calculations
Formula for Difficulty Index (P)
Where Ru is the count of correct answers in the upper group, Rl is the count in the lower group, and Nu + Nl is the combined upper and lower sample size.
Formula for Discrimination Index (D)
Where Ru - Rl represents the difference in correct responses between the upper and lower groups, divided by the number of students in one group (Nu, assuming Nu = Nl).
4. Making Action Decisions: Retain, Revise, or Discard
By combining both indices according to Ebel and Frisbie's classical criteria, every question is categorized into one of three actionable outcomes:
- Retain (Acceptable Item): An item has moderate difficulty (0.20 ≤ P ≤ 0.80) and strong discrimination (D ≥ 0.30). These items effectively test competence and can be safely deposited into the school's recurring exam test bank.
- Revise (Needs Modification): An item exhibits marginal discrimination (0.20 ≤ D < 0.30) or extreme difficulty (P < 0.20 or P > 0.80). The teacher must rewrite the question stem or replace implausible distractor options.
- Reject / Discard (Defective Item): An item produces low discrimination (D < 0.20) or a negative value (D < 0.00). When D is negative, lower-scoring students answered the question correctly more frequently than top-scoring students, pointing to severe ambiguity or an erroneous answer key.