Exam Item Difficulty (p-Value) & Upper/Lower 27% Discrimination Index Calculator

Audit test questions for ideal difficulty (0.3–0.7) and discrimination (D ≥ 0.30).

Item Discrimination Index (D)
0.5 D index
Item Difficulty (p-Value) 0.62 p (0–1)
Upper 27% Group Accuracy 86.67 %
Lower 27% Group Accuracy 36.67 %
Inputs
students/group
Number of examinees in the Upper 27% group (and equal Lower 27% group).
students
Examinees in the Upper 27% group who answered the item correctly.
students
Examinees in the Lower 27% group who answered the item correctly.
Results & Graph
Item Discrimination Index (D)
0.5 D index
Item Difficulty (p-Value)
0.62 p (0–1)
Upper 27% Group Accuracy
86.67 %
Lower 27% Group Accuracy
36.67 %

Item Discrimination Index (D)

Graph 1 • Group Size Each27 Pct Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 D index 0.5 D index 1.1 D index 50%: 1 D index 1 50% 75%: 0.67 D index 0.7 75% 100%: 0.5 D index 0.5 100% 125%: 0.4 D index 0.4 125% 150%: 0.33 D index 0.3 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Item Discrimination Index (D) 0.5 D index Item Difficulty (p-Value) 0.62 p (0–1) Upper 27% Group Accuracy 86.67 % Lower 27% Group Accuracy 36.67 %
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Item Discrimination Index (D)0.5 D indexItem Difficulty (p-Value)0.62 p (0–1)Upper 27% Group Accuracy86.67 %Lower 27% Group Accuracy36.67 %
Summary: Item difficulty p = 0.62 (61.7% correct) and discrimination index D = 0.5 (Strong discriminator ≥0.30).
Summary: Item difficulty p = 0.62 (61.7% correct) and discrimination index D = 0.5 (Strong discriminator ≥0.30).
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Interactive chart & math engine powered by CalculatorGraph

Formula & Mathematical Methodology: Item Difficulty & Discrimination Formula

pdifficulty = CorrectUpper + CorrectLower2 × Ngroup
Dindex = (CorrectUpper − CorrectLower) / Ngroup
p_difficulty = (CorrectUpper + CorrectLower) / (2 × N_group); D_index = (CorrectUpper − CorrectLower) / N_group
  • groupSizeEach27Pct: Group Size Each27 Pct (students/group)
  • correctInUpperGroup: Correct In Upper Group (students)
  • correctInLowerGroup: Correct In Lower Group (students)

Rounding: Standardized test and time rules follow official scoring rubrics; continuous outputs round to 2 decimal places.

Worked Example: Benchmark Scenario: Item Difficulty & Discrimination

Audit test questions for ideal difficulty (0.3–0.7) and discrimination (D ≥ 0.30).

  1. Enter your raw test counts, credit hours, or schedule parameters.
  2. Evaluate the formula: p_difficulty = (CorrectUpper + CorrectLower) / (2 × N_group); D_index = (CorrectUpper − CorrectLower) / N_group.
  3. Inspect the primary score/duration, supporting metrics, and 3 SVG graphs.
Result: Computes Item Difficulty & Discrimination via p_difficulty = (CorrectUpper + CorrectLower) / (2 × N_group); D_index = (CorrectUpper − CorrectLower) / N_group.

Frequently Asked Questions

How does the Exam Item Difficulty (p-Value) & Upper/Lower 27% Discrimination Index Calculator calculate results?

It evaluates p_difficulty = (CorrectUpper + CorrectLower) / (2 × N_group); D_index = (CorrectUpper − CorrectLower) / N_group directly in your browser and updates three custom SVG visualizations in real time.

Can I use Goal Seek to find the exact score or hours I need?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any input variable.

Are my academic or schedule inputs kept private?

Yes. All calculations run 100% locally in your browser.

Education · Writing, Research & Psychometrics

Exam Item Difficulty (p-Value) & Upper/Lower 27% Discrimination Index Calculator: inputs, method, and how to read the result

Audit test questions for ideal difficulty (0.3–0.7) and discrimination (D ≥ 0.30).

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Group Size Each27 Pct: Number of examinees in the Upper 27% group (and equal Lower 27% group).
  • Correct In Upper Group: Examinees in the Upper 27% group who answered the item correctly.
  • Correct In Lower Group: Examinees in the Lower 27% group who answered the item correctly.

What the calculation includes

With the default values shown, Item Discrimination Index (D) is 0.5 D index. The calculation follows Item Difficulty & Discrimination Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Group Size Each27 Pct from 30 students/group to 33 students/group changes Item Discrimination Index (D) from 0.5 D index to 0.45 D index. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses official published scoring scales, Carnegie unit conventions, and ISO calendar rules.
  • Official standardized test equating curves vary slightly by test form administration date.

Scope: Global Academic, Psychometric & ISO 8601 Time Standard Check the assumptions and limitations against your situation before relying on the estimate.

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