Modified Angoff Exam Cut Score, Passing Threshold & Cohen’s Kappa Agreement Calculator

Determine exam passing cut scores using Modified Angoff SME ratings and cohort normal distribution.

Modified Angoff Passing Cut Score
65 / 100 items (64.5%)
Estimated Cohort Passing Rate (%) 83.437 %
Estimated Failing Rate (%) 16.563 %
Cohort Mean Margin Above Cut (Z-Score) 0.95 SDs
Inputs
⚡ Scenarios:
items
Total number of scored questions on the certification or licensing exam.
%
SME panel mean probability (%) that a minimally competent candidate answers items correctly.
%
Observed examinee cohort mean percentage score (%).
%
Observed examinee cohort standard deviation (%).
Results & Graph
Modified Angoff Passing Cut Score
65 / 100 items (64.5%)
Estimated Cohort Passing Rate (%)
83.437 %
Estimated Failing Rate (%)
16.563 %
Cohort Mean Margin Above Cut (Z-Score)
0.95 SDs

Modified Angoff Passing Cut Score

Graph 1 • Modified Angoff Cut Score • Domain Architecture & Live Telemetry Maps Total Exam Questions, Sme Average Borderline Prob Pct, Examinee Cohort Mean Pct through Modified Angoff Cut Score Formula.
Modified Angoff Passing Cut Sc: 65 / 100 items (64 Modified Angoff Cut Score • Invariants & Metrics Modified Angoff Passing Cut 65 / 100 items (64.5%) Estimated Cohort Passing Rat 83.437 % Estimated Failing Rate (%) 16.563 % Cohort Mean Margin Above Cut 0.95 SDs
Graph 2 • Modified Angoff Passing Cut Score Across Total Exam Questions Sweep (40% → 160%) Evaluates CutScore_Raw = TotalItems × AverageBorderlineProbability; PassRate% = across 7 operating points (current input highlighted).
0 / 100 57.20 / 100 114.4 / 100 26 40items 39 60items 52 80items 65 100items 78 120items 91 140items 104 160items
Graph 3 • Joint Sensitivity: Total Exam Questions × Sme Average Borderline Prob Pct Compares Modified Angoff Passing Cut Score when Sme Average Borderline Prob Pct is shifted +25% (solid) vs. −25% (dashed).
0 / 100 57.75 / 100 115.5 / 100 --- Sme Average Borderline Prob Pct @ 75% 57 -30% 69 -15% 81 +0% 93 +15% 105 +30%
Summary: An Angoff borderline rating of 64.5% sets the minimum passing score at 65/100 items, resulting in an estimated 83.4% cohort pass rate (Z = +0.95).
Summary: An Angoff borderline rating of 64.5% sets the minimum passing score at 65/100 items, resulting in an estimated 83.4% cohort pass rate (Z = +0.95).
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Formula & Mathematical Methodology: Modified Angoff Cut Score Formula

CutScoreRaw = TotalItems × AverageBorderlineProbability
PassRate% = Φ( (CohortMean − CutScore%) / CohortSD )
CutScore_Raw = TotalItems × AverageBorderlineProbability; PassRate% = Φ( (CohortMean − CutScore%) / CohortSD )
  • totalExamQuestions: Total number of scored questions on the certification or licensing exam.
  • smeAverageBorderlineProbPct: SME panel mean probability (%) that a minimally competent candidate answers items correctly.
  • examineeCohortMeanPct: Observed examinee cohort mean percentage score (%).
  • examineeCohortSdPct: Observed examinee cohort standard deviation (%).

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Modified Angoff Cut Score Worked Example

Determine exam passing cut scores using Modified Angoff SME ratings and cohort normal distribution.

  1. Enter the input measurement, system configuration, or astronomical parameter.
  2. Apply the standard conversion or analytical equation: CutScore_Raw = TotalItems × AverageBorderlineProbability; PassRate% = Φ( (CohortMean − CutScore%) / CohortSD ).
  3. Inspect the primary metric, secondary equivalents, and 3 real-time SVG graphs.
Result: Computes Modified Angoff Cut Score via CutScore_Raw = TotalItems × AverageBorderlineProbability; PassRate% = Φ( (CohortMean − CutScore%) / CohortSD ).

Frequently Asked Questions

How does the Modified Angoff Exam Cut Score, Passing Threshold & Cohen’s Kappa Agreement Calculator perform the calculation?

It evaluates CutScore_Raw = TotalItems × AverageBorderlineProbability; PassRate% = Φ( (CohortMean − CutScore%) / CohortSD ) directly in your browser and renders three custom SVG charts in real time.

Can I solve backwards for an input parameter using Goal Seek?

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

Does this tool work offline?

Yes. All calculations run 100% locally in your browser with full offline PWA support.

Education · Psychometrics & Assessment

Modified Angoff Exam Cut Score, Passing Threshold & Cohen’s Kappa Agreement Calculator: inputs, method, and how to read the result

Determine exam passing cut scores using Modified Angoff SME ratings and cohort normal distribution.

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.

  • Total Exam Questions: Total number of scored questions on the certification or licensing exam.
  • Sme Average Borderline Prob Pct: SME panel mean probability (%) that a minimally competent candidate answers items correctly.
  • Examinee Cohort Mean Pct: Observed examinee cohort mean percentage score (%).
  • Examinee Cohort Sd Pct: Observed examinee cohort standard deviation (%).

What the calculation includes

With the default values shown, Modified Angoff Passing Cut Score is 65 / 100 items (64.5%). The calculation follows Modified Angoff Cut Score Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Total Exam Questions from 100 items to 110 items changes Modified Angoff Passing Cut Score from 65 / 100 items (64.5%) to 71 / 110 items (64.5%). This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses official NIST Special Publication 811, IEEE/RFC systems engineering, APA psychometric, and USNO astronomical formulas.
  • Empirical metallurgy and calendar conversions represent standard reference-condition approximations.

Scope: Global NIST, IEEE, APA & Astronomical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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