Spearman-Brown Prophecy Formula Test Length & Reliability Calculator

Predict how adding or removing exam questions changes test reliability.

Predicted New Test Reliability (r*)
0.86 r*
Test Length Multiplier (n) 2 ×
Reliability Gain (+Δr) 0.1 +r
Items Needed for 0.85 Reliability 54 items
Inputs
items
Current number of questions on the test.
r
Current test reliability coefficient (r).
items
Proposed new number of questions on the test.
Results & Graph
Predicted New Test Reliability (r*)
0.86 r*
Test Length Multiplier (n)
2 ×
Reliability Gain (+Δr)
0.1 +r
Items Needed for 0.85 Reliability
54 items

Predicted New Test Reliability (r*)

Graph 1 • Current Item Count Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
0 r* 0.5 r* 1.1 r* 50%: 0.93 r* 0.9 50% 75%: 0.89 r* 0.9 75% 100%: 0.86 r* 0.9 100% 125%: 0.84 r* 0.8 125% 150%: 0.81 r* 0.8 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Predicted New Test Reliability (r*) 0.86 r* Test Length Multiplier (n) 2 × Reliability Gain (+Δr) 0.1 +r Items Needed for 0.85 Reliability 54 items
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Predicted New Test Reliability (r*)0.86 r*Test Length Multiplier (n)2 ×Reliability Gain (+Δr)0.1 +rItems Needed for 0.85 Reliability54 items
Summary: Scaling the exam from 30 to 60 items (2× length) changes reliability from 0.76 to 0.864.
Summary: Scaling the exam from 30 to 60 items (2× length) changes reliability from 0.76 to 0.864.
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Formula & Mathematical Methodology: Spearman-Brown Prophecy Formula

rnew = (n × rold) / [ 1 + (n − 1) × rold ], where n = NewItems / OldItems
r_new = (n × r_old) / [ 1 + (n − 1) × r_old ], where n = NewItems / OldItems
  • currentItemCount: Current Item Count (items)
  • currentReliabilityR: Current Reliability R (r)
  • proposedItemCount: Proposed Item Count (items)

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

Worked Example: Benchmark Scenario: Spearman-Brown Prophecy

Predict how adding or removing exam questions changes test reliability.

  1. Enter your raw test counts, credit hours, or schedule parameters.
  2. Evaluate the formula: r_new = (n × r_old) / [ 1 + (n − 1) × r_old ], where n = NewItems / OldItems.
  3. Inspect the primary score/duration, supporting metrics, and 3 SVG graphs.
Result: Computes Spearman-Brown Prophecy via r_new = (n × r_old) / [ 1 + (n − 1) × r_old ], where n = NewItems / OldItems.

Frequently Asked Questions

How does the Spearman-Brown Prophecy Formula Test Length & Reliability Calculator calculate results?

It evaluates r_new = (n × r_old) / [ 1 + (n − 1) × r_old ], where n = NewItems / OldItems 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

Spearman-Brown Prophecy Formula Test Length & Reliability Calculator: inputs, method, and how to read the result

Predict how adding or removing exam questions changes test reliability.

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.

  • Current Item Count: Current number of questions on the test.
  • Current Reliability R: Current test reliability coefficient (r).
  • Proposed Item Count: Proposed new number of questions on the test.

What the calculation includes

With the default values shown, Predicted New Test Reliability (r*) is 0.86 r*. The calculation follows Spearman-Brown Prophecy Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Current Item Count from 30 items to 33 items changes Predicted New Test Reliability (r*) from 0.86 r* to 0.85 r*. 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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