Skip to content
ENExplore Calculators

Reliability Of A Test Calculator

Work out reliability of a test instantly with clear inputs, formula shown and shareable results.

About Reliability Of A Test Calculator

The Spearman-Brown prophecy formula predicts reliability after changing test length: k.r/(1 + (k-1)r). Doubling a test at reliability 0.72 lifts it to 0.837, a gain of 0.117. Reaching 0.90 would need 3.5 times the length, which shows the sharply diminishing returns of simply adding items.

Formulas

Spearman-Brown formula

r(new) = k x r / (1 + (k - 1) x r)

Length required

k = target(1 - r) / (r(1 - target))

Worked example

With the default values below, Reliability Of A Test Calculator returns Projected Reliability of 0.8372. Change any input above and every figure here is recalculated in your browser.

Inputs used

Current reliabilityaccepts 0–1
0.72
Multiply the test length byminimum 0.1
2

Results

Projected Reliability
0.8372
Length Factor Needed For 0.90
3.50 x
Gain In Reliability
0.1172
Error Variance Remaining
16.28%

Step by step

  1. 1Values used
  2. 2Spearman-Brown formula
  3. 3Length required
  4. 4Projected Reliability= 0.8372
  5. 5Length Factor Needed For 0.90= 3.50 x
  6. 6Gain In Reliability= 0.1172
  7. 7Error Variance Remaining= 16.28

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Does adding items always help?

Only if they are of comparable quality and measure the same construct. Adding poor items can lower reliability rather than raise it.

Why the diminishing returns?

Because reliability is bounded at one. Each extra item reduces the remaining error variance by a smaller absolute amount.

Related Calculators

Reliability Of A Test Calculator | Calcrivo