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Test Retest Reliability Calculator

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

About Test Retest Reliability Calculator

Test-retest reliability is the correlation between two administrations, and it converts into a standard error of measurement of sd times sqrt(1 - r). At r = 0.82 with a 12 point standard deviation the SEM is 5.09, so a change must exceed about 14.1 points to be distinguishable from measurement noise at 95% confidence.

Formulas

Standard error of measurement

SEM = sd x sqrt(1 - reliability)

Minimal detectable change

MDC = 1.96 x sqrt(2) x SEM

Worked example

With the default values below, Test Retest Reliability Calculator returns Test-Retest Reliability of 0.820. Change any input above and every figure here is recalculated in your browser.

Inputs used

Correlation between the two administrationsaccepts -1–1
0.82
Interval between testsminimum 0 days
14 days
Standard deviation of scoresminimum 0
12

Results

Test-Retest Reliability
0.820
Standard Error Of Measurement
5.091
Minimal Detectable Change
14.112
Interpretation
Good stability

Step by step

  1. 1Values used
  2. 2Standard error of measurement
  3. 3Minimal detectable change
  4. 4Test-Retest Reliability= 0.820
  5. 5Standard Error Of Measurement= 5.091
  6. 6Minimal Detectable Change= 14.112
  7. 7Interpretation= Good stability

Assumptions and limits

  • The result is derived only from the 3 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 3 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

How long should the retest interval be?

Long enough to prevent memory of the answers, short enough that the trait has not genuinely changed - usually two to four weeks.

Why is minimal detectable change larger than the SEM?

Because two measurements each carry error, so their difference has sqrt(2) times the error of one, and the 95% criterion adds the 1.96 factor.

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