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Paired T Test Calculator

Work out paired t test instantly with clear inputs, formula shown and shareable results.

About Paired T Test Calculator

The paired t-test reduces two related samples to a single set of differences, then tests whether their mean is zero. Pairing removes between-subject variation, which usually gives much greater power than an independent-samples test.

Formula

Paired t

t = d̄ / (s_d/√n), where d are the within-pair differences

Worked example

With the default values below, Paired T Test Calculator returns t statistic of 7.31925055. Change any input above and every figure here is recalculated in your browser.

Inputs used

Before values
12, 15, 14, 16, 13, 18
After values
14, 18, 15, 19, 16, 21

Results

t statistic
7.31925055
Mean difference
2.50000000
Two-tailed p value
0.00074612
Degrees of freedom
5

Step by step

  1. 1Values used
  2. 2Paired t
  3. 3t statistic= 7.31925055
  4. 4Mean difference= 2.50000000
  5. 5Two-tailed p value= 0.00074612
  6. 6Degrees of freedom= 5

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 8 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

For the sample before and after values?

The differences are 2, 3, 1, 3, 3 and 3, with mean 2.5 and t ≈ 8.0623 on 5 df — highly significant.

When must I use a paired test?

Whenever each observation in one group is naturally matched to one in the other, such as before-and-after measurements on the same subjects.

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