Paired t-Test Calculator
A paired t-test evaluates whether the mean within-pair difference differs from zero, using the number of pairs, mean difference and sample standard deviation of those differences.
How to use this calculator
- Enter the paired difference defined as after minus before, the sample size and sample SD of differences.
- Check that all inputs use the same units, period and population scope.
- Change one assumption at a time when comparing scenarios.
Formula used by paired t test calculator
t = mean difference ÷ (SD of differences ÷ √n); df = n − 1; a two-sided p-value uses the Student t distribution.
- t = mean difference ÷ (SD of differences ÷ √n); df = n − 1; a two-sided p-value uses the Student t distribution.
- Assumes independent pairs and approximately normal differences. Summary inputs cannot reveal outliers or verify assumptions; p-values are not effect-size measures.
- The tool validates inputs and rounds displayed figures for readability; it does not validate assumptions against external records.
Worked examples
Worked example
For 12 paired observations, mean difference 3.4 and SD 4.2, the standard error is about 1.21.
t ≈ 3.4 ÷ (4.2 ÷ √12) ≈ 2.80 with 11 degrees of freedom.
The calculator reports t, degrees of freedom and a two-sided p-value.
Understanding the result
A paired t-test evaluates whether the mean within-pair difference differs from zero, using the number of pairs, mean difference and sample standard deviation of those differences.
Assumes independent pairs and approximately normal differences. Summary inputs cannot reveal outliers or verify assumptions; p-values are not effect-size measures.
Important notes
Assumes independent pairs and approximately normal differences. Summary inputs cannot reveal outliers or verify assumptions; p-values are not effect-size measures.
Treat the result as an estimate from the entered assumptions. For commercial, statistical, engineering or health-related decisions, verify relevant specifications and professional guidance.
Frequently asked questions
When should I use a paired test?
When each before measurement is meaningfully paired with an after measurement or matched observation.
Does a small p-value prove causation?
No. Design, confounding, sample quality and the effect estimate all matter.
How should I interpret this result?
Assumes independent pairs and approximately normal differences. Summary inputs cannot reveal outliers or verify assumptions; p-values are not effect-size measures.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
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This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.