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Statistics

Paired T-Test Calculator

Compare matched before-and-after measurements by testing the mean of paired differences.

Data stays on this deviceConvention explained below
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Data explorer

Check the dataset and sample convention before interpreting results.

See the method

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Your statistical summary

Your result

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Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter sample a, sample b, alternative hypothesis, significance level.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

Input reference and sample values

Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.

InputFormat and unitsSample
Sample AKeep the structure and separators shown in the sample. Line breaks are retained in this input.8, 10, 9, 12, 11
Sample BKeep the structure and separators shown in the sample. Line breaks are retained in this input.5, 7, 6, 8, 9
Alternative hypothesisChoose Two-sided: different / One-sided: greater / One-sided: less.Two-sided: different
Significance levelNumeric value. Minimum: 0.0001. Maximum: 0.2.0.05

Result for these sample inputs

0.000688909365 probability
Test statistic
9.48683298
Degrees of freedom
4
Decision at chosen alpha
Reject the null hypothesis
Mean difference A − B
3
Matched pairs
5
SD of differences
0.707106781

The p-value is not the probability that the null hypothesis is true. Choose the hypothesis and significance level before inspecting the result; statistical significance does not measure practical importance.

Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.

The method, explained

Form each difference Aᵢ − Bᵢ. t = mean difference/(SD of differences/√n), with df = n−1.

A WORKED EXAMPLE

Using sample a = 8, 10, 9, 12, 11, sample b = 5, 7, 6, 8, 9, alternative hypothesis = two, significance level = 0.05, the result is 0.000688909365 probability. Change these example inputs to match your task; use the method above to check each step.

What to keep in mind

Pairs must be genuinely matched. Differences between pairs should be independent and approximately normal for small samples. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Reference: NIST: statistical methods handbook

Common questions

Does the order of my values matter?

Yes. The first A value is paired with the first B value, and so on. Keep subject order identical in both lists; sorting them independently destroys the pairing.

Why are identical differences rejected?

When all differences are identical, their estimated standard deviation is zero and the ordinary t statistic is undefined. The calculator reports this condition rather than inventing a finite result.

Methodology maintained by ClarityKit. How these tools are built and checked.