What makes a t-test "paired"?

A paired t-test is used when each observation in one sample has a direct one-to-one correspondence with an observation in the other sample — for example, the same subject measured before and after a treatment. It tests whether the mean of the within-pair differences is zero.

How is the p-value calculated here?

The tool uses a JavaScript implementation of the incomplete beta function to evaluate the two-tailed p-value from the t-distribution with (n-1) degrees of freedom. For very large samples the result converges to a z-test approximation.

What significance levels are available?

You can choose alpha = 0.10 (90% confidence), alpha = 0.05 (95% confidence, the most common default), or alpha = 0.01 (99% confidence). The null hypothesis is rejected when p < alpha.

What are the assumptions of this test?

The differences between pairs should be approximately normally distributed (or n should be large enough for the Central Limit Theorem to apply), the pairs should be independent of each other, and the data should be measured on at least an interval scale.

Can I use this for unpaired (independent) samples?

No. For two independent groups use a two-sample (independent) t-test. This tool only implements the paired design where each row in Sample A corresponds to the same subject or matched unit as the same row in Sample B.

How many data points do I need?

You need at least two pairs. In practice, a paired t-test is most reliable with n >= 10 pairs. Both samples must have the same number of values.

Paired T Test Calculator

Name: Paired T Test Calculator
Availability: InStock
Author: Nham Vu

Enter two related samples as comma-separated numbers, and instantly get the t-statistic, degrees of freedom, p-value, and significance result.

Enter Your Data

Sample A (before / group 1)

Sample B (after / group 2)

Significance Level (alpha)

Load Example

Enter your two paired samples and click Run Test

n (pairs)

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Mean Diff (d)

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SD of Diff

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Std Error

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t-statistic

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Deg. of Freedom

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Two-tailed p-value

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Alpha

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Pairwise Differences

#	A	B	d = A-B

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Summary

Enter two related samples as comma-separated numbers, and instantly get the t-statistic, degrees of freedom, p-value, and significance result.

How it works

Enter the first sample values as comma-separated numbers in the "Sample A" field.
Enter the matching second sample values in the "Sample B" field — each position must pair with the same position in Sample A.
Select your desired significance level (alpha): 0.10, 0.05, or 0.01.
Click "Run Test" to compute the mean difference, standard deviation of differences, standard error, t-statistic, and degrees of freedom.
The tool approximates the two-tailed p-value using the t-distribution and renders a clear significant / not significant decision.
Copy the results summary to clipboard for use in a report or homework submission.

Use cases

Compare pre-test and post-test scores for a student cohort.
Analyze before-and-after measurements in a clinical or lab study.
Evaluate whether a training program changed participant performance.
Test matched-pair experimental designs in psychology or biology.
Verify homework answers for introductory statistics courses.
Quick sanity-check for paired data before running full statistical software.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu