paired difference t test calculator

Use this tool for before-and-after or otherwise matched data. Enter values for each pair in the same order (one value in Sample A matched with one value in Sample B).

Sample A (e.g., before)

Sample B (e.g., after)

Hypothesized mean difference (μ₀)

Alternative hypothesis

Significance level (α)

Tip: You can separate numbers with commas, spaces, tabs, or new lines.

What is a paired difference t test?

A paired difference t test (also called a paired samples t test or dependent t test) evaluates whether the average difference between two related measurements is statistically different from a target value (usually 0). It is designed for data where observations come in natural pairs.

Typical use cases

Before vs. after scores for the same people
Left vs. right side measurements for the same subject
Two testing methods applied to the same items
Matched pairs studies (e.g., twins, matched participants)

How this calculator works

The calculator first computes each pair’s difference:

d_i = A_i − B_i

Then it estimates:

n: number of pairs
Mean difference: \(\bar{d}\)
Standard deviation of differences: \(s_d\)
Standard error: \(SE = s_d/\sqrt{n}\)
t-statistic: \(t = (\bar{d} - \mu_0) / SE\)
Degrees of freedom: \(df = n - 1\)
p-value based on your selected alternative hypothesis

Interpreting the output

p-value and significance

If p-value is less than α (for example 0.05), you reject the null hypothesis and conclude that the mean paired difference is statistically different from μ₀ (or greater/less, depending on your alternative).

Confidence interval

For two-sided tests, the confidence interval gives a plausible range for the true mean difference. If the interval excludes μ₀, that aligns with a significant result at the same α.

Assumptions of the paired t test

The data are paired correctly and pairs are meaningful.
Pairs are independent from each other.
The distribution of differences is approximately normal (especially important for small n).
The measurement scale is continuous (or close enough for practical use).

Common mistakes to avoid

Using an independent samples t test when the data are paired.
Mismatching pair order between Sample A and Sample B.
Interpreting significance as practical importance.
Ignoring effect size and confidence intervals.

Quick example

Suppose five participants take a quiz before and after a training session. If you enter before scores in Sample A and after scores in Sample B, the calculator evaluates whether the average change differs from zero. A negative mean difference (A − B) would suggest scores tended to increase after training (because B is larger).

Final note

This tool is great for fast analysis and learning. For formal reporting, include the test direction, t-statistic, degrees of freedom, p-value, and confidence interval, plus context about study design and assumptions.