paired student t test calculator - Aaron Graves, PhDude Replica

Sample 1 values (before, condition A, pre-test)

Enter numbers separated by commas, spaces, or new lines.

Sample 2 values (after, condition B, post-test)

Must contain the same number of values as Sample 1. Each row/position is a pair.

Alternative hypothesis

Significance level (α)

What this paired Student t test calculator does

This calculator performs a paired Student t test, which compares two related measurements from the same subjects. It calculates the test statistic, degrees of freedom, p-value, and a confidence interval for the mean difference.

Typical use cases include:

Before-and-after measurements on the same people
Matched pairs (such as twins or closely matched participants)
Two methods applied to the same items

When to use a paired t test

Use it when data are dependent

A paired t test is appropriate when each value in Sample 1 has a direct counterpart in Sample 2. The analysis is based on the differences within each pair, not on independent group means.

Do not use it for independent groups

If your two samples come from different, unrelated participants, you should use an independent samples t test instead.

Assumptions

The pairs are meaningfully matched.
The differences are approximately normally distributed (especially important for small sample sizes).
The data are measured on an interval or ratio scale.
Pairs are independent of other pairs.

How the statistic is computed

Let each paired difference be d_i = x_i - y_i. The calculator computes:

Mean difference \(\bar{d}\)
Standard deviation of differences \(s_d\)
Standard error \(SE = s_d / \sqrt{n}\)
t statistic \(t = \bar{d} / SE\)
Degrees of freedom \(df = n - 1\)

The p-value comes from the t distribution with df = n - 1.

How to interpret the output

p-value: if p < α, reject the null hypothesis of zero mean difference.
Mean difference: direction and size of the change (Sample1 - Sample2).
Confidence interval: plausible range of the true mean difference.
Cohen’s d_z: standardized effect size for paired data.

Example

Suppose 8 students take a quiz before and after a short intervention. Enter pre-scores in Sample 1 and post-scores in Sample 2. If the p-value is below 0.05, there is evidence that the mean score changed.

Common mistakes to avoid

Using unequal list lengths (every value must have a pair).
Mixing up pair order across lists.
Using paired test for independent groups.
Interpreting statistical significance as practical importance without effect size context.