paired t test calculator

Enter two equal-length lists of matched observations (for example, before vs after). Values can be separated by commas, spaces, or new lines.

Sample A (Before / Condition 1)

Sample B (After / Condition 2)

Significance level (α)

How to use this paired sample t test calculator

Paste your first list into Sample A and the matching list into Sample B.
Make sure both lists have the same number of values and each row (or position) is a true pair.
Choose your significance level, commonly 0.05.
Click Calculate to get the t-statistic, degrees of freedom, p-value, confidence interval, and effect size.

Important: this calculator computes differences as B - A. A positive mean difference means Sample B tends to be higher than Sample A.

What is a paired t test?

A paired t test (also called a dependent t test or matched-pairs t test) checks whether the average difference between two related measurements is statistically different from zero. The key word is related: every value in Sample A must pair with exactly one value in Sample B.

Common use cases

Before-and-after designs (weight before and after a program)
Repeated measures on the same participants (reaction time in two conditions)
Matched pairs (twins, matched subjects, or devices tested under two settings)

Paired t test formula (conceptual)

Let each paired difference be d_i = B_i - A_i. The test statistic is:

t = mean(d) / (s_d / √n)

Where:

mean(d) is the average of the paired differences
s_d is the sample standard deviation of the differences
n is the number of pairs
df = n - 1 are the degrees of freedom

The p-value comes from the Student's t distribution with n - 1 degrees of freedom.

Assumptions you should check

Pairs are meaningfully matched and independent from other pairs.
The difference scores are approximately normally distributed (especially important for small n).
Data are continuous or near-continuous.
No severe outliers in the difference scores.

How to interpret the output

p-value

If p is less than α (for example, 0.05), you reject the null hypothesis that the true mean difference equals zero.

Confidence interval

The 95% confidence interval for the mean difference gives a useful effect range. If it excludes zero, that aligns with statistical significance at α = 0.05.

Effect size (Cohen's d_z)

Cohen's d_z = mean(d) / s_d. Rough interpretation guidelines are often 0.2 (small), 0.5 (medium), and 0.8 (large), but context matters.

Paired vs independent t test

Use a paired t test when observations are linked (same person measured twice). Use an independent t test when observations come from two unrelated groups.

Common mistakes

Using paired t test on unmatched groups.
Reversing pair order unintentionally (which changes the sign of the mean difference).
Ignoring outliers in the differences.
Treating statistical significance as practical significance without considering effect size.

Quick FAQ

What if my sample size is very small?

The paired t test can still be used, but checking normality of differences becomes more important. Consider a nonparametric alternative like the Wilcoxon signed-rank test if assumptions are questionable.

Can I use percentages or scores?

Yes, as long as each pair is matched and values are numeric.

What does a negative mean difference mean?

Because this calculator uses B - A, a negative result means Sample B tends to be lower than Sample A.