Paired t-Test Calculator

Test whether the average difference between matched pairs, such as before and after measurements on the same people, is different from zero.

Paired data

Enter the pairs in the same order in both lists (person 1 first, and so on).

Alternative hypothesisConfidence level for the interval (%)

t statistic

3.274

p-value

0.0136

Differences (Before − After): 5, 1, 5, -1, 8, 1, 6, 3

Mean difference d̄ = 3.5, s_d = 3.0237, SE = s_d ÷ √n = 1.069

t = d̄ ÷ SE = 3.5 ÷ 1.069 = 3.274, df = n − 1 = 7

95% CI for the mean difference: 0.972 to 6.028 (t* = 2.365)

Effect size d_z = d̄ ÷ s_d = 1.158

At the 5% level there is significant evidence that Before and After differ (p = 0.0136). The average difference is 3.5. A significant p-value shows a difference is unlikely to be chance; the confidence interval and d_z show how big it is.

How to use this tool

Enter the first measurement for each subject in the first box and the second measurement in the second box, in the same order.
Choose a two-sided test, or a one-sided test if you decided the direction before collecting data.
Set the confidence level for the interval, usually 95.
Read the t statistic, p-value, confidence interval, and effect size, and the working shown below.

Formula Reference

Differences

dᵢ = xᵢ − yᵢ

t statistic

t = d̄ ÷ (s_d ÷ √n), df = n − 1

Confidence interval

d̄ ± t* × s_d ÷ √n

Effect size

d_z = d̄ ÷ s_d

Articlet-Tests: One-Sample, Two-Sample and Paired ArticleHypothesis Testing Framework ArticleEffect Size Calct-Test Calculator (one-sample, two-sample, paired)CalcEffect Size Calculator GlossaryGlossary: p-Value

Frequently Asked Questions

When should I use a paired t-test?+

Use it when each observation in one group is naturally matched with one in the other: the same people measured twice, twins, or matched pairs. Because it works on the differences within pairs, it removes person-to-person variation and is usually more powerful than treating the groups as independent.

What are the assumptions?+

The differences should be roughly normally distributed, particularly for small samples, and the pairs should be independent of each other. Outliers in the differences can distort the result, so plot them first.

What if my data are not normal?+

With a very small sample and clearly non-normal differences, consider a nonparametric alternative such as the Wilcoxon signed-rank test, or a permutation test on the differences.

When is a one-sided test appropriate?+

Only when the direction was fixed before seeing the data and a difference in the opposite direction would not matter. Choosing the direction after looking at the results inflates the false-positive rate.

Paired data

Enter the pairs in the same order in both lists (person 1 first, and so on).

Alternative hypothesis

Confidence level for the interval (%)

How to use this tool

Enter the first measurement for each subject in the first box and the second measurement in the second box, in the same order.

Choose a two-sided test, or a one-sided test if you decided the direction before collecting data.

Set the confidence level for the interval, usually 95.

Read the t statistic, p-value, confidence interval, and effect size, and the working shown below.