t test from summary data
Test the difference between two means, or a paired mean difference, from the numbers printed in a paper, without the raw data.
Your data does not go to our server. This tool runs in your browser; what you type or open never leaves your device.
This calculator needs JavaScript, because it calculates in your browser and sends nothing. Turn JavaScript on to use it. How it is calculated is explained below.
- Difference of the means
- Welch test (unequal variances)
- Confidence interval of the difference (Welch)
- Student test (equal variances)
- Confidence interval of the difference (Student)
- Paired t test
- Confidence interval of the mean difference
How it is calculated
P values are two-sided and come from the t distribution; the interval of the difference uses the matching critical t value.
Use the standard deviation, not the standard error. If a paper gives the standard error, multiply it by the square root of the group size first.
Welch: t = (M₁ − M₂) / √(SD₁²/n₁ + SD₂²/n₂), df by Welch–SatterthwaiteStudent: t = (M₁ − M₂) / √[SDpooled² × (1/n₁ + 1/n₂)], df = n₁ + n₂ − 2Paired: t = mean difference / (SD / √n), df = n − 1
Worked example: Means 10 and 12, SD 2, 10 per group: t = −2.236, df = 18, P = 0.038.
Sources
These calculators support research; they do not replace the advice of a statistician or a clinician.
Questions
Welch or Student?
Welch's test does not assume equal variances and is the safer default. Student's test gives almost the same answer when the groups are similar in size and spread.