T-Test Calculator (One-Sample, Two-Sample & Paired)
Run a one-sample, two-sample (Welch or pooled) or paired t-test from raw data or means and SDs: t, df, p-value, confidence interval and Cohen's d.
The t-test assumes independent observations and roughly normal data (or differences, for a paired test); with 30 or more per group it is robust to moderate skew. Welch's test does not assume equal variances and is the safer default for two independent groups.
| Group | n | Mean | SD | SE |
|---|---|---|---|---|
| Sample 1 | 10 | 26 | 2.7889 | 0.881917 |
| Sample 2 | 9 | 22.4444 | 2.2973 | 0.76578 |
A t-test asks whether a difference between means is larger than random sampling would usually produce. This calculator runs the one-sample test (a mean against a known value), the two-sample test for independent groups (Welch's version, or the pooled version that assumes equal variances) and the paired test for before/after or matched measurements, from raw data or from means, standard deviations and sample sizes.
How to use this tool
- Choose the test: two independent groups, paired measurements, or one sample against a known mean.
- Paste raw data, or switch to summary statistics and enter each mean, SD and n.
- Set the hypothesised difference (usually 0), the alternative and the confidence level.
- Read t, the degrees of freedom, the p-value, the confidence interval and Cohen's d.
Formula
Welch: t = (x̄₁ − x̄₂ − Δ₀) ÷ √(s₁²/n₁ + s₂²/n₂) · df = (s₁²/n₁ + s₂²/n₂)² ÷ [(s₁²/n₁)²/(n₁−1) + (s₂²/n₂)²/(n₂−1)] · Paired and one-sample: t = (d̄ − Δ₀) ÷ (s_d/√n), df = n − 1
The pooled test uses s_p = √[((n₁−1)s₁² + (n₂−1)s₂²) ÷ (n₁+n₂−2)] with df = n₁ + n₂ − 2. Cohen's d divides the mean difference by the pooled SD (two-sample), by s (one-sample) or by the SD of the differences (paired, d_z).
Example
Group 1 (24, 27, 21, 30, 26, 28, 25, 29, 23, 27; mean 26.0) against group 2 (21, 23, 20, 25, 22, 24, 19, 26, 22; mean 22.44) gives Welch's t = 3.044 with 16.89 df and a two-tailed p = 0.007372, so the difference of 3.56 is significant at the 5% level. The pooled test gives t = 3.012 with 17 df (p = 0.007853).
Frequently asked questions
Welch or pooled: which should I use?
Welch's test is the safer default. It stays accurate when the groups have different variances or sizes, and loses almost nothing when the variances happen to be equal.
When is a paired test right?
When each value in one sample is linked to one value in the other: the same people before and after, twins, or left and right eyes. Pairing removes the person-to-person variation, which usually makes the test more sensitive.
My data are not normal. Can I still use a t-test?
With 30 or more per group the t-test is fairly robust to skew. For small, clearly skewed samples or outliers, a rank-based test such as Mann–Whitney or Wilcoxon signed-rank is safer.
Sources
Last updated:
Page address with these inputs: https://kakao.mobile/tools/two-sample-t-test-calculator/
Cite or embed this tool
kakaoCalc. (2026, November 9). T-Test Calculator (One-Sample, Two-Sample & Paired). https://kakao.mobile/tools/two-sample-t-test-calculator/
“T-Test Calculator (One-Sample, Two-Sample & Paired).” kakaoCalc, 9 Nov. 2026, kakao.mobile/tools/two-sample-t-test-calculator/.
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