T-Test Calculator (Two Samples, Welch or Pooled)
Paste the two samples and choose the test and alternative hypothesis.
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T-Test Calculator (Two Samples, Welch or Pooled) by TheCalcTools
How the T-Test Calculator (Two Samples, Welch or Pooled) works
A two-sample t-test asks whether two group means differ more than chance would explain. t = (mean A − mean B) ÷ standard error. Welch’s version does not assume equal variances and adjusts the degrees of freedom (Welch–Satterthwaite); Student’s version pools the variances.
The p-value is the probability of a t at least this extreme if the true means were equal. The calculator computes it exactly from the t distribution.
The formula
Worked example
Using the default values shown in the calculator:
| Sample A | 12.1, 14.3, 13.8, 15.2, 12.9, 14.7, 13.5, 15.9 |
|---|---|
| Sample B | 11.2, 12.8, 12.1, 13.0, 11.9, 12.4, 13.3, 11.5 |
| Test | Welch (unequal variances, recommended) |
| Alternative hypothesis | Two-sided: means differ |
| Significance level α | 0.05 |
- Means 14.0500 and 12.2750: t = 3.4865 with 11.40 degrees of freedom.
- p = 0.004831. Reject the null hypothesis at α = 0.05: the difference is statistically significant.
Result:
| t statistic | 3.4865 |
|---|---|
| Degrees of freedom | 11.40 |
| p-value | 0.004831 |
| Conclusion | Reject the null hypothesis at α = 0.05: the difference is statistically significant |
| Mean A | 14.0500 |
| Mean B | 12.2750 |
| Difference in means | 1.7750 |
Frequently asked questions
Welch or Student?
Welch’s test is the safer default: it is nearly as powerful when variances are equal and much more reliable when they are not.
Does the data need to be normal?
Roughly, for small samples. With 30 or more per group the test is robust to moderate skew.
Sources and further reading
- NIST/SEMATECH e-Handbook of Statistical Methods
- Wikipedia: Welch's t-test
- Wikipedia: Student's t-test
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.