t-Test Calculator
Run Welch's two-sample t-test and get the t statistic, degrees of freedom and p-value.
Input Data
Results
At a glance:Welch's t = (x̄₁−x̄₂)/√(s₁²/n₁ + s₂²/n₂); df estimated by Welch–Satterthwaite.
Formula
t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂)
$$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{s_1^2/n_1 + s_2^2/n_2}}$$How to Use
- Enter the means, standard deviations and sample sizes of the two groups.
- The calculator outputs the t statistic and degrees of freedom df.
- Read the two-tailed p-value.
- If p < 0.05, the difference between the two group means is significant at the 5% level.
FAQ
How is Welch's t-test different from Student's t-test?
Student's t-test assumes equal variances; Welch's does not assume equal variances and is more robust to unequal variances. Most statistical software defaults to Welch's.
Does a significant p-value mean the difference is large?
No. The p-value only tells whether the difference is unlikely due to chance; it says nothing about effect size. With large samples, a tiny difference can be significant — interpret alongside an effect size (e.g. Cohen's d).
References
Content reviewed by the Calculatorism editorial team. Results are for reference only; please refer to the relevant authorities for the official figures.