Two-Sample Welch t-Test Calculator
Enter your own sample summary statistics. Two-sided test; fixed α = 0.05. No raw data or external dataset is loaded.
Two-sided test; fixed α = 0.05. No raw data or external dataset is loaded.
Null hypothesis: the population mean difference is 0.
- t
- Degrees of freedom
- Two-sided p value
- Lower bound
- Upper bound
Assumes independent samples, independent observations within each sample, and approximately normal populations for small samples. Unequal variances are allowed. t = (mean1 − mean2)/√(s1²/n1 + s2²/n2); df uses Welch–Satterthwaite. The interval estimates population mean1 − mean2. No pooled-variance option.
Numerical scope: each sample size is limited to 1,000,000. Extreme scales or nonconvergence are rejected; a p value displayed as 0 can reflect floating-point underflow.
A QUICK WALKTHROUGH
How to use this tool
- Enter your own sample summary statistics.
- Calculate the two-sided test at α = 0.05.
- Review t, degrees of freedom, p value and the 95% confidence interval.
Method and assumptions
Assumes independent samples, independent observations within each sample, and approximately normal populations for small samples. Unequal variances are allowed. t = (mean1 − mean2)/√(s1²/n1 + s2²/n2); df uses Welch–Satterthwaite. The interval estimates population mean1 − mean2. No pooled-variance option.
Local calculation
Only the summary statistics you enter are used. Calculations run in your browser. Numerical scope: each sample size is limited to 1,000,000. Extreme scales or nonconvergence are rejected; a p value displayed as 0 can reflect floating-point underflow.
GOOD TO KNOW
Common questions
Does a nonsignificant result prove equal means?
No. Failing to reject the null hypothesis does not establish equivalence. Check the confidence interval and whether the sampling assumptions apply.