Welch's Two-Sample t-test

Welch's t-test compares the means of two independent samples without assuming their variances (or sample sizes) are equal — the safer default over the classic Student's t-test. Enter two groups as raw data or as summary statistics.

How it works

The statistic is t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂), evaluated against a Student-t distribution whose degrees of freedom come from the Welch–Satterthwaite equation (generally non-integer). The two-sided p-value and a confidence interval for the difference in means follow from that distribution; a one-sided alternative returns a one-sided bound. Cohen's d (pooled) is reported as a standardised effect size. All math runs client-side and is verified against SciPy reference values — see Software & sources.