Welch's t-Test Calculator

Two-sample Welch's t-test — the drop-in replacement for Student's t when the two groups have unequal variances (which they almost always do in real data). Enter raw values or summary statistics for group A and group B, and get the t-statistic, Welch–Satterthwaite degrees of freedom, two-sided p-value, effect size (Cohen's d), and a 95% confidence interval for the mean difference. Everything runs in your browser.

Raw samples

Summary statistics

Drug vs placebo Landing page A/B API latency (ms)

Group A (comma / whitespace / newline separated)

Group B

Group A

mean

std dev

Group B

mean

std dev

Alternative hypothesis

Significance α

Confidence interval

Result

t-distribution with your t-statistic

Curve is Student's t with the Welch–Satterthwaite degrees of freedom above. The shaded tail area equals the reported one-sided p-value; for a two-sided test both tails are shaded and the sum equals the two-sided p-value.

How it works

Test statistic. t = (x̄_A − x̄_B) / √(s_A²/n_A + s_B²/n_B)

Welch–Satterthwaite df. ν = (s_A²/n_A + s_B²/n_B)² / ((s_A²/n_A)²/(n_A−1) + (s_B²/n_B)²/(n_B−1))

p-value. Uses the regularized incomplete beta function to evaluate the Student's t CDF at the observed t; two-sided doubles the smaller tail.

Effect size. Reported as Cohen's d using the pooled SD, plus Glass's Δ (using group A as reference) and Hedges's g for the small-sample correction.

When to use. Welch's test is recommended over Student's t whenever the two groups may have different variances or unequal n — it controls Type I error better and there is no downside when variances happen to be equal.