Two-Sample t-Test (Welch's)
Test whether two means differ. t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂).
Result
t-statistic
-1.7532
df ≈ 56.2 · two-tail p ≈ 0.079565.
- Mean diff (m₁ − m₂)-5.0000
- Standard error2.851900
- t-1.753217
- df (Welch)56.17
- p-value (two-tail)0.079565
- Significant α=0.05?✗
Step-by-step
- SE = √(s₁²/n₁ + s₂²/n₂) = 2.8519.
- t = (50 − 55) / 2.8519 = -1.7532.
- Two-tail p (normal approx) ≈ 0.0796.
How to use this calculator
- Enter mean, SD, n for each group.
About this calculator
Welch's t-test compares means of two independent samples without assuming equal variances. Formula: t = mean diff / SE. Welch-Satterthwaite df is more conservative than Student's. p < 0.05 conventionally significant. For paired observations: paired t-test (different formula). For >2 groups: ANOVA. Source: Welch (1947); Student's "Probable Error of a Mean" (1908).
Frequently asked
Welch doesn't assume equal variances. More conservative. Default in modern stats.
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