How it works
Set a = s₁²/n₁ and b = s₂²/n₂. Welch t = (mean₁ − mean₂)/√(a+b); approximate degrees of freedom = (a+b)² / (a²/(n₁−1)+b²/(n₂−1)).
Input definitions
- First sample mean
- Enter the value in the labeled unit.
- First sample standard deviation
- Enter the value in the labeled unit.
- First sample size
- Enter the value in the labeled unit.
- Second sample mean
- Enter the value in the labeled unit.
- Second sample standard deviation
- Enter the value in the labeled unit.
- Second sample size
- Enter the value in the labeled unit.
A worked example
- First sample mean
- 10
- First sample standard deviation
- 2
- First sample size
- 20
- Second sample mean
- 8
- Second sample standard deviation
- 3
- Second sample size
- 20
Assumptions & limits
Entered-data numeric worksheet. Floating-point calculations are rounded for display. Statistical results describe the entered sample and depend on the stated model assumptions.
Sources & review
Maintained by AnsRio. Methods and examples use automated checks; this does not imply independent professional certification.
Method updated 2026-10-17. Content checked against the stated method and examples. Our verification approach.
Common questions
Is this a paired t test or an equal-variance test?
Neither. Welch’s method handles two independent samples without assuming equal population variances. Paired observations require a test of within-pair differences.
How does Welch two-sample t statistic and degrees of freedom work?
Set a = s₁²/n₁ and b = s₂²/n₂. Welch t = (mean₁ − mean₂)/√(a+b); approximate degrees of freedom = (a+b)² / (a²/(n₁−1)+b²/(n₂−1)).
What are the limits of Welch two-sample t statistic and degrees of freedom?
Entered-data numeric worksheet. Floating-point calculations are rounded for display. Statistical results describe the entered sample and depend on the stated model assumptions.