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Welch Degrees of Freedom Calculator — result sheet
Calculate the Welch–Satterthwaite degrees of freedom for an unequal-variance two-sample mean comparison.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: ν=(s₁²/n₁+s₂²/n₂)²/((s₁⁴/(n₁²(n₁−1)))+(s₂⁴/(n₂²(n₂−1)))).
Welch’s approximation avoids forcing the two groups to share one population variance when their spreads may differ.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Group 1 standard deviation — minimum 0; maximum 1000000000000
- Group 1 sample size — minimum 2; maximum 1000000000
- Group 2 standard deviation — minimum 0; maximum 1000000000000
- Group 2 sample size — minimum 2; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| Group 1 standard deviation | 10 |
| Group 1 sample size | 30 |
| Group 2 standard deviation | 12 |
| Group 2 sample size | 28 |
Welch degrees of freedom ≈52.72.
Assumptions and limits
- The groups are independent and sample standard deviations are supplied.
- Each group has at least two observations.
- The degrees of freedom support a follow-on Welch procedure but do not provide a p-value alone.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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