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Two-Sample t-Test Statistic Calculator — result sheet
Calculate a two-sample t statistic using either a pooled-variance or Welch unequal-variance standard error.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Welch t=(x̄₁−x̄₂)/√(s₁²/n₁+s₂²/n₂), with Welch-Satterthwaite df; pooled mode uses sₚ²=((n₁−1)s₁²+(n₂−1)s₂²)/(n₁+n₂−2).
The variance mode is explicit because pooling and Welch procedures answer the same mean-difference question under different variance assumptions.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Sample 1 mean — minimum -1.0E+15; maximum 1.0E+15
- Sample 1 standard deviation — minimum 1.0E-6; maximum 1.0E+15
- Sample 1 size — minimum 2; maximum 1000000000
- Sample 2 mean — minimum -1.0E+15; maximum 1.0E+15
- Sample 2 standard deviation — minimum 1.0E-6; maximum 1.0E+15
- Sample 2 size — minimum 2; maximum 1000000000
- Variance assumption — 2 choices
Worked example
| Input | Value |
|---|---|
| Sample 1 mean | 105 |
| Sample 1 standard deviation | 10 |
| Sample 1 size | 25 |
| Sample 2 mean | 100 |
| Sample 2 standard deviation | 12 |
| Sample 2 size | 30 |
| Variance assumption | welch |
Welch t ≈ 1.6855 with about 53.0 degrees of freedom.
Assumptions and limits
- Samples are independent and the summary statistics use compatible units.
- Normality and independence assumptions should be assessed for inferential use.
- The calculator returns a statistic and degrees of freedom, not a final hypothesis decision.
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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