ARBIMETRA LAB
Independent Samples T-test
Compares the means of two independent groups, with both pooled-variance and Welch versions.
What it does
Compares the means of two independent groups, with both pooled-variance and Welch versions.
Use it to compare an outcome between two separate groups.
Data you need
- Numeric outcome
- Two groups
Supported data: Numeric, Categorical. Level: Beginner.
Formula and method
t = (x̄₁ − x̄₂) / SE, SE² = s²ₚ(1/n₁ + 1/n₂) for the pooled form
The difference in group means is divided by its standard error. The pooled version combines the two variances and uses n₁ + n₂ − 2 degrees of freedom; the Welch version keeps them separate. Both are shown, with a median-centred Levene check.
Assumptions
- The groups are independent
- Pooled form: equal variances
Input checks
- Exactly two groups
- Each group needs at least 2 values
How to read the result
Prefer the Welch result when spreads differ.
Worked example
Illustrative run on Simulated study data (teaching data). These figures are the actual output of this model on that example, and they say nothing about your own data.
- Difference in means = 0.8314; t = 0.512, df = 231.7103, p = 0.6091.
- The difference is not statistically significant at the 5% level.
Limitations
- Independence cannot be checked from the numbers
Numerical validation
Validated 17 of 17 automated checks passed, including numerical results, invalid input, missing values, small samples, constant variables, charts and the interpretation text.
| Check | Reference | Result | Abs. error | Tolerance | Source |
|---|---|---|---|---|---|
| Pooled t | -1.8608 | -1.86081347 | 1.3e-5 | 1e-4 | Published R documentation output (Student's sleep data) |
| Pooled p | 0.07919 | 0.07918671 | 3.3e-6 | 1e-3 | Published R documentation output (Student's sleep data) |
| Welch shown as well | -1.8608 | -1.86081347 | 1.3e-5 | 1e-4 | Published R documentation output (Student's sleep data) |
Computed with python 3.13.2, numpy 2.2.5, scipy 1.14.1, pandas 2.3.3, statsmodels 0.14.4, scikit-learn 1.7.0, in your browser. A passing check confirms the listed comparison only. It does not make any result suitable for your data, and it is not a claim of equivalence with other statistical software.
Questions
Pooled or Welch?
Welch does not assume equal variances and is a sensible default. The pooled test assumes equal variances. Both are displayed.
ARBIMETRA LAB is an educational and research tool. Results should be checked by the researcher and are not professional advice.