Welch’s vs Student’s t-Test: When Variances Differ
The independent-samples t-test comes in two flavors. Student's t-test assumes the two groups have equal variances; Welch's t-test drops that assumption and adjusts the degrees of freedom accordingly.
Modern methodological guidance (e.g. Delacre, Lakens, & Leys, 2017) recommends using Welch's by default: it controls the Type I error rate well even when variances and sample sizes are unequal, and it costs almost nothing when variances happen to be equal.
Student vs Welch at a glance
| Student's t | Welch's t | |
|---|---|---|
| Equal-variance assumption | Required | Not required |
| Degrees of freedom | n₁ + n₂ − 2 | Welch–Satterthwaite |
| Unequal n + unequal variance | Inflated error | Robust |
| Recommended default | No | Yes |
Why not just run Levene's test first?
Choosing Student vs Welch based on a preliminary Levene test creates a two-stage procedure that can distort error rates. Defaulting to Welch avoids that conditioning problem.
Effect size and reporting
Report Cohen's d alongside the t statistic, the Welch-adjusted df (often non-integer), and the p-value.
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