Welch's t-test vs Student's t-test: Why Welch's Should Be Your Default

You have two groups, continuous data, and you reach for a t-test. The software gives you a choice: Student’s (equal-variance) or Welch’s (unequal-variance). SPSS labels them “Equal variances assumed” and “Equal variances not assumed”; R’s t.test() defaults to Welch’s; Prism defaults to Student’s. The decision matters more than the labels suggest, and most introductory training points the wrong way.

Short version: use Welch’s by default. The next two sections cover why, when Student’s still has a niche, and what to do about the Levene’s-test routine many of us were taught.

What the Two Tests Actually Differ On

Both tests compute a t-statistic of the form (mean difference) / (standard error of the difference). They differ only in how the standard error and degrees of freedom are calculated.

Welch’s also uses the Welch–Satterthwaite approximation for degrees of freedom, which is generally fractional (you’ll see t(37.4) in the output, not t(38)). Student’s uses df = n₁ + n₂ − 2, always an integer.

When the two groups have equal variance and equal sample sizes, the two tests give nearly identical results. They diverge when (a) variances differ between groups, (b) sample sizes are unequal, or especially (c) both at once.

Comparison Criteria

Researchers comparing the two tests usually care about four things: validity when assumptions are violated, statistical power, sample-size flexibility, and what reviewers expect to see.

When Student’s Goes Wrong

The textbook claim is that Student’s is “robust” to violations of the equal-variance assumption. That claim has a critical qualifier: it only holds when sample sizes are equal. The worst case is when the smaller group has the larger variance — Type I error rates can inflate from a nominal 5% to 15% or higher (Delacre, Lakens, & Leys, 2017, in International Review of Social Psychology).

Welch’s does not have this fragility — it controls Type I error correctly across the full grid of variance ratios and sample-size ratios that practitioners actually encounter. The simulation evidence is unambiguous: Welch’s has α close to nominal in nearly all conditions; Student’s does not.

The Levene’s-Test Workflow Doesn’t Help

The workflow many of us learned is: run Levene’s test for equal variance first; if Levene’s p > .05, use Student’s; otherwise switch to Welch’s. This is a two-step procedure that inflates the Type I error rate of the combined test. Levene’s has poor power at small samples, so “Levene’s p > .05” often means “we lack power to detect unequal variance” rather than “variances are equal.” The decision then defaults to Student’s in conditions where Welch’s would have been safer.

The current methodological consensus, summarized by Delacre et al. and Lumley et al. (Annual Review of Public Health, 2002): skip the variance-equality test entirely and use Welch’s as the default. The tradeoff — a tiny power loss when variances really are equal — is dramatically outweighed by Welch’s correct Type I error under heterogeneity.

When Student’s Still Makes Sense

Student’s is still defensible in a narrow set of cases:

• Equal-variance assumption defensible from prior data. If you have meta-analytic or large-sample prior evidence that the two populations have very similar variances (e.g., physical-constant measurements, well-characterized assays), Student’s gives a small power boost. State the prior evidence in your methods.
• Equal group sizes by design AND theoretical reason for equal variance. Balanced randomized trials with no known reason for heteroscedasticity. Even then, the power gain from Student’s is small.
• Replication of a prior paper that used Student’s. Some replication frameworks demand using the original test even when a better one is now available. Report both if possible.

None of these apply to most field, clinical, or behavioral research, where sample sizes drift (dropouts, screen failures) and variance can differ between treatment and control by mechanism alone.

Reporting in the Methods Section

The methods section should name the test explicitly. “Welch’s independent-samples t-test” (not “independent t-test” or just “t-test”) tells the reviewer exactly which procedure ran. With Welch’s, the degrees of freedom in the results will be fractional — report it as given, don’t round to an integer. Example, APA-style:

Effect size for Welch’s: Cohen’s d is computed the same way (mean difference divided by a pooled or control-group SD). Hedges’ g is the small-sample-corrected version and is now preferred in many journals. The choice doesn’t hinge on Student’s vs. Welch’s — it’s an independent decision.

Verdict by Researcher Type

If you do biomedical or clinical research: use Welch’s by default. The Cochrane Handbook is variance-agnostic but reviewers in clinical trials and translational research increasingly expect Welch’s. The cost of getting Type I error wrong in a trial publication is far higher than the cost of a tiny power loss.

If you do social or behavioral research: use Welch’s. APA 7th edition is silent on the variance assumption but treats effect size and CI reporting as load-bearing, both of which are robust to the choice.

If you do bench biology: Welch’s if your group sizes can drift (technical failures, sample loss) or your treatment plausibly changes variance (e.g., a knockout that increases biological heterogeneity). Student’s only if equal variance is supported by prior data and your design enforces equal n.

If you’re responding to reviewer comments asking why you used Welch’s: cite Delacre, Lakens, & Leys (2017) and report that you used Welch’s by default because it controls Type I error correctly across both equal and unequal variances. That answer holds up.

When the Right Test Isn’t a t-test At All

Two situations push you off Welch’s entirely:

• Normality strongly violated, small samples. Welch’s assumes approximately normal data (the assumption applies to residuals, not raw values). For small samples with skewed distributions, the Mann-Whitney U test is more appropriate. It does not assume normality, has roughly 95% asymptotic relative efficiency vs. the t-test when normality holds, and gains power when it doesn’t.
• Three or more groups. Welch’s has a one-way ANOVA analog — the Welch heteroscedastic F-test, available as oneway.test(..., var.equal = FALSE) in R. It plays the same role as Welch’s t-test does for two groups. If you’re running multiple t-tests instead of a single ANOVA, see why this inflates your false-positive rate.

If you’re unsure which test fits your design, the test-selection decision guide walks through the variable-type and group-structure questions in order.

Summary Decision Table

If your data are already in a sheet and you want to check what the right test is for a specific structure, GraphHelix surfaces the variance check inline with the test recommendation — so you can see whether the equal-variance assumption is supported before committing to a methods-section claim.