Written by Dackohn; last reviewed November 2026.
Use Welch’s t-test by default. It does not assume equal variances, and it loses almost nothing when they are equal. Student’s test can go badly wrong when group sizes and variances both differ: in our simulation its false-positive rate reached 29.4% instead of 5%.
The difference
Student’s test pools the two variances into one estimate and uses df = n₁ + n₂ − 2. That assumes both groups have the same population variance. Welch’s test keeps the variances separate and adjusts the degrees of freedom. See how to do a t-test by hand.
What the simulation shows
We simulated 400,000 experiments for each scenario with no real difference between groups, and counted how often each test gave p < .05. A correct test should say 5%.
| Group sizes | SDs | Student false positives | Welch false positives |
|---|---|---|---|
| 20 and 20 | 1 and 1 | 5.0% | 5.0% |
| 20 and 20 | 1 and 4 | 5.6% | 5.0% |
| 10 and 40 | 4 and 1 | 29.4% | 5.1% |
| 40 and 10 | 4 and 1 | 0.1% | 5.0% |
Welch stays close to 5% throughout. Student fails in two opposite ways:
- Smaller group more variable: far too many false positives (29.4%).
- Larger group more variable: far too few (0.1%), which also costs power to detect real effects.
With equal group sizes, Student’s test is fairly robust even with unequal variances.
What does Welch cost?
Almost nothing. With equal variances, 20 per group and a true difference of 0.8 SD, power was 69.3% for Student and 69.2% for Welch.
Should I test for equal variances first?
No. Running Levene’s test and then choosing the t-test based on the result is a common recipe, but it adds a decision that can distort error rates, and the variance test has low power in small samples, which is when you need it most. Simply use Welch.
When Student’s test makes sense
- You have strong reason to believe the variances are equal, and very small samples, where the pooled estimate adds some power.
- You need consistency with ANOVA, since a pooled t-test equals a one-way ANOVA on two groups (F = t²). The ANOVA calculator also reports Welch’s ANOVA.
R’s t.test uses Welch by default, and so does our t-test calculator.
Try it yourself
T-Test From Means and SDs →See Welch and Student side by side on your numbers. T-Test Calculator →Run Welch’s test on raw data.Frequently asked questions
Is Welch's t-test better than Student's?
As a default, yes. It holds its error rate when variances differ and loses very little power when they are equal.
Does Welch's test need equal sample sizes?
No. It handles unequal sizes and unequal variances.
What does SPSS report?
SPSS shows both, on rows labelled equal variances assumed and not assumed. The second row is Welch's test.
Related reading: How to do a t-test by hand · T-test vs z-test · Paired vs independent samples
Sources & further reading: NIST/SEMATECH e-Handbook of Statistical Methods · OpenStax Introductory Statistics. How we compute & validate: methodology. Written & reviewed by Dackohn; last reviewed August 2026.