Welch or Student? Which t-Test Should You Use?

Open any statistics course and the independent-samples t-test arrives with an assumption attached: equal variances. Open modern software and the default is often a different test, Welch's. They are two versions of one idea, and the difference between them can flip a conclusion. Here is when it matters, and why.

What actually differs

Both tests compare the means of two independent groups. Student's version pools the two variances into one estimate, which makes sense only if the groups truly have equal spread. Welch's version keeps the variances separate and adjusts the degrees of freedom. When variances and sample sizes are equal, the two give essentially the same answer.

Example one: the small group is the noisy one

Suppose Group A has 12 people with a mean of 50 and a standard deviation of 15, while Group B has 48 people with a mean of 58 and a standard deviation of 6. Computed with the equal-variance assumption, the p-value is about 0.005. With Welch's correction it is about 0.095.

The pooled test treated the noisy small group as if it were as steady as the large one, and announced a difference that Welch's test does not support.

Example two: the small group is the quiet one

Now swap the spreads. Group A, still 12 people, has a standard deviation of 6, and Group B, still 48 people, has 15. The equal-variance test now gives p ≈ 0.077, while Welch's gives about 0.006. This time the pooled test is too cautious and misses a difference that Welch's test detects.

So the pooled test can err in either direction. When the smaller group has the larger variance it tends to be too liberal, and when the smaller group has the smaller variance it tends to be too conservative.

Why not test the variances first?

A tempting workflow runs a variance test and then picks Student or Welch. A paper arguing for Welch's test as the default shows that this two-step approach often fails to give an appropriate answer, that Welch's test controls false positives better when variances differ, and that it loses little when they are equal (Delacre, Lakens and Leys, 2017). The same group reached a similar conclusion for ANOVA, recommending Welch's F test by default (Delacre et al., 2019).

A practical rule

Use Welch's test by default for two independent groups. Report both means, both standard deviations, the group sizes, the difference with its confidence interval, and which version you used. Plot the data first with the descriptive statistics calculator to see whether the spreads differ, and use the raw-data t-test calculator when you have the individual values.

Welch's test does not cure everything. It still assumes roughly normal data or reasonably large samples. If outliers or heavy skew dominate, the Mann-Whitney test may be the better question, as discussed in our piece on t-test versus Mann-Whitney. Software defaults differ: some packages run Welch's test unless told otherwise, while others pool variances. Check which one your output reports, and say so in your methods. A p-value alone never says whether the difference matters, so describe its size in practical terms.

For measurements taken twice on the same people, neither test applies. The paired samples t-test calculator is the right tool, as our article on before-and-after data explains.