Welch versus pooled t-test, when variances differ

Question

You compare the means of two independent samples that may have different variances and different sizes.

When should you use Welch's t-test instead of the classic pooled (Student) t-test, and what is the risk of getting it wrong?

Accepted Answer

The two tests. Both compare \bar{x}1 - \bar{x}2, but they estimate its standard error differently. - Pooled (Student): assumes the two groups share a common variance and pools them into one estimate sp^2. Standard error = sp\sqrt{	frac{1}{n1} + 	frac{1}{n2}}, with n1 + n2 - 2 degrees of freedom. - Welch: does not assume equal variances. Standard error = \sqrt{	frac{s1^2}{n1} + 	frac{s2^2}{n2}}, with a fractional (Welch-Satterthwaite) degrees of freedom. When to use Welch. Whenever the variances might differ, especially with unequal group sizes. The pooled test is only exact when variances…

Welch versus pooled t-test, when variances differ

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