Two-sample t-test: pooled vs Welch — when to use each?

medium

Answer

$Compare two group means.$
$\mathrm{df}\; = \;n_{1}\; + \;n_{2}\; - \;2$
$Welch's: doesn't assume equal variances \to uses Satterthwaite df correction.$
$In practice, Welch is the safer default (behavior similar to Student when variances are equal, better when they aren't).$
$Both assume i.i.d. within groups and approximate normality (CLT-robust for larger n).$

Check yourself — multiple choice

Only pooled
Pooled: equal variance assumption; Welch: no equal-variance assumption + Satterthwaite df — Welch is the safer default
Same thing
Always use pooled

Two-sample t: Welch's is safer (no equal-variance assumption).

#hypothesis-testing#parametric-tests

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