When do you use a paired t-test?

easy

Answer

$Same subjects measured under two conditions (before / after treatment), or naturally paired observations (twins, matched pairs).$
$d_{i}\; = \;X_{A}i\; - \;X_{B}i$
$Much more powerful than an unpaired test when the within-pair correlation is high — cancels out subject-level variation.$
$Assumption: differences approximately normal (CLT-robust for n > 30).$

Check yourself — multiple choice

Independent samples
Same subjects / matched pairs: t-test on differences $d\; = \;X_{A}\; - \;X_{B}$ → cancels subject-level variation, higher power
Only for classification
Same as two-sample

Paired t: t on within-pair differences; higher power under correlation.

#hypothesis-testing#parametric-tests

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