When is a paired t-test the right design versus a two-sample t-test?
PICTURE THIS: DATA SPLIT
Fit on train, tune on val, report on test once.
Simple meaning
Paired tests use within-unit differences, such as before/after on the same user or matched markets, which removes stable unit-level noise and often raises power.
WHY — Hypothesis Testing instead of guessing?
Why interviewers care about Hypothesis Testing:
contrast on Hypothesis Testing, not two memorised paragraphs.
the developer, then one case where picking wrong hurts.
Name the idea, why it exists, then one short example.
End with when you use it and one common pitfall.
STEPS — What happens step by step?
Before you speak the answer, walk the interviewer through these steps:
- 1Paired tests use within-unit
differences, such as before/after on the same user or matched markets, which removes stable unit-level noise and often raises power.
- 2Two-sample tests compare independent
groups, which is the usual A/B assignment.
- 3Pairing incorrectly, for example
pairing unrelated users, manufactures dependence and invalidates p-values.
- 4Give an example
One tiny concrete case you can say aloud.
- 5Common mistake
What juniors usually get wrong.
- 6Close
When you pick this over the alternative.
EXAMPLE — See it in action
Here's a short line you can speak, broken into clear beats:
Note: Adapt this scaffold to your own project — keep it under 60–90 seconds.
Key takeaway
Paired tests use within-unit differences, such as before/after on the same user or matched markets, which removes stable unit-level noise and often raises power. Two-sample tests compare independent groups, which is the usual A/B assignment.