Practice — Causal Inference Basics (5 questions)

A "smart playlists" feature shipped to everyone last quarter. Users who turned it on have 30-day retention of 72%; users who did not have 55%. A PM writes "smart playlists lift retention by 17 points" in the quarterly review.

1. Write the naive difference as a decomposition into a causal quantity and a bias term, and explain in words what the bias term is.
2. Name the causal estimand the PM actually cares about, and give a concrete reason the bias term is probably positive here.
3. Sketch, in one paragraph, an observational analysis you would run instead, listing the assumption it needs and one check you would do.