##### Scenario Meta is evaluating a new social feature called **Circle** (similar to Facebook Groups), where members join a group and post and comment within it. You own product analytics for Circle and need to decide how to measure it and how to optimize it. ##### Question Assume Circle is the focus of analysis and that guardrail metrics and cannibalization concerns are **out of scope** — concentrate on engagement and retention. Answer the following: 1. **Success metrics.** What metrics would you track to measure the success of Circle? Define a primary north-star metric and the supporting metrics around it. 2. **Small vs. large groups (retrospective only).** Using only retrospective (observational) data — no live experiment — how would you decide whether Circle should be optimized for **small private groups** (≈5–6 members) or **large public groups** (tens to hundreds of members)? Detail the analysis, the confounders you would control for, and the decision rule. 3. **Comparing the charts.** You are shown three time-series plots of `total comments / total posts` for three different products, each with a different user base. Can these lines be compared directly? Explain. ##### Hints - Pick a single north-star metric that captures reciprocal conversation, then normalize it per active member; segment by group size, privacy, and cohort. - Retrospective data is observational — beware reverse causality (good groups grow) and survivorship; use within-unit fixed effects, threshold/event studies, or matching. - The comment/post ratio is sensitive to user-base composition, heavy tails, and measurement windows; normalize before comparing.