Compare Instagram vs. Facebook using causal experiments

Compare Instagram and Facebook in terms of consumer time and engagement: a) Define a single-objective OEC that reflects healthy cross-app ecosystem value without simply rewarding cannibalization (for example, weighted time, sessions, and creator interactions with guardrails on churn and ad quality). b) Design a causal measurement plan for a new Instagram feature (such as Reels remix) that might shift time away from Facebook: choose between user-level and geo-level cluster randomization; propose a staggered geo rollout with Facebook holdouts to measure cross-app impact; outline a difference-in-differences design with pre-trend checks, calendar effects, and cluster-robust standard errors; and specify interference mitigation (geo buffers, cross-over suppression). c) Compute a back-of-envelope sample size and test duration given baseline Facebook time of 20 minutes per day, geo-level ICC of 0.02, MDE of 1% on the ecosystem OEC, power of 0.8, and alpha of 0.05. d) List guardrail metrics (crashes, feed quality, creator DAU, ads LTV) and stopping rules. e) Explain how you would interpret results if Instagram improves the OEC but Facebook time drops by 3%, and propose follow-up experiments or pricing changes to preserve ecosystem health.

Overview: This question tests causal inference, experiment design, metric engineering, and ecosystem-level impact assessment for a Data Scientist in the Analytics & Experimentation domain, with particular focus on defining a single-objective OEC that avoids pure cannibalization and on measuring cross-app effects through randomized rollouts.