Design analysis to test social vs game engagement

Hypothesis: Among Oculus users, those who use 'social' features are more regularly engaged than those who use 'game' features. Define 'regularly engaged' as having >= 3 active days per week over the 8-week window ending 2025-08-31. Design a study to test this: (a) If you can randomize, what is the exact experiment (unit of randomization, treatment, exposure to social vs game, primary metric, guardrails, power/MDE at alpha = 0.05)? (b) If randomization is not feasible, propose an observational design comparing 'social-only' vs 'game-only' users in 2025-07-01 to 2025-08-31: specify inclusion/exclusion (tenure minimum, geography, device), primary metric(s), null/alternative hypotheses, statistical test(s) (e.g., two-proportion z-test for regular-week share; Welch’s t-test or Mann–Whitney for mean weekly active days), variance estimation (cluster-robust by user), and how you will control confounding (PSM/IPW with covariates like signup_date, baseline engagement, device, country, content supply; exact matching on tenure buckets). (c) Detail checks for bias and robustness: pre-trend checks, difference-in-differences on switchers, placebo outcomes, sensitivity analyses (e.g., Rosenbaum bounds), and multiple-testing control for secondaries. (d) Define decision thresholds that constitute practical approval (e.g., p < 0.05 and >= X% lift with CIs excluding 0), and how you'd communicate risks/assumptions to stakeholders.