A/B Test Design: 1‑Month Free Trial Impact on Paid Subscription Conversion

You are evaluating whether offering a 1‑month free trial increases paid subscription sign‑ups. Assume the product currently requires immediate payment (no trial). The treatment offers a 30‑day free trial that auto‑converts to paid unless canceled. Design an end‑to‑end A/B test and address:

1. Eligibility and Randomization
   • Who is included/excluded (e.g., prior payers, grace‑period users)?
   • Unit of randomization (user, device, household?)
   • How to prevent reassignment and cross‑device contamination.
2. Primary Outcome and Horizon
   • Define a single launch‑gating metric that captures true paid conversion given the 30‑day trial delay.
   • Justify an observation window (e.g., paid start within 60 days of first exposure).
   • Specify guardrail metrics (refunds, chargebacks, engagement, infra cost).
3. ITT vs. Triggered Analyses
   • Describe both intention‑to‑treat and triggered analyses and when each should drive the decision.
   • Handle users who never see the offer or churn before trial end.
4. Sample Size
   • Compute per‑arm sample size for: baseline paid conversion 4.0%, MDE +0.8 percentage points (absolute), two‑sided α=0.05, power=0.80. Show the formula and the result.
5. Bias Controls
   • Address seasonality, novelty effects, geographic heterogeneity, and pre‑existing conversion propensity (e.g., CUPED with a pre‑exposure covariate).
6. Interference and Fraud
   • Detect collusion or referral abuse; protect against multiple sign‑ups.
7. Decision Framework
   • Specify exact launch criteria (statistical significance, minimum practical effect, guardrail thresholds), how you’d adjust for peeking/sequential looks, and a staged ramp plan if results are borderline.
   • Provide precise analysis steps and examples of tables/figures you would produce.