Diagnose a 20% retail revenue drop

An e-commerce retailer you work with reports that weekly revenue in Week T dropped 20% relative to its 4-week moving average baseline. Put together a rigorous diagnosis and measure how much each driver contributed.

Known context and signals:

• Traffic sessions stayed essentially flat (+0.5% week over week), while conversion rate (CVR) declined and average order value (AOV) moved.
• Returns increased from 7% to 10%, cancellations from 1% to 2%, and stockouts among top-50 SKUs rose from 3% to 9%.
• A +8% price increase began three weeks earlier; a new $75 free-shipping threshold started two weeks earlier; paid spend mix moved toward upper-funnel; a competitor launched a 25%-off sitewide sale.

Tasks:

1. Break the revenue change into $\text{traffic} \times \text{CVR} \times \text{AOV}$, then further separate it into mix/price/discount effects, post-purchase deductions (returns/cancellations), and lost sales from stockouts. Provide formulas and a step-by-step waterfall that shows the approximate percentage-point contribution of each factor.
2. Identify the fastest falsifiable checks you would run within 24 hours (for example, device-specific CVR decline, out-of-stock by category, promo overlap, page latency, checkout errors, funnel step breakage, acquisition channel mix, new versus returning cohorts).
3. Causal assessment: propose a geo- or cohort-level difference-in-differences or interruption model to separate the free-shipping change from the competitor sale and seasonality. Specify control groups, pre-trend checks, and robustness tests.
4. Experiments and fixes: lay out targeted tests (pricing, threshold A/B testing, back-in-stock alerts, assortment substitution) and the success metrics to track (lift, profit, LTV impact).

Overview: This question tests a data scientist's skills in revenue decomposition, diagnostic analytics, causal inference, and experimentation design, including $\text{traffic} \times \text{CVR} \times \text{AOV}$ breakdowns, post-purchase deductions, stockout impacts, rapid falsifiable checks, and difference-in-differences-style attribution.