This question is five questions duct-taped together and they want you to treat it like one coherent story.
Start by framing the business problem and defining the target estimand: the platform-to-in-store price gap for identical items. Then walk through a full pipeline: data collection and cleaning, item matching, index construction, uncertainty quantification, forecasting with exogenous drivers, and power analysis for sizing. Emphasize practical trade-offs and validation at each stage.
Pro tip: Don't just list methods—show you understand the data-generating process: in-store prices are often collected via crowdsourcing or receipts, which introduces selection bias and measurement error. Propose a validation subsample with ground-truth audits to correct for these biases.
Identify sources: DoorDash platform data (menu prices, item IDs, restaurant IDs, timestamps, location) and in-store prices (crowdsourced receipts, store visits, third-party data). Clean by deduplicating, handling missing values, and standardizing units/currencies. Document data quality issues and potential biases.
Match identical items across sources using a combination of exact identifiers (e.g., GTIN, SKU) and fuzzy matching on name, description, size, and modifiers. Validate matches with a manually labeled sample. Build a price index (e.g., Laspeyres or Fisher) to track the gap over time, weighting by order volume or item popularity.
Quantify uncertainty without A/B tests using bootstrapping, Bayesian hierarchical models, or variance estimation from observational data. Forecast the gap using time series models (e.g., ARIMA, Prophet) with exogenous drivers like CPI, fuel costs, and local wages. Validate with backtesting and sensitivity analysis.
Determine sample size needed to detect a minimum detectable effect (MDE) under clustering (e.g., by restaurant or region) and autocorrelation (time series). Use formulas for clustered designs (intraclass correlation) and adjust for temporal correlation (effective sample size). Simulate power under different scenarios.
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