Design a switchback and choose block length
Overview
This question evaluates a candidate's competency in experimental design and causal inference for time-varying treatments, covering switchback experiments, handling spillovers and carryover, block randomization, variance and sample-size computation, temporal randomization (time-of-day and day-of-week), and covariate adjustment methods such as CUPED.
Switchback Experiment Design: Airport Pickup Pricing with Spillovers
Context
You are designing a switchback (time-based A/B) experiment for airport pickup pricing in a two-sided marketplace with known within-day seasonality and spillovers (drivers/dispatch queue). Because of spillovers, treatment must be assigned at the airport level and only one arm can run at a time.
Given empirical facts:
- Median trip duration ≈ 22 minutes.
- Demand autocorrelation function (ACF) falls below 0.1 at ≈ 75 minutes.
- Strong periodic peaks every ≈ 4 hours.
Tasks
(a) Choose a block length and rotation schedule that minimizes carryover yet retains power.
(b) Define diagnostics to detect residual carryover (e.g., pre/post contrasts around switches, lag terms/event-time models).
(c) Provide variance and sample-size computation under block randomization, including formulas and required inputs.
Also specify how you will randomize across time-of-day and days-of-week, and how you will incorporate covariate adjustment (e.g., CUPED) to reduce variance.
Solution
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