Experiment design under novelty-decay and residual (carryover) effects
Context
You are testing a new UI that creates a novelty spike that decays over roughly 21 days. The previous release may also leave residual (carryover) effects on users. You need to design an experiment that separately estimates novelty versus steady-state impact, while guarding against contamination from prior releases.
Assume:
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User-level randomization is available and can be made sticky for weeks.
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You can create a persistent holdback that never receives the new UI during the experiment.
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You can ramp traffic in stages and instrument the timestamp of a user’s first exposure to the new UI.
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Primary metrics are user-level or user-day outcomes (e.g., sessions, time spent, CTR), and you can analyze them by time-since-first-exposure.
Tasks
(a) Design a ramp plan and a persistent holdback to estimate novelty separately from steady-state.
(b) Specify a cohort analysis by time-since-first-exposure and a model that captures decay (e.g., spline or exponential).
(c) Propose a cool-off window and rehash strategy to address residual effects from the previous release.
(d) Determine experiment duration and sample size under decay, and explain how decay affects power.