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This took me way longer than it should have.
First, compute the required sample size per arm using the baseline rate (22%), minimum detectable relative lift (5%), and standard alpha (0.05) and power (0.80). Then, adjust for the 10% cluster correlation by inflating the sample size using the design effect (1 + (m-1)*ICC), where m is the average cluster size. Finally, convert to calendar days by dividing by the daily eligible traffic (120k * 20% = 24k) and accounting for day-of-week seasonality by ensuring full weeks are run and possibly using a stratified or blocked design.
Pro tip: Always clarify the unit of randomization and analysis: if households are clusters, the analysis must account for intra-cluster correlation, and the sample size must be inflated accordingly. Also, consider using a sequential or group sequential design to monitor the experiment and stop early if needed, but be cautious with peeking.
Use the formula for two-proportion z-test: n = (Zα/2 + Zβ)^2 * (p1*(1-p1) + p2*(1-p2)) / (p2-p1)^2, where p1=0.22, p2=0.22*1.05=0.231, alpha=0.05, power=0.80. This gives the required sample size per arm without clustering.
Compute the design effect (DE) = 1 + (m-1)*ICC, where m is the average cluster size (e.g., number of eligible checkouts per household) and ICC=0.10. Multiply the base sample size by DE to get the adjusted sample size per arm.
Divide the adjusted sample size per arm by the daily eligible traffic (120,000 * 0.20 = 24,000) to get the number of days per arm. Since both arms run concurrently, the total duration is the same as the days per arm. Round up to the nearest whole week to account for day-of-week seasonality.
Ensure the experiment runs for complete weeks (e.g., 7, 14, 21 days) to balance day-of-week effects, especially strong Sunday variation. Consider using a stratified randomization by day-of-week or including day-of-week as a covariate in analysis.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
I knew the concept but stumbled explaining the tradeoff clearly.
Start by framing the trade-off between early detection and false positive control, then propose a group sequential design with alpha spending (e.g., O'Brien-Fleming) tailored to Instacart's business metrics. Explain how peeking inflates Type I error and how alpha spending preserves it, then compare expected duration under fixed-horizon vs. sequential designs, highlighting the impact of effect size and stopping boundaries.
Pro tip: Quantify the expected sample size reduction using software like gsDesign or simulation, and mention that you'd pre-register the analysis plan to avoid p-hacking—this shows statistical rigor and business pragmatism.
Clarify the experiment's primary metric, desired power, significance level, and business constraints (e.g., cost of running longer, risk of shipping a bad feature).
Select a group sequential approach (e.g., O'Brien-Fleming, Pocock) or alpha spending function that balances early stopping and power, considering the number of interim looks and timing.
Use software (e.g., gsDesign, R) to derive stopping boundaries and calculate the expected sample size under the alternative hypothesis, comparing it to a fixed-horizon design.
Discuss how sequential testing can reduce expected duration when effects are large but may increase maximum sample size; also note the need for pre-registration and monitoring.
Outline how to implement the monitoring plan in practice, including data pipelines, decision rules, and communication with stakeholders.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Honestly the most interesting part of the whole thing.
Start by explaining how Sunday volatility inflates variance and why standard randomization may not balance covariates. Then describe how stratified randomization or CUPED can reduce variance, and quantify the expected reduction using historical data and the resulting impact on experiment duration.
Pro tip: Emphasize that CUPED requires a pre-experiment covariate correlated with the metric; for Sunday volatility, using the same day-of-week historical attach rate as the covariate can yield substantial variance reduction. Also, mention that stratification must be based on pre-experiment variables to avoid bias.
Analyze historical Sunday attach rate data to quantify its variance and identify potential covariates (e.g., user activity, past attach rate) that explain the volatility.
Decide between stratified randomization (if strong categorical covariates exist) and CUPED (if a continuous pre-experiment covariate is available). Explain the trade-offs.
Apply the chosen method: for stratification, define strata based on covariates and randomize within; for CUPED, compute the covariate-adjusted metric using pre-experiment data. Validate that the method reduces variance without introducing bias.
Use historical data to estimate the variance reduction: for CUPED, compute 1 - ρ² where ρ is the correlation between pre-experiment covariate and the metric; for stratification, compute the between-strata variance explained.
Translate variance reduction into sample size savings: required sample size is proportional to variance, so a variance reduction of X% reduces sample size by X% (for fixed power). Then compute the new duration based on traffic.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.