This is where I spent most of my time and also where I stumbled first.
Start by acknowledging the interference challenges in a two-sided marketplace and the need to choose a randomization unit that balances bias and variance. Compare cluster randomization (by seller or geography) and ego-cluster randomization, explaining when each is appropriate. Then define exposure and exclusion criteria precisely, considering user and seller activity, and propose metrics to measure both direct and spillover effects.
Pro tip: In marketplace experiments, always consider the Stable Unit Treatment Value Assumption (SUTVA) and design for interference; ego-cluster randomization often provides a good trade-off by randomizing at the user level but clustering by social or interaction graph to capture spillovers.
Map how sellers affect each other (e.g., competition for visibility) and how consumers influence each other socially (e.g., sharing, reviews). This determines the appropriate randomization unit.
Evaluate cluster randomization (by seller or geography) vs. ego-cluster randomization. Cluster randomization reduces interference but increases variance; ego-cluster randomization (randomizing users but clustering by social ties) can capture spillovers while maintaining power.
Specify which users and sellers are exposed to the treatment: e.g., users who perform a search in the treatment condition, sellers whose listings appear in treated searches. Ensure exposure is measurable and aligns with the randomization unit.
Exclude users or sellers with prior exposure to the treatment, bots, internal accounts, or those with insufficient activity. Also exclude clusters with high interference potential (e.g., sellers with many cross-cluster interactions).
Choose metrics that capture direct effects (e.g., CTR, conversion) and spillover effects (e.g., seller revenue, social sharing). Use appropriate statistical methods (e.g., cluster-robust standard errors, network exposure models) to analyze results.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
DEFF = 1 + (m-1)*rho, so 1 + 49*0.02 = 1.98.
First, recall the design effect formula for cluster randomization: DE = 1 + (m - 1) * ICC, where m is the mean cluster size and ICC is the intra-cluster correlation. Plug in m=50 and ICC=0.02 to compute DE, then interpret it as the factor by which the sample size must increase relative to individual randomization to achieve the same statistical power.
Pro tip: Always clarify that the design effect assumes equal cluster sizes and a common ICC; in practice, you might mention that varying cluster sizes can further inflate the required sample size, and that the ICC should be estimated from prior data or pilot studies.
State the standard formula for the design effect in cluster randomized trials: DE = 1 + (m - 1) * ICC, where m is the average cluster size and ICC is the intra-cluster correlation coefficient.
Substitute m = 50 and ICC = 0.02 into the formula: DE = 1 + (50 - 1) * 0.02 = 1 + 49 * 0.02 = 1 + 0.98 = 1.98.
Explain that a design effect of 1.98 means the variance of the treatment effect estimate is 1.98 times larger than under individual randomization, so the effective sample size is reduced by a factor of 1.98.
Conclude that the total sample size (number of individuals) must be 1.98 times larger than what would be needed under individual randomization to achieve the same power. Equivalently, you need 98% more participants.
Mention that this calculation assumes equal cluster sizes and a constant ICC; in reality, varying cluster sizes can increase the design effect further, and the ICC should be estimated from prior data. Also note that the number of clusters may need to be sufficiently large to avoid bias.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
The SRM part under clustering I hadn't thought through carefully.
Start by explaining that cluster reassignment can introduce treatment contamination if not handled carefully, so you need to define a clear reassignment policy and use techniques like cluster-level randomization with buffer periods. Then describe how you would validate the experiment using invariant metrics (e.g., pre-experiment covariates) and a sample ratio mismatch (SRM) check adapted for clustered data, such as checking cluster-level assignment ratios.
Pro tip: Emphasize that SRM checks should be done at the cluster level, not just user level, and that invariant metrics should be measured before the experiment starts to avoid contamination. Also, mention that you would pre-register the analysis plan to avoid p-hacking.
Specify when and how clusters are reassigned (e.g., due to churn or new clusters) and ensure reassignment is random and independent of treatment. Use a consistent rule to avoid bias.
Implement cluster-level randomization with a buffer period or washout period to avoid spillover effects. Consider using intent-to-treat analysis and track cluster membership over time.
Choose invariant metrics that should not be affected by treatment (e.g., pre-experiment user demographics, cluster size). Compare these metrics between treatment and control groups to detect imbalances.
Perform a sample ratio mismatch check at the cluster level: compare the observed number of clusters (or users within clusters) in each arm to the expected ratio. Use a chi-squared test or sequential testing to detect anomalies.
Continuously monitor for contamination and SRM during the experiment. If issues arise, investigate and potentially restart or adjust the analysis.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by framing the problem: cluster membership changes over time, so a static rehashing schedule is suboptimal. Propose an adaptive schedule based on monitoring cluster size distribution and hash table load, then detail a mixed-effects model with cluster random intercepts to analyze performance metrics, accounting for repeated measures and cluster-level heterogeneity.
Pro tip: Emphasize that rehashing is not just about performance but also about maintaining experiment validity; suggest using a consistent hashing scheme to minimize disruption and a mixed-effects model to separate cluster-level effects from treatment effects.
Clarify that cluster membership changes over time, affecting hash distribution and load. Discuss the need for a rehashing schedule that balances performance and stability, considering factors like cluster size, churn rate, and system load.
Propose a schedule that triggers rehashing based on thresholds (e.g., load factor, cluster size variance) or periodically with backoff. Use consistent hashing to minimize key remapping and consider incremental rehashing to avoid downtime.
Identify performance metrics (e.g., lookup latency, throughput) and cluster-level covariates (e.g., cluster size, churn rate). Collect data over time with repeated measures per cluster.
Specify a model where the outcome is a function of fixed effects (e.g., rehashing strategy, time) and random intercepts for clusters to account for unobserved cluster heterogeneity. Discuss assumptions and potential random slopes.
Use cross-validation or holdout sets to assess model fit. Interpret results to refine the rehashing schedule, ensuring robustness to membership changes.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.