This is Simpson's paradox dressed up in a product scenario and I knew it the second I read it, which almost made it worse because I rushed into the explanation without thinking through the decision layer.
Recognize this as Simpson's paradox, where a confounding variable (likely city-level differences in traffic mix or sample sizes) reverses the aggregate effect. Explain the paradox, then recommend analyzing the data stratified by city and other relevant dimensions to identify the confounder before making a decision. Emphasize that the correct decision depends on whether the cities are exchangeable and whether the confounder is a true effect modifier.
Pro tip: Don't just say 'it's Simpson's paradox'—show you understand that the aggregate result is misleading only if the confounder is not a true effect modifier. Propose a weighted analysis or a hierarchical model to estimate the overall effect while accounting for city-level heterogeneity.
State that this is a classic case of Simpson's paradox, where a trend appears in subgroups but reverses when groups are combined. Clarify that the overall result is not necessarily wrong but is confounded by city-level differences.
Investigate what differs between the cities: sample sizes, user demographics, traffic sources, or baseline conversion rates. Check if the treatment assignment was balanced within each city and whether the cities have different proportions of users who respond differently to the variants.
Determine whether the cities are exchangeable and whether the confounder is a true effect modifier. If the cities are not exchangeable, the overall effect may not be meaningful; if the confounder is an effect modifier, report city-specific results.
Perform stratified analysis, weighted averages, or a mixed-effects model to estimate the overall effect while accounting for city-level variation. Check for interactions between city and variant, and consider segmenting by other relevant dimensions.
Based on the analysis, decide whether to roll out variant A, B, or neither. If the effect is heterogeneous, consider a targeted rollout or further experimentation to understand the drivers.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.