This one sprawled in a way I wasn't ready for.
First, recognize this as Simpson's paradox and explain that the pooled result is misleading due to confounding between version and city/week. Then, propose a stratified analysis or a model that adjusts for city and week, and discuss how to check for and address allocation imbalance, including whether confidence intervals from the original analysis are trustworthy.
Pro tip: Emphasize that Simpson's paradox often arises from unequal sample sizes or allocation ratios across strata; always check the distribution of users across versions within each city and week before trusting pooled results.
Choose a primary metric (e.g., click-through rate or conversion rate) that directly measures email effectiveness, and guardrail metrics (e.g., unsubscribe rate, spam complaints) to ensure no harm.
Show that the pooled result reverses when stratifying by city and week, indicating confounding due to unequal allocation or different baseline rates across strata.
Check if version assignment is correlated with city or week (e.g., version A sent more to a city with higher baseline response), and examine other potential confounders like time of day or user demographics.
Use stratified analysis (e.g., Mantel-Haenszel) or regression with fixed effects for city and week to estimate the true effect, and compute adjusted confidence intervals.
If allocation was imbalanced, propose randomization within each city-week block, ensure equal sample sizes, and pre-register the analysis plan to avoid post-hoc bias.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.