How to analyze Simpson's paradox

A marketing team wants to evaluate a new email campaign. Two email versions, A and B, were tested over two weeks in two cities: San Francisco and New York. The overall pooled data suggests version A has a higher conversion rate than version B, but when you break the results down by city, and possibly by week, version B appears better in every subgroup. How would you determine whether the new email is actually better? In your answer, discuss: - what metric(s) you would define as primary and which guardrail metrics you would monitor, - how Simpson's paradox can arise in this setting, - what confounders or sources of imbalance you would check, - how you would re-analyze the existing data, - whether and how you can compute confidence intervals, and - how you would redesign the experiment if the original allocation across cities or time was imbalanced.