Detect and address Simpson’s paradox

A test reports a +1.2 percentage-point lift in overall conversion, while the segment-level estimates are −0.5 pp for New users and +2.0 pp for Returning users. a) Build a specific example in which a change in the mix of segments produces Simpson's paradox. b) Pre-specify a stratified estimator (or MMRM) that guards against aggregation bias. c) Define an interaction test for treatment effect heterogeneity and a decision rule for when that heterogeneity is substantial (for instance, rolling out per segment versus shipping globally).

Overview: This question assesses grasp of aggregation bias and Simpson's paradox, skill with stratified or mixed-model estimators, heterogeneity testing, and experiment decision-making in an Analytics & Experimentation context for a Data Scientist position.