Decide if subgroup increases imply overall increase
Company: TikTok
Role: Data Scientist
Category: Statistics & Math
Difficulty: medium
Interview Round: Technical Screen
If the average daily time spent on TikTok increases within each gender subgroup (male and female), must the overall average increase as well? Provide: (1) a formal statement and proof or counterexample (Simpson’s paradox) with concrete numbers; (2) necessary and sufficient conditions in terms of subgroup means and population weights under which the overall average is guaranteed to increase; (3) how composition shifts (e.g., male share changing) affect the conclusion; (4) a diagnostic you would run on real data to avoid incorrect inferences.
Quick Answer: This question evaluates understanding of aggregation effects (Simpson's paradox), weighted averages, subgroup composition, and the ability to reason about statistical inference and diagnostic checks across strata.