Decide if subgroup increases imply overall increase

Q: Decide if subgroup increases imply overall increase

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.

Q: How do I approach Statistics & Math interview questions?

Statistics & Math questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master statistics & math interviews.

Q: What difficulty level is this interview question?

This is a medium difficulty Statistics & Math question, commonly asked during Technical Screen rounds at TikTok.

Q: What role is this question designed for?

This question is commonly asked for Data Scientist candidates at TikTok during technical interviews.

Question

TikTok Time: Subgroup Increases vs Overall Average (Simpson's Paradox)

You are analyzing average daily time spent on TikTok by gender (male, female) across two periods (baseline t0 and follow-up t1). For each gender, the within-group average time increases from t0 to t1.

Answer the following:

Formal statement and proof or counterexample

State whether the overall average must increase when each subgroup's average increases.
Provide either a proof or a concrete counterexample (Simpson's paradox) with numbers.

Necessary and sufficient conditions

Express conditions, in terms of subgroup means and population weights, under which the overall average is guaranteed to increase.

Impact of composition shifts

Explain how changes in group shares (e.g., male share changing) affect the conclusion.

Diagnostic on real data

Describe a diagnostic you would run on real data to avoid incorrect inferences caused by composition changes.

Decide if subgroup increases imply overall increase

Quick Overview

Decide if subgroup increases imply overall increase

TikTok Time: Subgroup Increases vs Overall Average (Simpson's Paradox)

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