Google·Data Scientist·Technical Phone Screen·Senior

Senior

Apr 2026

Summary

Went through a technical screen for a DS role at Google and got hit with a pretty deep stats question about Simpson's paradox. Not a light conversation, they wanted the full picture: math, causality, and practical fixes.

Questions Asked (1)

Define Simpson's paradox and build a concrete numeric example where a treatment looks better in every subgroup but worse in the aggregate. Walk through the algebra of how weighted averaging reverses the trend, connect it to confounding and causal graphs, describe remedies like stratification and regression adjustment, and explain when the aggregate vs. the subgroup-conditioned estimate is actually the right answer.

A/B Testing & ExperimentationProduct Analytics & MetricsTechnical Trade-offs

Author's notes

This one wrecked me a little.

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AI HintsAI Generated

Suggested Approach

Start by clearly defining Simpson's paradox as a reversal of association when data are aggregated versus stratified, then construct a simple 2x2x2 example with explicit numbers. Walk through the weighted averages to show the reversal, explain the causal mechanism using confounding and DAGs, and discuss when to trust the aggregate versus subgroup estimates, emphasizing that the choice depends on the causal question and assumptions.

Pro tip: Use a real-world inspired example like a clinical trial with unequal group sizes, and explicitly state the causal assumptions (e.g., no unmeasured confounding) that justify your preferred estimate. This shows you understand that Simpson's paradox is not just a statistical artifact but a causal inference issue.

1. Define Simpson's Paradox

State that Simpson's paradox occurs when an association present in subgroups reverses or disappears when subgroups are combined. Emphasize it's a form of confounding by a third variable.

2. Construct a Numeric Example

Create a 2x2x2 table with a treatment, outcome, and a confounding variable (e.g., disease severity). Show treatment better in each severity stratum but worse overall due to unequal allocation.

3. Demonstrate the Algebra

Compute subgroup success rates and overall rates using weighted averages. Show that the overall rate is a weighted sum of subgroup rates, and the weights differ between treatment and control, causing reversal.

4. Connect to Confounding and Causal Graphs

Explain that the confounding variable is a common cause of treatment and outcome. Draw a DAG: Confounder -> Treatment, Confounder -> Outcome. The aggregate estimate is biased because it does not condition on the confounder.

5. Discuss Remedies and When to Use Which Estimate

Mention stratification, regression adjustment, propensity scores, and standardization. Explain that the subgroup-conditioned (adjusted) estimate is causal if the confounder is the only confounder and we condition on it. The aggregate estimate is appropriate if the subgroups are not meaningful or if the question is about the population as a whole without causal inference.

Key Points to Mention

Simpson's paradox is a reversal of association due to confounding and unequal group sizes.
Weighted averaging: overall rate = sum(weight_i * rate_i), where weights are subgroup proportions.
Confounding variable affects both treatment assignment and outcome, creating a backdoor path.
Causal graphs (DAGs) help identify when to adjust: condition on confounders to block backdoor paths.
Remedies: stratification, regression adjustment, propensity score matching, standardization.
Choice between aggregate and adjusted estimate depends on the causal question and assumptions (e.g., exchangeability, no unmeasured confounding).

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.