Google·Data Scientist·Technical Phone Screen·Senior

Senior

Jul 2026

Summary

Google DS interview with a meaty product analytics case about a search metric drop. The question had about six layers to it and I kept feeling like I was one step behind the whole time.

Questions Asked (1)

Searching time per user per session dropped 35% over the past three months. A teammate wants to model T1 (time to first successful result) and T2 (time to giving up) as separate distributions. Critique that approach and design a rigorous analysis to find the root cause.

Product Analytics & MetricsRoot Cause AnalysisA/B Testing & Experimentation

Author's notes

This question is basically five questions stacked on top of each other.

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AI HintsAI Generated

Suggested Approach

First, critique the proposed T1/T2 split by noting that T1 and T2 are not independent—they are competing risks in a survival analysis framework, and modeling them separately ignores censoring and the joint distribution. Then, design a rigorous root cause analysis that decomposes the 35% drop by user segments, query types, and time, and tests hypotheses about changes in user behavior, search quality, or system performance.

Pro tip: Frame the problem as a survival analysis with competing risks (success vs. giving up) rather than two separate distributions, and emphasize that the drop could be due to a mix shift (e.g., more easy queries) rather than a true improvement—always check for Simpson's paradox.

1. Critique the T1/T2 separation

Explain that T1 and T2 are not independent; they are competing events in a survival model. Modeling them separately ignores censoring (sessions still ongoing) and the correlation between them, leading to biased estimates.

2. Define the metric and validate the drop

Clarify the exact definition of 'searching time per user per session' and verify the 35% drop is real, not due to logging errors, metric changes, or data pipeline issues. Check for seasonality and external events.

3. Decompose the drop by dimensions

Break down the metric by user segments (new vs. returning, device, geography), query types (navigational, transactional, informational), and time (daily/weekly). Look for Simpson's paradox: the overall drop might be driven by a mix shift.

4. Form and test hypotheses

Generate hypotheses: (a) improved search quality (faster T1), (b) users giving up faster (shorter T2) due to frustration, (c) changes in user behavior (e.g., more direct answers), (d) system performance changes. Use A/B tests, quasi-experiments, or causal inference methods to test.

5. Synthesize and recommend

Combine evidence to identify the root cause. If it's a mix shift, adjust the metric; if it's a real improvement, quantify the impact; if it's a degradation, propose fixes. Recommend monitoring T1 and T2 jointly via survival analysis.

Key Points to Mention

Competing risks framework: T1 and T2 are not independent; use survival analysis (e.g., cause-specific hazards) to model them jointly.
Censoring: Sessions where neither T1 nor T2 occurs by the end of the session must be handled properly.
Simpson's paradox: The overall drop could be due to a change in the mix of queries or users, not a true improvement.
Segment decomposition: Analyze by user cohorts, query intent, device, and geography to isolate the driver.
Hypothesis testing: Consider search quality improvements, UI changes, and external factors; use A/B tests or causal inference.
Metric definition: Ensure the metric is well-defined and stable; check for logging or pipeline issues.

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