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Google·Data Scientist·Technical Phone Screen·Senior

Senior
May 2026

Summary

Google DS interview with a meaty A/B testing question that goes way deeper than just 'is the p-value under 0.05.' The whole thing revolves around a CTR lift that looks real but might not be, and you have to walk through a bunch of layers to figure out what's actually going on.

Questions Asked (1)

Q1

An A/B test shows a statistically significant +1.2% relative increase in CTR (clicks/impressions) in the treatment group. How would you diagnose whether this change is real or an artifact, covering numerator/denominator decomposition, composition effects, instrumentation guardrails, statistical methodology for ratio metrics, and follow-up analyses?

A/B Testing & ExperimentationProduct Analytics & MetricsRoot Cause Analysis
Author's notes

This question is basically five questions stapled together, which I did not fully appreciate until I was already two minutes into talking about variance estimation and realized I hadn't touched Simpson's paradox yet.

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AI HintsAI Generated

Suggested Approach

Start by decomposing the metric into numerator (clicks) and denominator (impressions) to see which component drove the change, then check for composition effects (e.g., traffic mix, device, geography) and instrumentation issues (e.g., logging, bot filtering). Finally, apply appropriate statistical methods for ratio metrics (e.g., delta method, bootstrap) and run follow-up analyses (e.g., segment-level, novelty effects, pre-period A/A tests) to confirm robustness.

Pro tip: Always check the denominator first: a drop in impressions can inflate CTR even if clicks are flat. Also, look for Simpson's paradox by examining segment-level data—aggregate gains can hide losses in key segments.

1. Decompose numerator and denominator

Break down the change into clicks (numerator) and impressions (denominator) to identify which component is driving the +1.2% relative increase. Check if clicks increased, impressions decreased, or both.

2. Investigate composition effects

Examine whether the treatment and control groups differ in traffic composition (e.g., device, browser, geography, user demographics) that could affect CTR. Use stratification or regression to adjust for imbalances.

3. Validate instrumentation and data quality

Check for logging errors, bot traffic, or changes in data collection that could artificially inflate CTR. Ensure both groups have consistent instrumentation and no missing data.

4. Apply correct statistical methodology for ratio metrics

Use methods like the delta method, bootstrap, or linearized metrics to compute variance correctly for ratio metrics (CTR). Avoid naive t-tests that assume independent observations.

5. Conduct follow-up analyses

Perform segment-level analyses, check for novelty effects, run A/A tests, and examine pre-period trends to confirm the change is real and not an artifact.

Key Points to Mention

  • Numerator/denominator decomposition: clicks vs. impressions
  • Composition effects: traffic mix, device, geography, user segments
  • Instrumentation guardrails: logging, bot filtering, data pipeline changes
  • Statistical methodology for ratio metrics: delta method, bootstrap, linearization
  • Follow-up analyses: segment-level, novelty effects, A/A tests, pre-period trends
  • Simpson's paradox and heterogeneity of treatment effects

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