Google·Data Scientist·Technical Phone Screen·Senior

Senior

May 2026

Summary

Google DS interview, one big causal inference question that took up basically the whole session. The depth they expected was pretty serious, covering everything from identification assumptions to sensitivity analysis. Felt like a take-home problem crammed into a live conversation.

Questions Asked (1)

You have observational data on a recommender feature where users self-selected into treatment. Walk through how you'd use propensity score matching to estimate the causal effect on 7-day retention, covering identification assumptions, covariate selection, matching mechanics, balance checks, ATE vs ATT, uncertainty quantification, and what you'd do if PSM falls short.

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

Author's notes

This was a lot to hold in your head at once.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Structure your answer around the causal inference roadmap: start with identification assumptions (conditional ignorability, positivity, SUTVA), then detail propensity score estimation and matching mechanics, followed by balance diagnostics and effect estimation. Emphasize that PSM is not a magic bullet—discuss its limitations and when to pivot to alternative methods like doubly robust estimation or sensitivity analysis.

Pro tip: Always frame PSM as a design step, not an analysis step: the goal is to create a balanced pseudo-population that mimics randomization. Mention that you would pre-register the analysis plan and check balance before looking at outcomes to avoid p-hacking.

1. Clarify the causal question and assumptions

Define the treatment (feature adoption), outcome (7-day retention), and target estimand (ATE vs ATT). State the identification assumptions: conditional ignorability (no unmeasured confounders), positivity (overlap), and SUTVA.

2. Select covariates and estimate propensity scores

Choose pre-treatment covariates that predict both treatment and outcome, avoiding post-treatment variables. Use logistic regression or ML (e.g., gradient boosting) to estimate propensity scores, and check overlap via histograms or propensity score distributions.

3. Match and assess balance

Apply matching algorithm (e.g., nearest neighbor with caliper, optimal matching) to create matched sample. Check balance using standardized mean differences (SMD < 0.1) and variance ratios; iterate on model specification if balance is poor.

4. Estimate effect and quantify uncertainty

Estimate ATE/ATT on matched sample using difference in means or weighted regression. Quantify uncertainty via bootstrap or Abadie-Imbens standard errors, and conduct sensitivity analysis for unmeasured confounding (e.g., Rosenbaum bounds).

5. Address limitations and alternatives

If PSM falls short (e.g., poor overlap, hidden bias), consider doubly robust methods (AIPW), instrumental variables, regression discontinuity, or synthetic control. Discuss the trade-offs and when to recommend a randomized experiment.

Key Points to Mention

Identification assumptions: conditional ignorability, positivity, SUTVA, and no interference.
Covariate selection: include confounders, exclude instruments and post-treatment variables; use domain knowledge and directed acyclic graphs (DAGs).
Matching mechanics: caliper, with/without replacement, 1:1 vs 1:k matching, and propensity score trimming.
Balance diagnostics: standardized mean differences, variance ratios, and love plots; balance is more important than matching algorithm.
ATE vs ATT: ATE requires full overlap and weights all units; ATT focuses on treated and is often more feasible with self-selection.
Uncertainty quantification: bootstrap, Abadie-Imbens SE, and sensitivity analysis (e.g., E-value, Rosenbaum bounds).
Alternatives when PSM fails: doubly robust estimators, instrumental variables, regression discontinuity, or encourage randomized experiments.

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