← Robinhood Interview Insights
This is where I spent most of my mental energy.
Start by framing the problem as a causal inference question and define a clear treatment group (users exposed to the new product) and a control group (similar users not exposed) based on the July 10, 2025 release. Then specify a difference-in-differences model with user and time fixed effects, test parallel pre-trends using event-study plots and placebo tests, and if pre-trends fail, consider alternative methods like synthetic control or matching to strengthen the causal claim.
Pro tip: Emphasize that in a real-world setting like Robinhood, the 'control group' is often not perfectly clean—users may be partially exposed or affected by spillovers. Discuss how you'd handle imperfect compliance or contamination, and always complement DiD with robustness checks and qualitative insights.
Identify users who were exposed to the new product (treatment) and those who were not (control), ensuring they are comparable on pre-release characteristics. Consider using propensity score matching or stratification to create a balanced control group.
Use a two-way fixed effects model: Y_it = α + β*(Treatment_i * Post_t) + γ_i + δ_t + ε_it, where Y is trades per active user, Treatment_i indicates the group, Post_t indicates post-July 10, and γ_i, δ_t are user and time fixed effects. Cluster standard errors at the user level.
Plot average trades per active user over time for both groups pre-release to visually inspect trends. Formally test by including leads and lags in an event-study specification and checking if pre-period coefficients are jointly zero.
If pre-trends fail, consider alternative identification strategies: synthetic control, matching combined with DiD, or instrumental variables. Also explore whether the pre-trend difference is due to confounding factors and adjust for them.
Conduct placebo tests (e.g., fake treatment dates), check for spillovers, and test sensitivity to different control groups. Use alternative outcome definitions and model specifications to ensure results are not driven by arbitrary choices.
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BSTS was fine for me to talk through conceptually but I got a little shaky on the reconciliation part.
Start by explaining how you would apply CUSUM and Bayesian Structural Time Series (BSTS) to detect and quantify the drop, then discuss a systematic approach to reconcile differences by examining model assumptions, uncertainty, and robustness. Emphasize that the goal is not to pick one method but to triangulate evidence and communicate uncertainty to stakeholders.
Pro tip: When methods disagree, treat it as a signal to investigate the data generation process and model assumptions rather than a failure. Present both estimates with confidence intervals and explain which is more reliable for the business decision at hand.
Use CUSUM (or Bai-Perron) to detect breakpoints and estimate the drop size, and BSTS to model the counterfactual and estimate the causal effect with credible intervals. Ensure both methods are properly tuned and validated.
Compare the effect sizes, timing, and uncertainty from both methods. Investigate potential reasons for divergence, such as different assumptions (e.g., linear vs. probabilistic), sensitivity to outliers, or model misspecification.
Perform sensitivity analyses: vary hyperparameters, test on subsets, or use placebo tests. Check if one method is more robust to violations of its assumptions in your specific context.
Incorporate other data sources or methods (e.g., A/B test results, domain knowledge, or simpler heuristics) to see which estimate aligns better with external validity.
Present both estimates with their confidence/credible intervals, explain the trade-offs, and recommend a decision based on the business impact and risk tolerance. If needed, propose further data collection or experiments.
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Honestly the most straightforward of the four.
First, clarify that the minimum detectable effect (MDE) is the smallest true relative change in the mean trades per user that the test can detect with 80% power at a 5% significance level. Then, use the pooled-variance t-test formula for two independent samples to compute the required sample size per group, and finally translate that into the number of days needed given 200,000 users per day split into control and treatment.
Pro tip: Always state your assumptions explicitly (e.g., equal variances, two-sided test, 50/50 split) and note that in practice you might use a more robust method like Welch's t-test if variances are unequal. Also, mention that the MDE is often expressed as a relative change (e.g., 10% drop) but the formula uses absolute effect sizes.
State the null and alternative hypotheses for a two-sided test. Identify the baseline mean (μ = 1.0), standard deviation (σ = 1.5), significance level (α = 0.05), power (1-β = 0.80), and the desired relative MDE (10% drop, so absolute effect δ = 0.10 * 1.0 = 0.1).
For a two-sample t-test with equal variances, the required sample size per group is n = 2 * (z_{1-α/2} + z_{1-β})^2 * σ^2 / δ^2, where z_{1-α/2} = 1.96 and z_{1-β} = 0.84 for α=0.05 and power=0.80.
Plug in the values: n = 2 * (1.96 + 0.84)^2 * (1.5)^2 / (0.1)^2 = 2 * (2.8)^2 * 2.25 / 0.01 = 2 * 7.84 * 225 = 3528. So, approximately 3,528 users per group are needed.
Total sample size = 2 * n = 7,056 users. With 200,000 active users per day, if split evenly, each day provides 100,000 users per group. Thus, days needed = n / 100,000 = 3528 / 100,000 = 0.03528 days, which is less than an hour. However, in practice, you might need to account for daily variation and ensure the metric is stable over full days, so round up to 1 day.
The calculation shows that even a small fraction of a day's traffic is sufficient to detect a 10% drop. But in reality, you should consider factors like novelty effects, day-of-week seasonality, and the need for full days to avoid bias. Also, note that the MDE is for a 10% drop; if you want to detect smaller effects, you'd need more data.
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The pass/fail criteria part tripped me up more than the methods.
Start by framing the goal: ensure the analysis is robust to specification choices and can guide a ship/no-ship decision. Then walk through each check (placebo dates, randomization inference, wild bootstrap, sensitivity to controls) explaining what it tests and how to interpret results. Finally, define clear pass/fail criteria that combine statistical significance, effect size stability, and practical impact to make a ship decision.
Pro tip: Tie every robustness check to a specific risk (e.g., false positives from multiple testing, clustered errors, confounding by market regimes) and propose a pre-registered decision rule to avoid p-hacking. Emphasize that the goal is not to eliminate all uncertainty but to ensure the result is stable enough to act on.
Restate the analysis goal, the metric, and the ship/no-ship decision it informs. Identify the key assumptions (e.g., parallel trends, independent errors) that robustness checks will stress-test.
Use placebo dates (e.g., pre-treatment periods) to test for spurious effects. Perform randomization inference at the symbol level by permuting treatment assignment across symbols to build a null distribution and compute exact p-values.
Apply wild bootstrap to account for clustered or heteroskedastic errors, especially with few clusters. Compare bootstrap confidence intervals to analytical ones to check for understated uncertainty.
Re-estimate the model with and without volatility controls (VIX, SPX returns) and holiday effects. Check if the treatment effect remains stable in sign, magnitude, and significance across specifications.
Set thresholds: e.g., effect size within ±20% of baseline, p-value < 0.05 after multiple testing correction, and no placebo effects. If all pass, ship; if some fail, iterate or abandon.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.