Quantitative Research and Analysis Questions

Covers end to end quantitative research methods used to measure and validate product and user behavior hypotheses. Topics include experimental and quasi experimental design, split testing and controlled experiments, metric definition and success criteria, sample size calculation and statistical power, selection of appropriate statistical tests and interpretation of statistical significance and effect sizes, confidence intervals, correlation versus causation, common statistical pitfalls and biases, analytics instrumentation and metric tracking, survey design and quantitative measurement, and data analysis workflows and tools used to analyze large scale user data. Candidates should be able to design experiments, justify metric choices, calculate sample size and duration, analyze results rigorously, and make data driven recommendations.

MediumTechnical

109 practiced

You plan an experiment to detect a 0.5 percentage point absolute lift from a 5% baseline conversion with 80% power and alpha 0.05. Show the approximate sample size calculation per variant for a two-sided test for proportions and explain each term in the formula. You may use z-scores for normal approximation.

MediumTechnical

100 practiced

Design a difference-in-differences (DiD) analysis to measure the impact of a regional marketing campaign on conversions. Specify the pre- and post-periods, treatment and control groups, necessary assumptions (e.g., parallel trends), typical checks, and potential confounders to control for.

Sample Answer

Design summary:- Objective: Estimate causal effect of a regional marketing campaign on conversions using DiD.

Setup:- Treatment group: users (or sessions/zip codes) located in regions where the campaign ran.- Control group: similar regions where the campaign did not run (no overlapping exposure).- Pre-period: at least 4–8 weeks before campaign start (long enough to check trends).- Post-period: 4–8 weeks after start (or longer to capture sustained effects); if campaign phased, align windows to exposure timing.

Key assumptions:- Parallel trends: absent treatment, conversions in treatment and control would have followed the same trajectory.- No contemporaneous shocks that differentially affect treatment vs control.- Stable unit treatment value assumption (SUTVA): no spillovers between regions.

Model specification:- Basic DiD regression: Conversions_it = α + β·TreatRegion_i + γ·Post_t + δ·(TreatRegion_i × Post_t) + X_it·θ + ε_it δ is the DiD estimate. Include region and time fixed effects if panel data.

Typical checks and robustness:- Visualize pre-period trends (line plots) and test pre-period leads (placebo DiD with leads of treatment).- Event study / dynamic DiD to estimate effects by week and check pre-trend coefficients ≈ 0.- Placebo tests: randomize treatment regions or use a falsification period.- Covariate balance: compare demographics, baseline conversion rates.- Sensitivity: alternative windows, matching (propensity-score or exact) to improve comparability, weighted DiD (e.g., entropy balancing), cluster-robust SEs at region level.- Check for spillovers by excluding border areas or measuring cross-region ad exposure.

Potential confounders to control for:- Local promotions or pricing changes, seasonality, competitor actions, changes in traffic acquisition (paid search/bid changes), product launches, macroeconomic shocks, measurement changes (tracking or attribution updates).- Include time-varying controls X_it (ad spend by channel, web traffic volume, holiday indicators) and region fixed effects.

Interpretation and caveats:- DiD estimates local average treatment effect for treated regions under assumptions.- If parallel trends fail, prioritize matched controls, synthetic control, or panel event-study approaches.- Report confidence intervals, discuss possible violations (spillovers, differential shocks), and present multiple robustness checks to support causal claims.

HardTechnical

53 practiced

You are a senior data scientist presenting inconclusive experiment results to executives: the primary metric is not significant but some segments show positive signals. How would you structure the conversation, recommend next steps, convey uncertainty, and balance speed of product rollout against statistical evidence?

Sample Answer

Situation: I ran a randomized experiment for a new personalization feature. The primary metric (overall conversion) showed a non-significant lift (p=0.12, CI: -0.5% to +2.1%), but predefined customer segments (new users, mobile web) showed positive, consistent signals (~+4% lift, p≈0.02).

How I’d structure the conversation1. Start with the headline: what we tested, the primary result (not significant), and why it matters. Be explicit and concise.2. Show the data: primary metric, confidence intervals, power/post-hoc power, and segment results. Use visuals (forest plot, cumulative lift over time) to make uncertainty tangible.3. Explain reliability: pre-specification, multiple testing correction, sample size and stopping rules, heterogeneity checks, and potential confounders.4. Translate to business impact: estimated incremental conversions/revenue and downside scenarios.

Recommend next steps- Conservative path: Hold full rollout, run a targeted follow-up experiment focused on high-signal segments with increased power and stratified randomization (pre-register analysis).- Iterative path: Phased rollout to the positive segments only (canary), with strict monitoring and kill-switch metrics, while continuing experiments on remaining population.- Parallel investigations: Qualitative research (user interviews), instrumentation checks, and feature variants to isolate mechanism.

Conveying uncertainty- Use probabilistic language: present confidence intervals, probability of non-negative lift, and expected value models (e.g., expected revenue given uncertainty).- Explicitly call out assumptions and risks (multiple comparisons, seasonality).- Offer scenario analysis: best/likely/worst cases with numeric estimates.

Balancing speed vs evidence- Propose risk-based decision framework: if downside is small and operational cost of rollback is low, prefer faster, phased rollout for commercial momentum. If downside or cost of rollback is high, require stronger statistical evidence.- Recommend guardrails for fast paths: short canary with predefined stopping criteria, automated monitoring, and rollback plan so we can move quickly without accepting uncontrolled risk.

Closing: propose a clear decision: choose one of the above paths, with timelines, success criteria, and owner. That gives executives a principled, data-informed recommendation that balances speed and uncertainty.

HardTechnical

57 practiced

Compare sequential A/B testing with multi-armed bandit methods for product experimentation. Discuss objectives (fast learning versus maximizing cumulative reward), regret, exploration-exploitation trade-offs, and situations where bandits are inappropriate for measurement tasks.

Sample Answer

Objective framing- Sequential A/B testing (fixed-horizon or sequentially monitored tests) aims for fast, unbiased learning about treatment effects and rigorous inference (confidence intervals, p-values). The primary objective is accurate estimation and decision correctness at the end of the experiment.- Multi-armed bandits (MAB) aim to maximize cumulative reward during experimentation by adaptively allocating more traffic to better-performing variants (online optimization). Objective: minimize cumulative regret.

Regret and metrics- Regret = sum_t (reward_optimal − reward_chosen). Bandits optimize this quantity (e.g., minimize expected regret). Sequential A/B prioritizes Type I/II error control and estimation accuracy, not regret minimization.- Inference-focused metrics: unbiased treatment effect, coverage, statistical power. Optimization-focused metrics: cumulative conversions, revenue, or user utility during deployment.

Exploration–exploitation trade-off- Sequential A/B: exploration is typically fixed (equal allocation) or pre-specified; analysis accounts for peeking via alpha-spending or sequential methods (Wald SPRT, alpha correction). Exploitation happens after a clear stopping decision.- Bandits: continuously balance exploration (trying uncertain arms) vs. exploitation (allocating to top arms). Algorithms: ε-greedy, UCB (optimistic bounds), Thompson Sampling (Bayesian). UCB emphasizes low regret with confidence bounds; Thompson Sampling trades off probabilistically and often performs well in practice.

Statistical inference vs. online optimization- Bandits produce biased sample proportions (adaptive allocation) and complicate standard estimators: selection bias, non-iid sampling, and inflate Type I error if naive tests used. Post-hoc corrections (re-weighting, sequential inference, bootstrapping, causal estimators with propensity weighting, or using methods for adaptive experiments) are required for valid inference.- Sequential testing methods (group sequential, alpha-spending, sequential probability ratio test) provide valid p-values and CIs under repeated looks.

When bandits are inappropriate for measurement tasks- When the goal is precise, unbiased estimation of treatment effect (e.g., regulatory A/B tests, product decisions requiring effect size estimates, experimentation to inform causal models).- When effects are small and need high power—bandits may starve underperforming arms and lose power to detect small differences.- When heterogeneous effects must be estimated across segments: bandits optimizing global reward may conflate subgroup differences and give poor coverage for subgroup treatment effects.- When long-term guardrails or learning requirements (e.g., feature evaluation before rollout) require full randomization to ensure validity.

Practical guidance- Use sequential A/B or group-sequential designs when inference is primary. Use bandits when short-term business value matters and you accept biased allocation but still monitor with appropriate statistical corrections. For hybrid: run a randomized "burn-in" to collect unbiased estimates, then switch to a bandit for optimization, or use Thompson Sampling with careful logging and offline causal estimation.

EasyTechnical

65 practiced

Describe p-hacking and the multiple comparisons problem. Provide three practical strategies a data team can adopt to reduce the likelihood of false discoveries when running many experiments or testing many metrics.

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