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

55 practiced

A feature was rolled out to Region A but not Region B. After rollout you observe a metric change in Region A. As a Design Researcher, propose a difference-in-differences (DiD) analysis plan: list key assumptions (parallel trends), pre-period checks, regression specification, interaction terms, and threats to validity. What additional data would you request to strengthen causal claims?

Sample Answer

**Overview & goal** Estimate causal effect of rollout in Region A using DiD: compare outcome change pre→post in A versus B, controlling covariates and time effects.

**Key assumptions**- Parallel trends: in absence of treatment, A and B would have similar outcome trends.- No simultaneous shocks differentially affecting A.- Stable composition: user mix constant or controlled.- No spillovers between regions.

**Pre-period checks**- Visualize trends (weekly/monthly) for several pre-period periods.- Formal test: regress outcome on region*time in pre-period; expect non-significant interaction.- Check covariate balance pre (demographics, device, traffic source).- Examine seasonality and policy changes.

**Regression specification**

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Y_it = β0 + β1*Post_t + β2*Treat_i + β3*(Treat_i * Post_t) + γX_it + δ_t + ε_it

- Y_it: metric (conversion rate, time-on-task)- Treat_i: 1 if Region A- Post_t: 1 if post-rollout- β3 is DiD estimate- X_it: time-varying controls; δ_t: time fixed effects; cluster SEs by region.

**Interaction terms & extensions**- Add triple interactions for subgroups: Treat*Post*NewUser- Include region-specific trends: α_i * t or region*time spline to relax parallel trends.- Heterogeneous effects: interactions with device, cohort.

**Threats to validity**- Violation of parallel trends, spillovers, composition changes, measurement shifts, concurrent product changes.

**Additional data to request**- Longer pre-period time series (more granularity)- User-level panel identifiers to control fixed effects and attrition- Covariates: user demographics, acquisition channel, device, account age- Other metrics to triangulate (engagement, retention)- Logs of other product launches/promotion by region and external events

This plan balances practical checks and robustness to support design recommendations.

EasyTechnical

105 practiced

Explain in plain language what a p-value represents in an experiment. Define Type I and Type II errors and the role of alpha and beta. Give one realistic product example of the practical consequence of making a Type I error and one example for a Type II error.

MediumTechnical

69 practiced

When comparing a continuous metric such as 'time-to-complete-task' between control and treatment, how do you decide between using a t-test, Mann-Whitney U, or bootstrapping? As a Design Researcher, outline diagnostic steps (plots and tests) you would run on the raw data and justify the final method selection based on sample size and distribution properties.

Sample Answer

**Approach summary (why this matters)** As a Design Researcher I need a defensible test choice so product decisions reflect real user behavior. I run diagnostics on raw time-to-complete-task, then pick the simplest valid method given sample size and distribution.

**Diagnostic steps (plots & tests)** - Visuals - Histogram + kernel density per group — check modality and skew. - Boxplots / violin plots — compare central tendency and spread; spot outliers. - Q–Q plots per group — assess normality visually. - Overlaid empirical CDFs — compare distributions nonparametrically.- Numeric diagnostics - Sample size per group (n). - Skewness and kurtosis. - Shapiro–Wilk normality test (for n < ~2000) — interpret cautiously. - Levene’s or Brown–Forsythe test for equality of variances. - Check for many equal values/ties and extreme outliers; record measurement granularity.

**Decision rules / justification**- If both groups approximately normal, variances equal (or corrected with Welch) and n reasonably large (n ≥ 30 each): use two-sample t-test (or Welch t-test if unequal variances). Rationale: high power and direct inference on means.- If distributions are skewed, have heavy tails or many outliers, and sample sizes small (< 30) or unequal: prefer Mann–Whitney U if the goal is to test for stochastic dominance/median shift and assumptions (independent samples, similar-shaped distributions) hold. Rationale: robust to non-normality but tests shift in distribution not strictly the mean.- If distributions are skewed, heteroskedastic, have complex shapes, or you want an effect estimate (difference in means/medians) with confidence intervals — use bootstrap (resampling) for CIs and p-values. Bootstrapping is especially useful when n is moderate to large (n ≥ 20–30) and analytic assumptions fail. It handles skewness and heterogeneity and yields an interpretable CI for mean or median difference.- If many ties or discrete measurement: be cautious with Mann–Whitney (ties affect exact p-values); bootstrap on medians or trimmed means often preferable.

**Practical note** I present both an effect size (difference in means or medians) with bootstrap CIs and the test result chosen per diagnostics, so stakeholders see magnitude and uncertainty, not just a p-value.

MediumTechnical

58 practiced

You are launching a checkout redesign to reduce cart abandonment on a product with 500k monthly active users and baseline checkout conversion 20%. As a Design Researcher, design the A/B test: define the primary metric, specify a success criterion and guardrail metrics, compute the required sample size to detect a 2 percentage-point absolute uplift with 80% power and alpha=0.05 (describe formula or tools), estimate test duration given traffic, and list operational considerations for launch and monitoring.

Sample Answer

**Approach (role lens)** As a Design Researcher I frame the experiment to measure user behavior change (checkout completion) while protecting business and UX health. I'll define metrics, compute sample size, estimate duration from traffic, and list operational checks for reliable results.

**Primary metric**- Checkout conversion rate: % of eligible users who complete checkout (binary, user-level).

**Success criterion & guardrails**- Success: statistically significant absolute uplift ≥ 2 percentage points (from 20% → 22%) at alpha = 0.05 and power = 80%.- Guardrail metrics (must not degrade): - Checkout error rate / technical failures - Page load time (ms) - Revenue per session / average order value - Support tickets or negative qualitative feedback - Drop-off earlier in funnel (cart → checkout entry)

**Sample-size calculation**- Use two-proportion z-test formula or online calculators (e.g., statsmodels power.prop_test, Evan Miller calculator).- Parameters: p1 = 0.20, p2 = 0.22, delta = 0.02, alpha = 0.05 (Z 1.96), power 0.80 (Z 0.84).- Approximate per-group n formula (pooled approach):

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n_per_group = [ (Z_alpha/2 * sqrt(2 * p_bar * (1-p_bar)) + Z_power * sqrt(p1*(1-p1)+p2*(1-p2)))^2 ] / delta^2

- With p_bar = 0.21 this yields: - n_per_group ≈ 6,503 → total ≈ 13,006 users.

**Test duration estimate**- With 500k MAU and baseline checkout conversion 20% → ~100k checkouts/month (eligible events).- If experiment randomizes at user-level evenly: ~50k checkout-eligible users/month per arm.- Required total 13k users ≈ 13% of one month of checkout traffic → ~4 days ideal traffic. - Operationally allow more time for: - Warm-up, QA, segmentation, and achieving stable behavior (avoid novelty/weekday effects). - Recommended duration: 2–3 weeks to cover weekday/weekend and capture variability.

**Operational considerations**- Randomization at user-id; ensure uniqueness and stickiness.- Pre-register primary metric, analysis plan, and stopping rules.- Instrumentation: events, funnel checkpoints, server and client metrics; verify telemetry with smoke tests.- Monitor in real time for guardrail breaches; set automated alerts.- Segment analysis plan (new vs returning users, device, geography) but avoid peeking for early stopping.- Rollout plan: feature flag for immediate rollback if issues; QA on edge cases.- Qual + quantitative mix: run short usability sessions or session replay sampling during test to surface UX friction.- Post-test: check consistency, run significance and practical significance, compute uplift CI, and examine heterogeneity before rollout.

Tools: statsmodels / R power.prop.test, Optimizely/VWO experiment platform, GA/BigQuery for reporting, FullStory/Hotjar for qualitative.

EasyTechnical

62 practiced

You are asked to evaluate a new onboarding flow intended to increase user activation. As a Design Researcher, propose a clear primary metric to use in an experiment, specify a sample success criterion (quantitative), and list two guardrail metrics you would track. Justify each choice in terms of user behavior and business impact.

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