MediumTechnical

71 practiced

Case study: A marketing experiment shows treatment lifts sign-ups by 8% (statistically significant) but average revenue per user (ARPU) falls by 3% (statistically insignificant). You're asked to estimate weekly revenue impact and recommend next steps. Given: 100k weekly active users, baseline sign-up rate 4%, average ARPU $25. Show calculations and reasoning for decision to ship, iterate, or kill.

Sample Answer

Approach: compute incremental weekly revenue change from lift in sign-ups and change in ARPU, account for statistical significance, then recommend action with experiments to mitigate ARPU drop.

Calculations:- Weekly active users = 100,000- Baseline sign-up rate = 4% → baseline sign-ups/week = 100,000 * 0.04 = 4,000- Treatment sign-up lift = +8% relative → new sign-ups = 4,000 * 1.08 = 4,320 → incremental sign-ups = 320- Baseline ARPU = $25- Observed ARPU change = -3% (statistically insignificant) → point estimate ARPU_treatment = $25 * 0.97 = $24.25

Estimate incremental revenue (point estimate):- Baseline revenue = 4,000 * $25 = $100,000/week- Treatment revenue = 4,320 * $24.25 = $104,760/week- Incremental revenue ≈ $4,760/week (+4.76%)

Uncertainty & significance:- Sign-up lift is statistically significant → likely real increase in conversion.- ARPU drop is statistically insignificant → could be noise. Important to inspect CI for ARPU change; if CI includes 0 and both negative and positive values, we shouldn’t assume a true decline.

Recommendation:1. Short term: Ship to a limited rollout (e.g., 10–25% of traffic) rather than full roll-out, because revenue uplift is positive in point estimate and sign-up lift is robust.2. Collect more data to reduce variance on ARPU — extend experiment or run a focused A/B test on monetization metrics until ARPU CI is narrow enough to accept/reject a real decline.3. Analyze heterogeneity: segment new sign-ups by cohort, channel, product usage, LTV predictors to see if new users are lower quality (e.g., churn-prone).4. If ARPU drop persists for specific segments, iterate product or onboarding (pricing, upsell flows) to recover ARPU while preserving sign-up gains.5. Monitor leading indicators (activation, 7/30-day retention, purchase-rate) and project LTV impact before full ship.

Decision call: Proceed with cautious rollout + monitoring and targeted analysis/iterations; kill only if further data confirms a meaningful, persistent ARPU decline that erodes lifetime revenue beyond the conversion gains.

EasyBehavioral

72 practiced

Behavioral: Tell me about a time when you had to convince a product manager or executive to run an A/B test rather than launch a feature directly. Use the STAR format: describe situation, task, action, and result. Highlight how you framed possible risks and benefits and how the decision affected the business.

HardTechnical

127 practiced

Overlapping experiments: multiple product teams run experiments concurrently that may affect the same users and product surfaces. Describe strategies to manage overlapping experiments: from organizational rules to statistical adjustments (e.g., factorial designs, blocking, regression adjustment). Provide pros and cons for each approach.

Sample Answer

Clarify requirements first: Are experiments independent or likely to interact (non-additive effects)? What’s acceptable bias vs. power loss? How many concurrent teams/users? With that context, here are practical strategies (organizational + statistical), each with pros/cons and BI implications.

1) Organizational rules / experiment registry- What: Central catalogue of active experiments, ownership, target surfaces, sample frames, and overlap rules.- Pros: Prevents accidental conflicts, enables coordination, easier attribution in BI dashboards.- Cons: Slows velocity, requires governance; doesn't solve statistical interference if overlaps are allowed.

2) Mutual exclusivity / enforced holdouts- What: Assign users to at most one experiment (global allocation).- Pros: Simple, eliminates interference, straightforward metrics.- Cons: Reduces eligible sample for each experiment (lower power); engineering coordination required; BI tracking simpler.

3) Factorial design (fully crossed experiments)- What: Intentionally run experiments in a factorial layout so users receive combinations; estimate main and interaction effects.- Pros: Efficient use of traffic; directly measures interactions; unbiased estimates if randomized properly.- Cons: Complexity explodes with many factors; requires pre-planned coordination and larger sample sizes for interaction detection; dashboarding needs cell-level metrics.

4) Blocking / stratified randomization- What: Stratify randomization on key user attributes or experiment membership (block by experiment exposure).- Pros: Balances covariates and reduces variance; can control known interaction drivers.- Cons: Only controls for stratified factors; needs consistent strata across teams and increased implementation complexity.

5) Regression adjustment / covariate adjustment- What: Use regression models (ANCOVA, interaction terms) to adjust for concurrent experiment exposures and covariates.- Pros: Flexible post-hoc control; leverages observational overlap data; integrates well in BI pipelines.- Cons: Requires correct model specification; may not fully remove bias from unmeasured interactions; more complex to interpret for stakeholders.

6) Holdout arms + overlap indicators- What: Include explicit “no other experiment” holdouts or add exposure indicator variables in analysis.- Pros: Enables estimation of pure treatment effects and interaction contrasts; simpler than full factorial.- Cons: Increases sample needs; complicated to manage if many experiments.

7) Sequential or temporal separation- What: Stagger experiments in time for same user segments.- Pros: Avoids concurrent interference; easier causal claims.- Cons: Slower learning; time trends confounders need adjustment.

BI operational considerations:- Instrument exposures and timestamps; capture experiment IDs and cell assignments in event logs.- Build an experiment-status dashboard (registry, overlap matrix, heatmap of affected surfaces).- Provide standardized analysis templates: A/B summary table, stratified reports, regression scripts (SQL/R/Python) that include overlap covariates.- Communicate limitations and required sample sizes for testing interactions.

Recommendation: Combine governance (registry + minimal overlap rules) with technical measures (instrumentation + factorial or regression when teams agree). For BI, prioritize reliable exposure logging and automated reporting that surfaces overlaps and flags potential interaction risk so analysts can choose the appropriate adjustment.

HardTechnical

86 practiced

Describe how you would implement sequential testing with alpha-spending in a production experimentation infrastructure. Include how you'd represent stopping rules, how to log interim looks, and how to prevent biased post-hoc stopping decisions from product teams.

Sample Answer

Clarify goals: enable valid sequential testing (multiple interim looks) while preserving type I error via an alpha‑spending function, make stopping rules explicit/automated, log immutable audit trails of looks, and prevent product teams from gaming stopping timing.

Design summary:- Pre-registration & experiment config: require each experiment to store a JSON config in the experiments table before launch with: primary metric, direction, max sample or max duration, planned look schedule (e.g., daily/weekly or sample-based), chosen alpha‑spending function (e.g., Lan‑DeMets with O’Brien‑Fleming or Pocock parameters), and minimum look spacing. This config is immutable once activated.- Representing stopping rules: encode stopping boundaries as a function of look index and cumulative information fraction. Store the chosen alpha‑spending function and parameters; compute critical z thresholds per look server-side using a standard library (e.g., statsmodels or custom numeric integration). Example JSON fields: {"alpha":0.05,"spend":"lan-deMets","params":{"type":"obf"},"max_looks":10,"min_days_between_looks":2}.- Automated interim looks: schedule looks via a job that (1) validates experiment active and spacing constraints, (2) computes interim test statistic and the corresponding alpha spent & critical value, (3) evaluates stop/continue and (4) writes a single immutable look record.- Immutable logging: create an append-only audit table (experiment_id, look_id, timestamp, sample_size, info_fraction, metric_value, test_stat, p_value, alpha_spent, critical_value, decision, job_id, code_version, config_hash). Use database features (append-only partitions, event sourcing, or write-once S3 logs) and restrict delete/update permissions.- Prevent biased post-hoc decisions: - Enforce pre-registration: disallow ad-hoc looks unless experiment is paused and re-registered (with higher governance). - Automate looks: only allow results evaluated by the scheduled job; disallow manual ad-hoc executions except by governance with audit entry explaining reason. - Lock experiment config on activation and record code_version and user_id for activation. - Expose dashboards that only surface finalized interim look records (read-only) and show cumulative alpha spent and remaining alpha to stakeholders; do not surface raw unlogged computations. - Require sign-off or threshold for early stopping: e.g., automated stop if test_stat exceeds critical_value and product owner + data reviewer confirm within a governance workflow — record confirmations in audit table.- Implementation snippets:SQL to log a look:

sql

INSERT INTO experiment_looks_audit
(experiment_id, look_id, ts, sample_n, info_frac, metric_val, z_stat, p_val, alpha_spent, crit_z, decision, job_id, config_hash)
VALUES (...)

Python sketch to compute critical value:

python

from statsmodels.stats.multitest import _alpha_spend  # pseudo
crit_z = compute_critical_z(alpha, spent_to_date, info_frac, method='lan-deMets', params=...)

- Monitoring & QA: nightly checks to ensure no unauthorized edits, alerts if look frequency violates min spacing, and periodic re-computation to verify logged statistics.Trade-offs:- Fully automated looks + immutable logs maximize statistical validity but reduce analyst flexibility; provide a governed exception process.- Choice of spending function affects early-power vs later-power; document recommendations.

This approach gives BI dashboards a trustworthy, auditable source of interim results, preserves experiment integrity via immutable logging and enforced pre-registration, and prevents biased post-hoc stopping through automation, governance, and visibility of alpha spending.

EasyTechnical

77 practiced

Describe Minimum Detectable Effect (MDE) and why it's important when planning experiments. Provide an example calculation narrative: baseline conversion = 4%, desired MDE = 0.6% absolute (i.e., 15% relative), alpha 0.05, power 0.8 — explain how MDE affects sample size and experiment duration in words (no formulas required).

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