Problem Definition and Hypothesis Formation Questions

Break down ambiguous business questions into specific, answerable analytics problems and define what success looks like. Ask clarifying questions about business context, constraints, stakeholder expectations, and acceptance criteria. Use structured diagnosis and root cause analysis to isolate where a problem occurs by segmenting users, products, time periods, or geographies. Generate multiple testable hypotheses that explain observed outcomes, distinguish correlation from causation, and prioritize hypotheses by likelihood, potential impact, and ease of validation. Frame measurable metrics for each hypothesis and propose high level validation approaches or experiments to confirm or reject the hypotheses.

HardTechnical

34 practiced

You have 10 plausible hypotheses explaining an increase in customer support tickets. Resources allow testing only 3 hypotheses. Propose a principled approach to select which ones to test, quantify uncertainty in your selection, and design an adaptive testing plan that updates priorities as new data arrives.

Sample Answer

Approach (goal): pick the 3 hypotheses whose tests give the highest expected reduction in uncertainty and highest expected business impact (tickets reduced), subject to cost constraints.

Step 1 — formalize priors- For each hypothesis i, encode a prior belief p_i (probability hypothesis is true) and an estimated effect size E_i (expected ticket reduction if true), plus test cost c_i and time t_i. Priors come from historical data, SME elicitation, and quick exploratory analyses (e.g., correlational signals in logs).

Step 2 — compute Expected Value of Information (EVoI)- For each hypothesis compute EVoI_i = p_i * E_i * business_value − test_cost adjusted by test sensitivity/specificity. Rank by EVoI per unit cost or per unit time and pick top 3. This balances impact and uncertainty.

Quantify uncertainty- Use Bayesian models: treat p_i and E_i as distributions (Beta for p_i, Normal for E_i). Propagate uncertainty via Monte Carlo to produce distributions of EVoI_i and credible intervals. Report probability that a hypothesis is among top-3 (selection risk).

Adaptive testing plan- Phase 0 (quick probes): run lightweight data checks/AB tests or log analyses to update priors quickly.- Phase 1 (sequential experiments): run up to 3 parallel tests; allocate sampling adaptively using a Bayesian multi-armed bandit (Thompson Sampling) that favors hypotheses with higher posterior probability of impact while still exploring.- Use pre-specified stopping rules: stop if posterior probability hypothesis effect > 95% (success) or < 5% (futility), or when marginal EVoI < threshold.- Recompute EVoI weekly as new data arrives; if a negative/futile outcome frees resources, pick the next-highest EVoI hypothesis.

Implementation notes- Define metrics: ticket volume, time-to-resolution, severity-weighted tickets. Ensure instrumentation and randomization where possible.- Simulation: before running, simulate the adaptive policy with plausible priors to estimate power, expected regret, and resource use.- Communication: present expected gains, uncertainty bands, and decision triggers to stakeholders.

This approach is principled (EVoI + Bayesian uncertainty), quantifies selection risk via posterior probabilities, and adapts using sequential decision rules and Thompson Sampling to maximize learning and business impact.

EasyTechnical

42 practiced

Given three hypotheses each rated by qualitative impact (high/medium/low), confidence (high/low) and effort (small/medium/large), describe a simple numeric scoring method to rank them (e.g., ICE/RICE). Show a short example ranking using your method for three sample hypotheses.

MediumTechnical

38 practiced

What diagnostics and visualizations would you run to detect potential confounding variables before concluding a relationship is causal? Provide three concrete diagnostic checks or plots and explain what each would reveal.

Sample Answer

1) Covariate balance / Standardized Mean Differences (SMD) — Love plot- What: Compute SMD = (mean_treated - mean_control)/pooled_sd for each covariate and plot before/after any adjustment (matching, weighting, regression).- What it reveals: Large SMDs (commonly >0.1–0.2) indicate imbalance and potential confounding. A Love plot visually shows which covariates remain imbalanced after adjustment.- Practical tip: Report absolute SMD and show separate markers for pre/post-adjustment.

2) Propensity score overlap / Common support plot (density/histogram + rug)- What: Estimate propensity scores (logistic regression or ML) and plot treated vs control score densities or jittered rug along score axis.- What it reveals: Non-overlap (regions where only treated or only controls exist) indicates you cannot reliably estimate causal effects there — treatment effect outside common support is extrapolation and likely confounded.- Practical tip: Trim or restrict analysis to common support, or use weighting with diagnostics.

3) Negative-control (placebo) outcome or covariate-time trace- What: Test association between treatment and an outcome that should be unaffected (negative-control) or plot pre-treatment trends of the outcome by treatment group (event-study / parallel trends plot).- What it reveals: A significant association with a negative-control or diverging pre-treatment trends suggests unobserved confounding or violation of assumptions (e.g., parallel trends in diff-in-diff).- Practical tip: Combine with falsification tests (lead/lag coefficients) and report p-values and effect sizes.

Optional quick SMD calculation (Python):

python

import numpy as np
def smd(x_t, x_c):
    return (np.mean(x_t)-np.mean(x_c))/np.sqrt((x_t.var(ddof=1)+x_c.var(ddof=1))/2)

Together these diagnostics show observable imbalance, support for causal identification, and evidence of hidden bias — use them before claiming causality.

EasyTechnical

37 practiced

Define what 'success' looks like for an analytics project aimed at reducing customer churn. List at least three measurable success criteria: a primary metric tied to business outcome, a secondary metric to explain mechanism, and a guardrail to prevent negative side-effects. Explain how you'd operationalize each metric.

MediumTechnical

44 practiced

Suppose retention decreased only for users in Country A and only for users on Android 12. Design a diagnostic plan to determine whether the root cause is product (release/SDK), data (instrumentation/schema), or external (regulatory/payment provider). List analyses, metrics, and checks in order of priority.

Sample Answer

High-level plan: triage quickly to isolate whether the drop is product, data, or external. Prioritize checks that are fast, high-signal, and decisive.

1) Sanity & scope checks (minutes)- Confirm the signal: plot retention by country × OS × OS version (day-1, day-7, day-28). Verify significance (CI / bootstrapped difference).- Verify cohort definitions and date ranges; check for time-shifted events or timezone issues.

2) Data/instrumentation checks (high priority)- Compare raw event volumes (installs, opens, key retention event) for Country A on Android 12 vs Android 11 and other countries on Android 12. Large drops in events but not installs → instrumentation break.- Inspect event schema/versions and SDK version distributions for Android 12 users in Country A. Look for recent SDK rollout or schema change.- QA logs: sample device-level logs for missing events, errors, or crash spikes; check backend ingestion pipeline for errors, rejections, or mapping failures.- Check analytics SDK initialization and opt-in/consent flags (e.g., GDPR/local consent flow) for Country A.

3) Product/release checks- Cross-reference release timeline: was a feature/flag/AB test targeting Country A or Android 12 rolled out? Map retention drop start to release timestamps.- Segment by app version and feature flags; if only certain app versions show the drop → product bug.- Check crash rate/ANR by app version/OS version in Country A — increased crashes can explain retention loss.

4) External checks- Investigate external events: payment provider failures, app store removals, regional regulatory changes, network outages. Check payment success rates and subscription churn specifically for Country A Android 12.- Monitor social/PR channels and support tickets for region-specific complaints.

5) Deeper analyses (if ambiguous)- User-level funnels: compare first-session behaviors (time to first meaningful event) and abandonment points.- Survival analysis controlling for confounders (device model, app version, acquisition source).- A/B rollback simulation: compare retention for users before vs after reverting suspected change.

6) Decision rules & next steps- If event counts drop but installs constant → data/instrumentation; roll back instrumentation change, patch SDK, or reprocess data.- If crash/feature-correlated with specific app version → product release bug; hotfix release and rollback.- If payments or legal/regulatory indicators present → external; coordinate with legal/partners, show mitigation plan.

Deliverables: concise executive summary (root-cause hypothesis, evidence, confidence), recommended short-term mitigation, and a monitoring dashboard (retention by country×OS×app_version) to validate fix.

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