I started with KS test because that's the reflex answer, but they pushed back pretty quickly asking when I'd use Anderson-Darling instead or why I might care about Wasserstein distance.
Start by clarifying the variable type (continuous, categorical, ordinal) and the goal (detecting any difference vs. specific differences). Then outline a hypothesis testing framework, choosing appropriate tests based on assumptions, and discuss interpretation and practical significance.
Pro tip: Always check assumptions and consider the sample size; with large samples, even trivial differences become significant, so complement statistical tests with effect size measures and visualizations.
Determine if the variable is continuous, categorical, or ordinal, and whether the goal is to test for any difference or specific differences (e.g., mean, variance).
Select a test based on variable type and assumptions: e.g., Kolmogorov-Smirnov, Anderson-Darling, or Mann-Whitney U for continuous; chi-square or Fisher's exact for categorical.
Verify assumptions like independence, normality (if applicable), and ensure sample sizes are adequate; consider non-parametric alternatives if assumptions are violated.
Run the test, obtain p-value, and assess statistical significance; also compute effect size (e.g., Cohen's d, Cramer's V) to gauge practical significance.
Plot distributions (histograms, boxplots, ECDFs) to visually inspect differences and validate test results; consider bootstrapping or permutation tests for robustness.
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Start by clarifying the goal: are we comparing distributions, measuring similarity, or testing for differences? Then discuss distance metrics (e.g., Euclidean, cosine, Mahalanobis) and dimensionality reduction techniques (e.g., PCA, t-SNE, UMAP) to handle the curse of dimensionality, and finally mention statistical tests or machine learning approaches for rigorous comparison.
Pro tip: Emphasize that the choice of method depends on the data's properties and the specific question—there's no one-size-fits-all. Also, mention that you'd validate results with cross-validation or bootstrapping to ensure robustness.
Determine whether the comparison is for similarity, difference detection, or classification, as this guides the choice of methods.
Select an appropriate metric like Euclidean, cosine, or Mahalanobis, considering feature scaling and correlation.
Apply dimensionality reduction (PCA, t-SNE, UMAP) or feature selection to mitigate the curse of dimensionality and improve interpretability.
Use multivariate tests (e.g., Hotelling's T², MANOVA) or machine learning models (e.g., SVM, random forest) to compare samples.
Assess significance and effect size, and validate findings with resampling or cross-validation to ensure reliability.
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Probably my strongest part of the interview.
Frame your answer around a decision-making framework that starts with statistical significance, then moves to practical significance via effect sizes and confidence intervals, and finally addresses robustness through multiple testing corrections and clustered data adjustments. Emphasize that the goal is to inform product decisions, not just achieve p < 0.05.
Pro tip: Always tie effect sizes back to business metrics (e.g., revenue, engagement) and consider the cost of implementation. A statistically significant 0.1% lift might not justify engineering effort, while a 2% lift in a key metric could be a game-changer.
Calculate the effect size (e.g., Cohen's d, relative lift) and its confidence interval to understand the magnitude and precision of the effect. Compare it to the minimum detectable effect (MDE) or a business-relevant threshold to judge if it's meaningful.
If you're testing multiple metrics or variants, apply corrections like Bonferroni, Holm-Bonferroni, or Benjamini-Hochberg to control the family-wise error rate or false discovery rate. This prevents false positives from inflating significance.
When data is clustered (e.g., users within regions, sessions within users), use methods like cluster-robust standard errors, mixed-effects models, or aggregated analysis at the cluster level to avoid underestimated variance and inflated Type I error.
Translate the effect size into business terms (e.g., incremental revenue, user retention) and weigh it against implementation costs, risks, and strategic alignment. Use decision frameworks like cost-benefit analysis or expected value.
Perform sensitivity analyses, such as bootstrapping, permutation tests, or checking for novelty effects, to ensure the result holds under different assumptions. If possible, validate with a holdout or replication study.
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Ran through the usual list: simple random, stratified, cluster, reservoir for streaming data.
Start by categorizing sampling methods into probability and non-probability, then explain when each is appropriate based on evaluation goals, data characteristics, and resource constraints. Emphasize that the choice depends on the need for representativeness, cost, and potential biases, and give concrete examples from A/B testing and product analytics.
Pro tip: Mention that in A/B testing, simple random sampling is often used for user assignment, but stratified sampling can improve power by balancing key covariates; however, be cautious of over-stratifying leading to complexity. Also, highlight that non-probability methods like convenience sampling can be acceptable for quick iteration but require validation against a random sample.
Clarify what you're evaluating (e.g., model performance, product feature impact) and the available resources (time, budget, access to population). This determines whether you need a representative sample or can tolerate bias.
If generalizability is critical, use probability methods (simple random, stratified, cluster, systematic). If speed or cost is prioritized, consider non-probability methods (convenience, purposive, quota) but acknowledge limitations.
For heterogeneous populations, use stratified sampling to ensure key subgroups are represented. For naturally clustered data (e.g., by city or device), use cluster sampling. For large, homogeneous populations, simple random sampling suffices.
In A/B tests, random assignment is key; stratified randomization can balance covariates. For product analytics, if tracking user behavior, be mindful of sampling bias (e.g., only active users) and consider weighting or post-stratification.
After collecting data, check for representativeness (e.g., compare sample statistics to known population parameters). If bias is detected, adjust via weighting or resampling, and document limitations.
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Acknowledge that the datasets are not directly comparable due to different time coverage, which introduces confounding from time-of-day effects. Propose aligning the comparison by restricting to overlapping time windows or reweighting to a common distribution, and validate with sensitivity analysis.
Pro tip: Always check for time-based confounders before comparing datasets; if you can't align them, quantify the bias and communicate its impact on conclusions rather than ignoring it.
Recognize that one dataset covers only rush hour while the other covers the full day, meaning they represent different populations and conditions.
Determine how time of day affects key metrics (e.g., traffic density, user behavior) and whether it could confound the comparison.
Restrict the full-day dataset to rush hour periods or reweight it to match the rush-hour distribution, ensuring a fair comparison.
Check if conclusions hold under different alignment methods or if residual confounding remains, and report uncertainty.
Clearly state any remaining biases and how they might affect the comparison, suggesting further data collection if needed.
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Caught me a little off guard because I'd been thinking about means and full distributions.
Start by acknowledging that rare tail events are often safety-critical and cannot be tested with standard A/B tests due to low frequency. Propose a multi-pronged strategy: use simulation and stress testing to generate synthetic tail scenarios, apply extreme value theory to model tail distributions, and design targeted experiments with stratified sampling or importance sampling to increase event frequency. Emphasize the need for rigorous validation and monitoring in production.
Pro tip: Highlight the trade-off between statistical power and safety: in safety-critical domains, you often need to prioritize recall over precision, and you should be prepared to use sequential testing or Bayesian methods to make decisions with limited data.
Clearly specify what constitutes a rare safety-critical event (e.g., near-miss collisions, sudden braking) and establish metrics for detection and impact. Use historical data and domain expertise to estimate base rates and severity.
Use simulation (e.g., Monte Carlo, agent-based models) and adversarial generation to create realistic but rare edge cases that would be unsafe or unethical to test in the real world. Incorporate domain randomization to cover unknown unknowns.
Leverage extreme value theory (EVT) to model tail distributions, importance sampling to oversample rare events, and stratified sampling to ensure adequate representation. Consider Bayesian hierarchical models to borrow strength across scenarios.
When real-world testing is possible, use sequential testing or group sequential designs to allow early stopping for safety. Use matched case-control studies or propensity score matching to compare treatments in rare-event contexts.
Implement continuous monitoring with anomaly detection and alerting for tail events. Use shadow mode or canary deployments to test new models safely, and conduct post-market surveillance to catch unforeseen edge cases.
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