Statistics
196 bites tagged Statistics — interview questions with model answers, and 60-second explainers.
A/B Test Results with Skewed Traffic: What's Next?
This tests your ability to spot confounding variables. A good answer invalidates the results due to sampling bias, proposes segmenting the data by device to find the true effect, and suggests re-running the test with correct randomization.
Why use median/p95 for API latency instead of the mean?
This tests if you understand how long-tail distributions make averages misleading for user experience. A good answer explains that median (p50) shows the typical user, while p95 captures the worst-case experience.
SARIMA vs. LightGBM for Forecasting with External Variables
Tests your grasp of practical trade-offs in model selection. A strong answer contrasts SARIMA's interpretability with LightGBM's power for handling many non-linear variables, covering performance and implementation costs.
When is A/B testing not feasible, and what is an alternative?
Tests your grasp of causal inference when randomization isn't possible. A great answer names a scenario (like a regional launch), proposes Difference-in-Differences (DiD), and explains its core 'parallel trends' assumption.
Calculate Sample Size for a 2% A/B Test Lift
This tests if you connect statistical inputs to business goals. A good answer defines baseline rate, minimum detectable effect (MDE), and power, then explains MDE as a cost/benefit trade-off.
What does a p-value of 0.03 mean in an A/B test?
This tests your practical grasp of statistical significance. A good answer defines p-value (probability of the result if the null hypothesis is true), explains that p=0.03 is significant vs. alpha=0.05, and concludes you can reject the null.
What is the 'multiple comparisons problem' in A/B testing?
Tests your grasp of statistical pitfalls in large-scale A/B testing. Define the problem (inflated false positives), explain the business risk (wasted effort), and propose a mitigation like Bonferroni correction.
Describe two methods for generating prediction intervals
This tests your understanding of forecast uncertainty. Describe two methods: 1) assuming normally distributed errors and using a standard deviation multiplier, and 2) bootstrapping residuals to simulate future paths.
Forecasting inventory with trend and weekly seasonality?
This tests mapping a business problem to a statistical tool. A good answer names Holt-Winters, explains its level, trend, and seasonal components, and discusses additive vs. multiplicative seasonality.
Explain stationarity in a time series
This tests your grasp of core time series modeling assumptions. A strong answer defines stationarity (constant mean/variance), explains its importance for ARIMA (stable patterns), and names a test (ADF) and a fix (differencing).
How does CUPED increase the statistical power of an experiment?
Tests your grasp of variance reduction. Explain CUPED as ANCOVA, using pre-experiment data (X) to remove predictable noise from the outcome (Y). Effectiveness depends on correlation (rho), reducing variance by (1-rho^2).
Why is stopping an A/B test when it hits significance problematic?
Tests your understanding of the 'peeking problem' in A/B testing. A great answer defines peeking, explains how it inflates the Type I error rate (false positives), and states the need for a predetermined sample size.
How do you determine A/B test sample size and duration?
This tests your ability to connect business goals to statistical parameters. A good answer defines the four power analysis inputs (baseline, MDE, alpha, power) and explains trade-offs, then converts sample size to duration using business cycles.
Why not t-test p99 latency? Describe a valid alternative.
This tests your grasp of statistical test assumptions. A good answer explains why p99 violates t-test normality, then outlines a resampling method like bootstrapping to build a confidence interval on the *difference* of p99s.
Explain Simpson's Paradox with a user engagement example
This tests your understanding of statistical pitfalls in A/B testing. A good answer defines the paradox, gives an example where a feature fails in aggregate but wins in every segment, and attributes it to a confounding variable.
How to Statistically Test a 10% DAU Drop?
Tests your knowledge of hypothesis testing. A good answer outlines the steps: state a null hypothesis, choose a test (e.g., Z-test), calculate a p-value, and compare it to a significance level (alpha).
Explain the difference between correlation and causation
Tests if you can avoid statistical fallacies. First, define correlation (association) and causation (cause-effect). Then, explain the difference via a confounding variable. A red flag is giving an example where one metric actually could cause the other.
p-value is 0.08, significance is 0.05. Ship it?
This tests your ability to translate statistical risk for business partners. Explain that p=0.08 means an 8% chance of a false positive, quantify the cost of a bad decision, and suggest extending the test to increase power.
What does a p-value of 0.03 mean in an A/B test?
Tests your practical statistical literacy. A good answer defines the p-value (3% chance of this result if the null is true), compares it to alpha (0.03 < 0.05) to reject the null, and decides to ship.
Mean vs. Median for API Response Times?
Tests if you know latency data has outliers. A good answer chooses median because it's robust to extremes. Explain that mean gets skewed by a few slow requests (e.g., GC pauses), hiding the typical user experience.
An A/B test has imbalanced traffic. What do you do?
This tests your ability to spot confounding variables and Simpson's Paradox. A good answer first invalidates the aggregate result, then proposes segmenting by device to salvage insights, and finally investigates the root cause.
How do you visually represent statistical uncertainty in a chart?
This tests your ability to communicate statistical nuance beyond simple averages. A great answer discusses error bars (specifying CI vs. SD), then moves to richer visualizations like graded error bars or violin plots.
Why use p50/p95 over mean for API response times?
Tests your grasp of statistical distributions for UX metrics. A good answer explains how outliers skew the mean, while percentiles (p50, p95) better represent typical and worst-case user experiences.
How would you handle 10% nulls in a key column?
This tests your ability to diagnose data issues before solving. First, investigate why data is null. Then, discuss trade-offs of dropping vs. imputing with the mean or median, considering the impact on the dashboard's accuracy.
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