Statistics Interview Prep
Statistics interview prep — estimation, hypothesis testing, regression, MLE, MAP, confidence intervals, A/B testing, and statistical inference for engineering candidates.
Quick answer
Statistics is the science of inferring properties of a population from observed data.
Statistics questions test whether candidates can reason about uncertainty correctly under interview pressure.
Editorial review
Written by
CompoundLearn editorial team
Wireless / RF / hardware engineering
Reviewed by
CompoundLearn editorial team
Wireless / RF / hardware engineering
Last reviewed
Built from curated topic maps, editorial validation, and subject-matter review so the page stays aligned with the interview intent and the current content pipeline.
What it is
Statistics is the science of inferring properties of a population from observed data. Standard topics include descriptive statistics (sample mean, variance, quartiles, robust measures), point estimation (method of moments, MLE, Bayesian estimators), confidence intervals and their interpretation, hypothesis testing (Type I and II errors, power, p-values, the Neyman-Pearson framework), parametric tests (z, t, F, chi-squared), non-parametric tests (sign test, Wilcoxon rank-sum, Kolmogorov-Smirnov), analysis of variance (ANOVA), linear regression and its assumptions, multiple regression and the omitted-variable bias, generalized linear models (logistic, Poisson), regularization (ridge, lasso, elastic net) viewed as Bayesian priors, multiple-comparison correction (Bonferroni, FDR), the bootstrap and other resampling methods, sampling theory (simple random, stratified, cluster), survey design and biases, and an introduction to causal inference (RCTs, observational studies, instrumental variables, propensity scores). For engineering candidates, statistics is the layer between probability theory and decision-making — it is how you turn data into models, how you evaluate models, and how you reason about the uncertainty in those evaluations. ML evaluation, A/B testing, sensor calibration, quality control, reliability engineering, and any data-driven engineering decision rest on statistical methods.
Why interviewers ask
Statistics questions test whether candidates can reason about uncertainty correctly under interview pressure. ML interviews probe regression assumptions (linearity, homoscedasticity, exogeneity), regularization tradeoffs (ridge vs lasso, the Bayesian-prior interpretation), and model evaluation (cross-validation, AIC/BIC, hypothesis testing on coefficients). A/B-testing interviews are nearly entirely about statistics — sample-size planning, power analysis, multiple comparisons, sequential-testing pitfalls, peeking bias, and the difference between statistical and practical significance. Quantitative-research interviews probe MLE derivations, the Cramer-Rao bound, and asymptotic properties of estimators. Senior interviews additionally test causal-inference fundamentals: distinguishing correlation from causation, recognizing confounders, understanding identification strategies (RCT, IV, regression discontinuity, diff-in-diff). The strongest candidates know which statistical tool fits which problem, can derive results when needed (e.g. derive the OLS estimator from the normal equations or via MLE under Gaussian errors), and articulate the assumptions explicitly. The single most-tested concept is the misinterpretation of confidence intervals and p-values — interviewers love asking for the precise statement, and many candidates fall back on the colloquial wrong answer.
Common mistakes
The most common mistake is misinterpreting confidence intervals and p-values, two of the most-misunderstood concepts in applied statistics. A confidence interval is a property of the procedure (95% of constructed intervals contain the parameter, in repeated sampling), not a probability statement about a specific interval. A p-value is the probability of observing data as extreme as the actual data, under the null — not the probability that the null is true, and not the probability of replication. A second mistake is failing to correct for multiple comparisons when running many tests — running 20 metrics on the same A/B test at α = 0.05 produces an inflated false-positive rate above 64%. A third mistake is mishandling regression assumptions: candidates report standard errors from OLS in the presence of heteroscedasticity or autocorrelated errors, producing inflated significance. A fourth mistake is using parametric tests on heavy-tailed or skewed data without checking — the t-test's nominal level is reasonably robust to mild non-normality but breaks for distributions with heavy tails; the Wilcoxon or bootstrap is preferable. A fifth mistake is conflating MLE with MAP: candidates write down the likelihood and call it the posterior, missing the prior and the Bayesian interpretation entirely. A sixth mistake is sloppy reasoning about causal claims — observed correlations, even with massive sample sizes, do not establish causation, and senior interviewers will press candidates on confounders, selection bias, and the specific identification strategy. Seventh, candidates underestimate the role of sample size: small samples produce wide confidence intervals and underpowered tests, but candidates report point estimates as if they were precise. Finally, candidates often miss that "absence of evidence is not evidence of absence" — failing to reject the null does not prove the null, and the distinction matters for any conclusion drawn from non-significant results.
Frequently asked questions
- What is the difference between a Type I and Type II error, and how do you control them?
- Type I error (α, false positive) is rejecting the null hypothesis when it is true. Type II (β, false negative) is failing to reject when the null is false. Power = 1 - β is the probability of correctly rejecting under the alternative. The two trade off: shrinking α (more conservative test) typically grows β unless you increase sample size. The standard approach: fix α at 0.05 (or 0.01), increase n until β is acceptable for the effect size of practical interest. A/B testing interviews probe this constantly.
- When do you use a t-test vs z-test vs Wilcoxon?
- Z-test: known population variance, large sample, normal data — rare in practice. T-test: unknown population variance, sample variance estimated from data, applicable for normal or near-normal data; large-sample t-test is robust to non-normality via CLT. Wilcoxon (or Mann-Whitney): non-parametric rank-based test, no normality assumption, robust to outliers, but trades efficiency under normality. Modern practice: default to t-test when n is moderate and tails are not extreme; use Wilcoxon when distributions are clearly skewed or contaminated with outliers; bootstrap when neither assumption holds.
- What is the difference between MLE and MAP, and when does each make sense?
- Maximum Likelihood Estimation (MLE) chooses the parameter that maximizes the likelihood of observed data, treating the parameter as a fixed unknown quantity. Maximum A Posteriori (MAP) maximizes the posterior — likelihood times prior — treating the parameter as a random variable with prior beliefs. With a uniform prior, MAP equals MLE. MAP regularizes via the prior: ridge regression is MAP with a Gaussian prior, lasso is MAP with a Laplace prior. Bayesian estimation goes further and integrates over the posterior rather than just maximizing it.
- What is a confidence interval and what is it NOT?
- A 95% confidence interval is constructed so that, in repeated sampling, the procedure produces an interval containing the true parameter 95% of the time. It is a statement about the procedure, not about a specific interval. The common misinterpretation is "there is a 95% probability the true parameter is in this interval" — that is a Bayesian credible interval, which requires a prior. The frequentist CI does not assign probability to the parameter (which is fixed, not random). The distinction matters for science communication and for any interview that probes statistical foundations.
- What is multiple-comparison correction and why does it matter?
- Running k independent tests at α = 0.05 inflates the family-wise error rate to 1 - (1 - 0.05)^k. With k = 20 tests, the FWER exceeds 64% — a "significant" result is more likely than not to be a false positive. Bonferroni correction divides α by k (conservative). Benjamini-Hochberg controls false discovery rate (FDR), accepting more discoveries while bounding the proportion of false positives among them. Genomics, A/B testing platforms with many metrics, and any large-scale hypothesis testing requires explicit correction.
- How does linear regression assume what, and what breaks when those assumptions fail?
- OLS regression assumes: (1) linearity in parameters, (2) independent errors, (3) homoscedasticity (constant error variance), (4) errors uncorrelated with predictors (exogeneity), and for inference (5) errors normally distributed. Heteroscedasticity inflates standard errors — fix with robust (sandwich) standard errors or weighted least squares. Correlated errors (autocorrelation in time series) require GLS or robust methods. Non-linearity requires either feature engineering or a non-linear model. Endogeneity (predictors correlated with errors) breaks consistency entirely — IV or natural-experiment designs are needed.
Related topics
Essential AI-Native Skills for Statistics
Modern engineering work increasingly uses AI tools for design and code review, debugging, documentation, test and testbench generation, and workflow automation. The goal is not to let AI replace engineering judgment — it is to move faster while keeping verification discipline.
- Use AI to explain unfamiliar code, logs, waveforms, datasheets, or test failures.
- Break large problems into small, reviewable steps you can verify independently.
- Ask AI for hypotheses, then validate them against tests, measurements, simulations, or lab data.
- Version-control your analysis scripts, testbenches, and configs — keep changes small and reviewable.
- Document your assumptions, design tradeoffs, and debugging decisions.
- Verify AI output before trusting it: run the checks that fit the domain — unit tests, linters, simulations, or bench/lab measurements.
- Review AI output for correctness, edge cases, and real-world consequences.
Statistics — coming to the question bank
The adaptive practice engine is already live for core wireless, RF, and ML systems. Statistics isn't covered in the question bank yet — get notified when it's added.