Top 50 Statistics Interview Questions and Answers (2026)
Statistics rounds decide data scientist, data analyst, ML engineer, quant and product analytics interviews, and increasingly they show up for product managers who run experiments. They are rarely about reciting formulas. The interviewer wants to see you define a random variable, name the assumption you are making, and avoid the classic traps: reading a p-value as the probability the null is true, peeking at an A/B test, or mistaking a confounder for a cause.
The 50 questions below escalate the way a real round does: descriptive statistics, probability, distributions and limit theorems, hypothesis testing, regression, then bias and causality. After the 50 there is a bonus part on A/B testing and causal inference (questions 51-58), the shape product and senior data science rounds are built on, and a quick-fire round.
Practice alongside this post. The same ground is drilled as timed multiple-choice in the statistics question bank (71 graded questions, from the 68-95-99.7 rule to LATE vs ATE) and the A/B testing question bank; the free daily challenge gives you one question a day with no account needed. If your loop is a data science one, the data scientist prep track puts this in order with SQL and machine learning, and the sibling posts are Top 50 machine learning interview questions and Top 50 data analyst interview questions.
Part 1: Descriptive Statistics (1-7)
When the data is skewed or has outliers. The mean is pulled toward the long tail; the median is not. Income, house prices, session lengths and response latency are all right-skewed, so their mean sits above the median and describes almost nobody. The follow-up: report both, plus a high percentile (p95, p99) for latency, because users feel the tail.
2. What does the standard deviation measure, and why does the sample version divide by n - 1?
The standard deviation is the typical distance of observations from the mean, in the data's own units (the square root of the variance). The sample variance divides by n - 1 (Bessel's correction) because deviations are measured from the sample mean, which is itself fitted to the data and so sits closer to the points than the true mean does. Dividing by n would underestimate the population variance on average; n - 1 makes the variance estimator unbiased.
3. Standard deviation vs standard error?
The standard deviation describes the spread of individual observations. The standard error describes the spread of an estimate across repeated samples; for a sample mean it is σ / √n. More data does not shrink the standard deviation of the population, but it does shrink the standard error, which is why bigger samples give narrower confidence intervals. Confusing the two is a common reason for error bars that are far too narrow or far too wide.
4. What is a z-score?
The number of standard deviations an observation lies from the mean: z = (x - μ) / σ. It puts values from different scales on one scale, and for roughly normal data it maps directly to a percentile (z = 2 is about the 97.7th percentile). It is also the basis of simple outlier rules, which break down for skewed data (question 7).
5. Covariance vs correlation?
Both measure how two variables move together. Covariance is in the product of the two variables' units, so its size is hard to interpret. Pearson correlation divides covariance by both standard deviations, giving a unitless number between -1 and 1. Correlation measures only linear association: y = x² on x symmetric around zero has correlation zero while y is completely determined by x. Zero correlation does not mean independence.
6. Pearson vs Spearman correlation: when do you use each?
Pearson measures linear association and is sensitive to outliers. Spearman is Pearson computed on ranks, so it measures any monotonic relationship and is robust to outliers and to skewed scales. Use Spearman when the relationship is monotonic but curved, when the data is ordinal (ratings), or when a few extreme values would dominate Pearson.
7. How do you handle outliers?
First investigate: is it a data error (a unit mistake, a bot, a duplicated event) or a real extreme value? Fix or drop errors with a documented rule. For real extremes, use methods that are robust to them rather than deleting them: the median and IQR instead of the mean and standard deviation, winsorising or capping at a percentile, log transforms for multiplicative data, or robust regression. In an experiment, decide the rule before looking at results, or the choice becomes a way to manufacture significance.
Part 2: Probability (8-17)
8. What is conditional probability?
The probability of A given that B happened: P(A | B) = P(A and B) / P(B). It restricts the sample space to the outcomes where B occurred. Example: with two fair coins, the probability both are heads is 1/4, but given that at least one is heads it is 1/3, because "at least one head" leaves three equally likely outcomes (HH, HT, TH).
9. Independent vs mutually exclusive events?
Independent: knowing one happened does not change the probability of the other, P(A and B) = P(A) P(B). Mutually exclusive: they cannot both happen, P(A and B) = 0. The trap: two mutually exclusive events with non-zero probabilities are never independent, because knowing one happened tells you the other did not.
10. State Bayes' theorem and work an example.
P(A | B) = P(B | A) P(A) / P(B).
A disease affects 1% of people. A test detects it 99% of the time and gives a false positive 5% of the time. You test positive. What is the probability you have the disease?
- P(positive) = 0.01 x 0.99 + 0.99 x 0.05 = 0.0099 + 0.0495 = 0.0594
- P(disease | positive) = 0.0099 / 0.0594 ≈ 0.17
About 17%, despite the "99% accurate" test, because healthy people vastly outnumber sick ones and 5% of a large group is a lot of false positives.
11. What is the base rate fallacy?
Ignoring the prior probability (the base rate) and judging only from how well the evidence fits. Question 10 is the canonical case: people anchor on the 99% sensitivity and answer "about 99%." It shows up in fraud detection and alerting: a rare event plus an imperfect detector means most alerts are false, which is why precision matters as much as recall.
12. Combinations vs permutations?
Permutations count ordered arrangements: choosing k of n where order matters, n! / (n - k)!. Combinations count unordered selections: n! / (k! (n - k)!). Choosing a president, vice president and treasurer from 10 people is a permutation (720); choosing a committee of 3 is a combination (120). The question to ask yourself: does swapping two chosen items produce a different outcome?
13. What is expected value, and why is linearity so useful?
The probability-weighted average of a random variable's outcomes. Linearity of expectation, E[X + Y] = E[X] + E[Y], holds even when X and Y are dependent, which turns hard problems into sums of easy ones. Example: the expected number of people who get their own hat back when n hats are handed out at random is 1, for any n, because each person has a 1/n chance and there are n people.
14. What is the expected value of the maximum of two fair dice?
P(max ≤ k) = (k/6)², so P(max = k) = (k² - (k - 1)²) / 36 = (2k - 1) / 36.
E[max] = Σ k (2k - 1) / 36 for k = 1 to 6 = (1 + 6 + 15 + 28 + 45 + 66) / 36 = 161 / 36 ≈ 4.47.
The method (find the CDF of the maximum first, then difference it) is what the interviewer is checking; it works for the max of any number of independent variables.
15. The Monty Hall problem: should you switch?
Yes: switching wins with probability 2/3. Your first pick is right 1/3 of the time. The host, who knows where the car is, always opens a losing door from the other two. If your first pick was wrong (2/3 of the time), the only remaining closed door has the car. The key detail is that the host's choice is not random; if he opened a door at random and happened to reveal a goat, switching would win only 1/2 of the time.
16. How many people do you need for a better-than-even chance that two share a birthday?
23 (ignoring leap years and assuming birthdays are uniform). Compute the complement: the probability all n birthdays differ is (365/365)(364/365)...((365 - n + 1)/365), which drops below 0.5 at n = 23. It is surprising because the number of pairs grows quadratically: 23 people form 253 pairs. The same reasoning tells you when hash collisions become likely (around the square root of the number of buckets).
17. What is the law of total expectation?
E[X] = E[E[X | Y]]: average the conditional expectations over the distribution of Y. Example: what is the expected number of rolls of a fair die to get a 6? Condition on the first roll: with probability 1/6 you are done in 1 roll; otherwise you have used 1 roll and are back where you started. E = 1 + (5/6) E, so E = 6. Conditioning on the first step is the standard way to solve "expected time until" questions.
Part 3: Distributions and Limit Theorems (18-26)
18. What is the 68-95-99.7 rule?
For a normal distribution, about 68% of values fall within one standard deviation of the mean, 95% within two (more precisely 1.96 for exactly 95%), and 99.7% within three. It is a quick sanity check, and it only applies to roughly normal data; for heavy-tailed data, "three sigma" events happen far more often.
19. When does the binomial distribution apply?
A fixed number n of independent trials, each with the same success probability p, counting successes. Mean np, variance np(1 - p). Examples: conversions out of n visitors, defective items in a batch. Each single trial is a Bernoulli variable with variance p(1 - p), which is largest at p = 0.5; that is why proportions near 50% need the biggest samples to estimate precisely.
20. When does the Poisson distribution apply?
Counts of events in a fixed interval when events occur independently at a constant average rate λ: requests per second, defects per meter, support tickets per hour. Its mean and variance are both λ. If the observed variance is much larger than the mean (overdispersion), the Poisson assumption is wrong, often because the rate itself varies, and a negative binomial model fits better. Poisson also approximates the binomial when n is large and p is small.
21. What does "memoryless" mean for the exponential distribution?
The time between events in a Poisson process is exponential with rate λ, mean 1/λ. Memorylessness means P(T > s + t | T > s) = P(T > t): having already waited s minutes does not change the distribution of the remaining wait. The exponential is the only continuous distribution with this property (the geometric is the discrete one). Its median is ln 2 / λ ≈ 0.69 / λ, below its mean, because the distribution is right-skewed.
22. What is the log-normal distribution, and what is its mean?
X is log-normal if log X is normal with mean μ and standard deviation σ. It models positive, multiplicative, right-skewed quantities: incomes, file sizes, latencies, revenue per user. Its median is e^μ but its mean is e^(μ + σ²/2), so the mean is always above the median and grows quickly with σ. Exponentiating the mean of the logs gives you the median, not the mean, a common error when reporting results from a log-transformed model.
23. Why is the Beta distribution used as a prior for a conversion rate?
It lives on [0, 1] and is the conjugate prior for binomial data: start with Beta(a, b), observe k successes in n trials, and the posterior is Beta(a + k, b + n - k). Updating is just adding counts, and a and b behave like pseudo-counts of prior successes and failures (Beta(1, 1) is uniform). This is the basis of Bayesian A/B testing and Thompson sampling for bandits.
24. What does the central limit theorem say, and what does it not say?
For independent, identically distributed variables with finite variance, the distribution of the sample mean approaches a normal distribution as the sample size grows, whatever the shape of the original distribution, with standard error σ / √n. It is why z-tests and t-tests work on non-normal data like conversion rates.
What it does not say: it does not make the data normal, it says nothing about medians or maxima, it needs larger samples for heavily skewed data, and it fails for distributions without finite variance (such as Cauchy, or some power laws).
25. What is the law of large numbers?
As the sample size grows, the sample average converges to the expected value. It is the guarantee that more data gives a more accurate estimate. The CLT goes further and describes the shape of the error around that limit. The gambler's fallacy misreads the law: it does not say outcomes "balance out" in the short run; it says early deviations get diluted, not corrected.
Conditioning a uniform variable on an interval gives a uniform variable on that interval, so X | X > 0.5 is uniform on (0.5, 1) and its expectation is the midpoint, 0.75. The general skill is recognising the truncated distribution rather than integrating from scratch.
Part 4: Hypothesis Testing (27-40)
27. What are the null and alternative hypotheses, and why does the direction matter?
The null (H0) is the default claim you test against, usually "no effect" or "no difference." The alternative (H1) is what you would conclude if the evidence is strong enough. You never prove the null; you either reject it or fail to reject it. The direction matters because it sets what counts as "extreme": a one-sided alternative (the new variant is better) puts all of α in one tail, and choosing the direction after seeing the data inflates the false positive rate.
28. What is a p-value?
The probability, assuming the null hypothesis is true, of observing a result at least as extreme as the one you got. A p-value of 0.03 means that if there were no effect, you would see data this extreme about 3% of the time.
What it is not: the probability that the null is true, the probability the result is a fluke, or a measure of the size or importance of the effect. A tiny effect on a huge sample gives a tiny p-value.
29. If the null hypothesis is true, what is the distribution of the p-value?
Uniform on (0, 1), for a continuous test statistic and a correctly specified test. That is exactly why a threshold of α = 0.05 gives a 5% false positive rate when there is no effect: 5% of a uniform distribution lies below 0.05. It is also a useful diagnostic: a pile of p-values just under 0.05 across many studies suggests selective reporting.
30. Type I vs type II errors?
A type I error is a false positive: rejecting a true null. Its probability is α, which you choose. A type II error is a false negative: failing to reject a false null. Its probability is β, and power is 1 - β. For a fixed sample, lowering α raises β; the only way to lower both is more data or less noise.
31. What is statistical power, and what increases it?
The probability of detecting an effect when it really exists. Power increases with a larger sample, a larger true effect, lower variance in the metric, and a higher α (accepting more false positives). Underpowered experiments are worse than they look: they miss real effects, and the "significant" results they do find overestimate the effect size, because only the lucky draws cross the threshold.
32. How do you compute the sample size for an experiment?
For comparing two means with equal groups, two-sided α = 0.05 and 80% power, a good approximation is
n per group ≈ 2 (z₀.₉₇₅ + z₀.₈₀)² σ² / δ² = 2 (1.96 + 0.84)² σ² / δ² ≈ 16 σ² / δ²
where δ is the minimum effect you care about detecting. For a conversion rate, σ² = p(1 - p). With a 10% baseline and a 1 percentage point minimum detectable effect: 16 x 0.09 / 0.0001 = 14,400 users per group. The interview point: halving the detectable effect quadruples the sample, so the minimum detectable effect is a business decision, not a statistics one.
33. How do you interpret a 95% confidence interval?
If you repeated the experiment many times and built an interval the same way each time, about 95% of those intervals would contain the true value. It is not "a 95% probability that the true value lies in this interval": in frequentist statistics the parameter is fixed and the interval is the random thing. (A Bayesian credible interval does support the probability statement, given its prior.) Practically, read the interval as the range of effect sizes consistent with the data.
34. What makes a confidence interval wider?
A higher confidence level (99% is wider than 95%), more variability in the data, and a smaller sample. Width shrinks with the square root of the sample size, so halving the width takes four times the data.
They are two views of the same calculation. A two-sided test at level α rejects H0: θ = θ₀ exactly when θ₀ lies outside the (1 - α) confidence interval (for the matching test and interval). An interval for a difference that excludes zero means the difference is significant at that level, and the interval tells you more than the p-value: it shows the plausible effect sizes.
36. t-test vs z-test?
Use a z-test when the population standard deviation is known, or for proportions with large samples. Use a t-test when the standard deviation is estimated from the sample, which is almost always. The t distribution has heavier tails to account for that extra uncertainty, and it converges to the normal as the sample grows, so with thousands of observations the two give practically the same answer. Welch's t-test, which does not assume equal variances, is the safe default for two groups.
37. Paired vs unpaired t-test?
A paired test is for two measurements on the same units (before and after on the same users, two models on the same test examples): it tests whether the mean of the differences is zero, which removes between-unit variation and is usually much more powerful. An unpaired (two-sample) test compares independent groups. Using an unpaired test on paired data throws away that power; using a paired test on independent data is simply wrong.
38. When do you use a chi-square test?
For categorical counts. The test of independence checks whether two categorical variables are related (device type vs converted or not); the goodness-of-fit test checks whether observed counts match expected proportions (did a 50/50 split actually produce 50/50 traffic? see question 54). The statistic sums (observed - expected)² / expected over cells, and the approximation needs reasonably large expected counts; a common rule of thumb is at least 5 per cell, with Fisher's exact test for small tables.
39. What does ANOVA test, and what do you do after a significant result?
One-way ANOVA tests whether the means of three or more groups are all equal, by comparing variation between group means to variation within groups (the F statistic). A significant result says at least one mean differs, not which. Follow up with post-hoc comparisons that control for multiple testing (Tukey's HSD, or Bonferroni-adjusted pairwise tests). Running many pairwise t-tests instead inflates the false positive rate (next question).
40. What is the multiple comparisons problem, and how do Bonferroni and Benjamini-Hochberg differ?
Each test at α = 0.05 has a 5% false positive chance, so many tests almost guarantee one: with 20 independent tests and no real effects, P(at least one false positive) = 1 - 0.95²⁰ ≈ 64%.
- Bonferroni controls the family-wise error rate (the chance of even one false positive) by testing each hypothesis at α / m. Simple and conservative; it costs a lot of power when m is large.
- Benjamini-Hochberg controls the false discovery rate (the expected share of false positives among the discoveries). Sort the p-values, find the largest k with p₍ₖ₎ ≤ (k / m) q, and reject the first k. Much more power when many tests are run, such as many metrics or many segments.
Choose by the cost of one false positive: FWER for a launch decision on one primary metric, FDR for screening.
Part 5: Regression and Correlation (41-45)
41. What are the assumptions of linear regression?
- Linearity: the expected outcome is a linear function of the predictors (after any transforms).
- Independence of errors (violated by repeated measures and time series).
- Homoscedasticity: constant error variance across fitted values.
- Normality of errors, which matters for small-sample inference, not for the coefficient estimates themselves.
- No perfect multicollinearity among predictors.
Check them with residual plots, and say what you would do when one fails: transform, use robust (heteroscedasticity-consistent) standard errors, cluster standard errors, or switch models.
42. What does R² tell you, and what doesn't it?
The share of the outcome's variance explained by the model, between 0 and 1 for ordinary least squares with an intercept. It never decreases when you add predictors, even useless ones, which is why adjusted R² and out-of-sample error exist. A high R² does not mean the model is correct or causal, and a low R² can still come with a precisely estimated, important coefficient. For prediction, judge on held-out data.
43. How do you interpret a logistic regression coefficient?
A coefficient β is the change in the log-odds of the outcome for a one-unit increase in the predictor, holding the others fixed. Exponentiate it to get an odds ratio: β = 0.7 means e^0.7 ≈ 2.0, so the odds roughly double. It is not a change in probability; the effect on probability depends on where you start, because the logistic curve is flattest near 0 and 1.
44. What is multicollinearity, and why does it matter?
Predictors that are highly correlated with each other. It does not bias predictions, but it makes individual coefficients unstable: their standard errors inflate, signs can flip between samples, and you cannot tell which variable is doing the work. Detect it with correlation matrices and variance inflation factors (VIF); handle it by dropping or combining predictors, or with regularisation (ridge regression).
45. What is regression to the mean, and how does it fool people?
Extreme measurements tend to be followed by less extreme ones, because part of any extreme value is luck that does not repeat. The trap: the worst-performing stores get a new manager and improve; the best performers get praised and slip; neither change proves the intervention worked. The fix is a control group drawn from the same extreme set, so the comparison isolates the treatment from the bounce back.
Part 6: Bias and Causality (46-50)
46. Correlation vs causation: what turns a correlation into a causal claim?
A correlation can come from causation in either direction, a common cause (confounding), selection, or chance. To claim causation you need a design that rules the others out: a randomised experiment, or an observational design with explicit, defensible assumptions (difference-in-differences, instrumental variables, regression discontinuity, matching; see Part 7). Interviewers want you to name the specific alternative explanation for the correlation in front of you, not recite the slogan.
47. What is a confounding variable, and how do you control for it?
A variable that affects both the treatment and the outcome, creating a spurious association. Users who enable a feature retain better, but engaged users are more likely to enable features and to retain anyway. Control it by randomisation (best), or in observational data by stratifying, matching or including it in a regression, which only works for confounders you measured. Unmeasured confounding is the reason observational results need sensitivity analysis.
48. What is Simpson's paradox?
A trend that appears within every subgroup reverses when the groups are combined, because a confounder changes the mix. In a well-known kidney stone study, treatment A had a higher success rate than B for small stones (93% vs 87%) and for large stones (73% vs 69%), yet a lower rate overall (78% vs 83%), because A was mostly given to the harder large-stone cases. Which number is right depends on the causal structure: here, stratify by stone size.
49. What is sampling bias? Give examples.
The sample systematically differs from the population you want to describe. Selection bias: surveying only users who opened the email. Non-response bias: unhappy customers are more likely to answer a satisfaction survey (or less, depending on the survey). Survivorship bias (next question). Convenience sampling: studying the users who are easiest to reach. More data does not fix any of these; it just makes the wrong answer more precise.
50. What is survivorship bias?
Drawing conclusions from the cases that made it through a filter while ignoring the ones that did not. The classic story is Abraham Wald's analysis of returning WWII bombers: the bullet holes showed where a plane could be hit and still come home, so the armour belonged where the returning planes had no holes. In product work: studying only retained users to learn what drives retention, or backtesting a strategy only on companies that still exist.
Bonus Part 7: A/B Testing and Causal Inference (51-58)
This is where product data science and senior rounds spend their time. Expect a scenario ("we changed the checkout button and conversion went up 2%; ship it?") and a series of "what could be wrong with that?" follow-ups. The A/B testing question bank drills this half separately.
51. Walk me through designing an A/B test.
- Hypothesis and primary metric, decided up front, plus guardrail metrics (latency, errors, revenue, unsubscribes).
- Randomisation unit: usually the user, not the session or page view, so one person sees one variant; it must match the unit you analyse.
- Minimum detectable effect and sample size (question 32), which fixes the duration. Run whole weeks to cover weekly cycles.
- Run without peeking at significance (question 53), and check the assignment ratio (question 54).
- Analyse the pre-registered metric with a confidence interval, check guardrails and pre-planned segments, and correct for multiple metrics.
- Decide on practical significance as well as statistical: is the effect worth the cost of shipping and maintaining it?
52. The test is significant on day 3. Can you stop it early?
Not if the design was a fixed-horizon test. Checking repeatedly and stopping at the first p < 0.05 inflates the false positive rate far above 5%, because you are giving random noise many chances to cross the line. If you need to stop early, design for it: sequential testing with an alpha-spending function or always-valid p-values, or a Bayesian decision rule set in advance. Early results also overweight the users who visit most, and novelty effects fade (question 55).
53. What is the "peeking problem" in one sentence?
Repeatedly testing an accumulating sample and stopping when it looks significant turns a 5% false positive rate into a much higher one, because each look is another draw. (It is question 52 compressed; interviewers ask for the one-liner too.)
54. What is a sample ratio mismatch, and why is it serious?
The observed split between variants differs from the designed split by more than chance allows: a 50/50 test with 50,000 vs 48,500 users. Check it with a chi-square goodness-of-fit test (question 38). An SRM means assignment or logging is broken (a redirect that loses users in one arm, a bot filter that treats variants differently, a crash in one variant), and the users who remain are no longer comparable. Do not trust the results until the cause is found, however good they look.
55. What are novelty and primacy effects?
Users react to change itself. A novelty effect inflates early engagement with a new feature because it is new; a primacy effect depresses it because users are used to the old one. Both fade, so a short test can reach the wrong conclusion. Run long enough, look at the effect over time, and compare new users (who have no habit to break) with existing ones.
56. What is interference, and when does it break an A/B test?
Standard analysis assumes one user's treatment does not affect another user's outcome (no interference, or SUTVA). It fails in networks and marketplaces: a new sharing feature affects friends in the control group; a ranking change for riders in one arm takes drivers away from the other. The measured difference is then biased. Fixes: randomise by cluster (city, social cluster), switchback designs that alternate treatment over time, or two-sided marketplace designs.
57. What does difference-in-differences assume?
You compare the change over time in a treated group with the change in an untreated group; the difference of the two differences estimates the effect. The key assumption is parallel trends: without treatment, both groups would have moved the same way. You cannot test it directly after treatment, but you can check that pre-treatment trends were parallel with an event study plot: if the treated group was already diverging before the intervention, the estimate is not credible.
58. Regression discontinuity and instrumental variables: what do they estimate?
Regression discontinuity uses a cutoff that assigns treatment (a credit score threshold for an offer, a test score for a programme). Units just above and just below are comparable, so the jump in the outcome at the cutoff estimates the effect at the cutoff. It assumes outcomes would be continuous at the threshold without treatment, which fails if people can manipulate where they land (check for bunching).
Instrumental variables use something that shifts treatment but affects the outcome only through treatment (random encouragement to use a feature). The estimate is the local average treatment effect (LATE): the effect for compliers, the units whose treatment the instrument actually changed, not the average treatment effect for everyone. Saying "LATE, for compliers" instead of "the effect" is the senior answer.
Quick-Fire: Statistics Interview Questions and Answers
- Population vs sample - the population is everything you want to describe; the sample is what you measured. A statistic estimates a parameter.
- Bias vs variance of an estimator - bias is systematic error, variance is spread across samples; mean squared error = bias² + variance.
- Markov's inequality - for non-negative X, P(X ≥ a) ≤ E[X] / a. Chebyshev: P(|X - μ| ≥ kσ) ≤ 1 / k² for any distribution with finite variance.
- Sampling with vs without replacement - with replacement the draws are independent (binomial); without, they are not (hypergeometric), which matters when the sample is a large share of the population.
- P(second ace | first ace) from one deck - 3/51, because one ace and one card are gone.
- One-tailed vs two-tailed - one-tailed tests a pre-specified direction and is more powerful in it; choose it before seeing data or not at all.
- Effect size - the magnitude of a difference (absolute or relative lift, Cohen's d), which significance alone never gives you.
- Bootstrap - resample the data with replacement many times and recompute the statistic to estimate its sampling distribution; useful for medians, ratios and other statistics without a simple formula.
- CUPED - variance reduction for experiments: adjust each user's metric using their pre-experiment value, Y - θ(X - mean of X) with θ = cov(X, Y) / var(X); same expected effect, narrower intervals.
- Negative control outcome - an outcome the treatment cannot affect; finding an "effect" on it reveals confounding or bias in the design.
- Matching assumption - conditional independence (no unmeasured confounders given the matched variables) plus overlap (comparable units exist in both groups).
- Publication bias - significant results get reported and null results do not, so the published literature overstates effects.
How to Practice for a Statistics Interview
- Work problems by hand, out loud. Define the random variable, state the assumption ("assume independence"), then compute. Interviewers score the setup more than the arithmetic.
- Simulate anything you doubt. Ten lines of Python with
numpy will settle Monty Hall, the birthday problem or a peeking simulation, and running one builds intuition no formula gives.
- Learn the traps as a list: p-value misreadings, base rates, peeking, multiple comparisons, SRM, Simpson's paradox, regression to the mean. Many questions are one of these in disguise.
- Practise the A/B scenario end to end with a timer: design, sample size, what can go wrong, decision. It is the most common senior question.
- Drill the recall questions under time pressure so the definitions take seconds and the time goes on reasoning.
Keep going
- Drill it under pressure: the statistics and A/B testing question banks cover everything above as timed multiple-choice, the machine learning bank covers the modelling side, and the free daily challenge gives you one a day with no account.
- Follow a track: data scientist prep, data analyst prep or ML engineer prep.
- Practise the queries too: most statistics rounds come with a SQL round; the SQL playground runs real queries in the browser, and the SQL essentials cheat sheet covers the window functions analysts get asked about.
- Round out the loop: Top 50 machine learning, data analyst, Python and product manager interview questions, and Top 45 SQL interview questions.
- Practise the follow-ups: the chat-based AI mock interview asks the "and what if the split was 52/48?" questions a real round runs on.
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