Statistics interview questions

What a strong answer covers

• Define mean as the arithmetic average (sum of values divided by count).
• Define median as the middle value in a sorted dataset.
• Explain that the mean is sensitive to outliers, while the median is robust to them.
• Provide examples: mean for symmetrically distributed data, median for skewed data (e.g., income, housing prices).

Where people lose the point

• ×Confusing the definitions or calculation methods for mean and median.
• ×Failing to explain the impact of outliers on each measure.
• ×Not providing clear examples of when to use each.

What a strong answer covers

• Define standard deviation as a measure of the average distance of data points from the mean.
• Explain that a larger standard deviation indicates greater spread or variability in the data.
• Describe its units are the same as the original data, making it more interpretable than variance.
• Relate it to variance: standard deviation is the square root of the variance, and variance is the average of the squared differences from the mean.

Where people lose the point

• ×Confusing standard deviation with variance or range.
• ×Failing to explain what 'spread' or 'variability' means in practical terms.
• ×Not mentioning that its units are the same as the data.

What a strong answer covers

• Define p-value as the probability of observing data as extreme as, or more extreme than, the sample data, assuming the null hypothesis is true.
• Explain that a small p-value (typically < 0.05) suggests strong evidence against the null hypothesis, leading to its rejection.
• A large p-value suggests insufficient evidence to reject the null hypothesis.
• Emphasize that a p-value does not represent the probability that the null hypothesis is true or false.

Where people lose the point

• ×Incorrectly stating that a p-value is the probability the null hypothesis is true.
• ×Failing to mention the assumption that the null hypothesis is true when defining p-value.
• ×Not linking the p-value to the decision of rejecting or failing to reject the null hypothesis.

What a strong answer covers

• Define Type I error as rejecting a true null hypothesis (false positive).
• Define Type II error as failing to reject a false null hypothesis (false negative).
• Explain that the probability of a Type I error is alpha (α), and the probability of a Type II error is beta (β).
• Provide a clear, distinct example for each type of error (e.g., medical testing, quality control).

Where people lose the point

• ×Confusing the definitions of Type I and Type II errors.
• ×Providing examples that are unclear or don't distinctly illustrate each error.
• ×Not mentioning the relationship with alpha and beta.

What a strong answer covers

• State the CLT: for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the population's original distribution.
• Mention the conditions for CLT (large sample size, independent samples).
• Explain its importance: allows us to use normal distribution theory for inference about population means, even if the population is not normal.
• Connect it to confidence intervals and hypothesis testing for means.

Where people lose the point

• ×Incorrectly stating that the population itself becomes normally distributed.
• ×Failing to mention the 'sampling distribution of the sample mean'.
• ×Not explaining *why* it's important for inferential statistics.

What a strong answer covers

• Define A/B testing: randomly splitting users into two groups (control A, variant B) to compare outcomes.
• Outline the setup: define clear hypotheses (H0: no difference in conversion, Ha: variant B increases conversion), define metrics (conversion rate), random assignment of users.
• Discuss statistical considerations: sample size calculation (power analysis), choosing a significance level (alpha), duration of the test, and potential biases (e.g., novelty effect).
• Explain how to analyze results: compare conversion rates using a statistical test (e.g., chi-squared test for proportions) and interpret the p-value.

Where people lose the point

• ×Failing to mention random assignment as a core principle.
• ×Overlooking the importance of sample size calculation or test duration.
• ×Not specifying a statistical test for analysis or how to interpret its output.

What a strong answer covers

• Define the intercept (β0) as the expected value of the dependent variable when all independent variables are zero.
• Define the slope (β1) as the expected change in the dependent variable for a one-unit increase in the independent variable, holding other variables constant (in multiple regression).
• Emphasize interpreting coefficients in the context of the specific problem and units of the variables.
• Discuss limitations: extrapolation beyond data range, 'zero' not always meaningful for intercept.

Where people lose the point

• ×Interpreting the intercept as always meaningful, even when X=0 is outside the data range or impossible.
• ×Failing to mention 'holding other variables constant' for multiple regression slopes.
• ×Not relating the interpretation back to the specific units of the variables.

What a strong answer covers

• Define R-squared as the proportion of the variance in the dependent variable that is predictable from the independent variable(s).
• Explain that it ranges from 0 to 1, with higher values indicating a better fit (more variance explained).
• Discuss limitations: does not indicate causality, can be artificially inflated by adding more predictors (even irrelevant ones), does not tell if the model is biased or if assumptions are met.
• Mention Adjusted R-squared as a way to mitigate the issue of adding too many predictors.

Where people lose the point

• ×Stating that R-squared indicates causality.
• ×Failing to mention that adding more predictors always increases R-squared.
• ×Not discussing that a high R-squared doesn't guarantee a good model or valid predictions.

What a strong answer covers

• Define statistical significance: refers to the unlikelihood of an observed effect occurring by chance, indicated by a small p-value.
• Define practical significance: refers to the real-world importance or magnitude of an effect, regardless of its statistical significance.
• Explain that a statistically significant result might not be practically significant (e.g., a tiny effect in a large sample).
• Explain that a practically significant effect might not be statistically significant (e.g., small sample size).
• Emphasize the importance of considering both for decision-making.

Where people lose the point

• ×Confusing the two concepts or treating them as interchangeable.
• ×Failing to provide clear examples where one exists without the other.
• ×Not explaining *why* both are crucial for making informed decisions.

What a strong answer covers

• Define sampling bias as a systematic error in a sampling method that results in a sample that is not representative of the population.
• Describe common types: selection bias (e.g., convenience sampling), non-response bias, survivorship bias.
• Explain how these biases can lead to inaccurate conclusions.
• Suggest mitigation strategies: random sampling, stratified sampling, increasing response rates, careful study design.

Where people lose the point

• ×Confusing sampling bias with random error or measurement error.
• ×Only listing one type of bias or providing vague descriptions.
• ×Not offering concrete strategies for mitigation.

What a strong answer covers

• State Bayes' Theorem formula: P(A|B) = [P(B|A) * P(A)] / P(B).
• Explain each component: P(A|B) as posterior probability, P(B|A) as likelihood, P(A) as prior probability, P(B) as marginal probability.
• Describe its purpose: updating the probability of a hypothesis based on new evidence.
• Provide a clear, simple example, such as medical diagnostic testing or spam detection.

Where people lose the point

• ×Incorrectly stating the formula or mislabeling its components.
• ×Failing to explain the concept of updating beliefs with new evidence.
• ×Providing an example that is too complex or unclear.

What a strong answer covers

• Describe its bell-shaped, symmetric curve, with the mean, median, and mode all being equal.
• Mention that it is defined by two parameters: mean (μ) and standard deviation (σ).
• Explain the Empirical Rule (68-95-99.7 rule) for data within 1, 2, and 3 standard deviations of the mean.
• Highlight its importance due to the Central Limit Theorem and its prevalence in natural phenomena.

Where people lose the point

• ×Confusing its parameters with those of other distributions.
• ×Forgetting to mention its symmetry or the mean=median=mode property.
• ×Not connecting its importance to the Central Limit Theorem.

What a strong answer covers

• Define a confidence interval as a range of values within which the true population parameter is estimated to lie with a certain probability.
• Explain that a 95% confidence interval means that if we were to take many samples and construct a confidence interval from each, about 95% of those intervals would contain the true population mean.
• Emphasize that it does NOT mean there is a 95% probability that the true mean falls within *this specific* interval.
• Discuss its use in quantifying the precision of an estimate.

Where people lose the point

• ×Incorrectly stating that there is a 95% chance the true mean is in *this specific* interval.
• ×Failing to explain the frequentist interpretation of '95% confidence'.
• ×Not mentioning that it provides a range, not a single point estimate.

What a strong answer covers

• Identify the variables: two independent groups, continuous dependent variable (average spending).
• Propose a two-sample t-test (independent samples t-test) as the appropriate test.
• Explain the rationale: it compares the means of two independent groups to determine if they are significantly different.
• Mention key assumptions of the t-test: independence of observations, approximate normality of data (or large sample size), and homogeneity of variances (though robust to violations with unequal variance t-test).

Where people lose the point

• ×Suggesting an inappropriate test (e.g., ANOVA, chi-squared, paired t-test).
• ×Failing to justify the choice of test based on data type and research question.
• ×Not mentioning the key assumptions of the chosen test.

What a strong answer covers

• Define multicollinearity as a high correlation between two or more independent variables in a multiple regression model.
• Explain why it's a problem: makes it difficult to determine the individual effect of each predictor, inflates standard errors of coefficients, leading to unstable and unreliable coefficient estimates.
• Describe detection methods: Variance Inflation Factor (VIF > 5 or 10), high pairwise correlations between predictors.
• Suggest addressing strategies: remove one of the highly correlated variables, combine them into an index, collect more data, or use regularization techniques (e.g., Ridge regression).

Where people lose the point

• ×Confusing multicollinearity with correlation between independent and dependent variables.
• ×Failing to explain *why* it's problematic for coefficient interpretation and stability.
• ×Not providing concrete detection or mitigation strategies.