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Two Sigma·Data Scientist·Technical Phone Screen·Senior

Senior
May 2026

Summary

Two Sigma data science interview with a statistics-heavy question about t-statistics. One question, pretty deep, felt like they wanted to see if you actually understood what the math was doing rather than just reciting a formula.

Questions Asked (1)

Q1

You have an estimated coefficient from a regression or A/B test and its standard error. Why is the t-statistic a useful summary of evidence? What does it capture that the raw estimate alone doesn't, how does it connect to p-values and confidence intervals, and when can it be misleading?

A/B Testing & ExperimentationProduct Analytics & MetricsTechnical Trade-offs
Author's notes

I started with the intuitive angle: a coefficient of 0.5 means nothing if you don't know how noisy the estimate is.

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AI HintsAI Generated

Suggested Approach

Start by defining the t-statistic as the ratio of the estimated effect to its standard error, emphasizing that it standardizes the effect size by its uncertainty. Then explain how it directly yields p-values and confidence intervals, and finally discuss its limitations, such as sensitivity to assumptions and misinterpretation in multiple testing or non-normal settings.

Pro tip: Frame the t-statistic as a signal-to-noise ratio that quantifies evidence in a unitless way, enabling comparisons across metrics and experiments. Mention that while it's powerful, it's not a substitute for practical significance or robust design.

1. Define the t-statistic

State that t = estimate / standard error, representing how many standard errors the estimate is away from zero (or a null value).

2. Explain what it captures beyond the raw estimate

Highlight that the raw estimate alone ignores uncertainty; the t-statistic incorporates both effect size and precision, enabling assessment of statistical significance.

3. Connect to p-values and confidence intervals

Describe how the t-statistic maps to a p-value via the t-distribution (or normal approximation) and how it determines the width of confidence intervals (estimate ± critical value * SE).

4. Discuss when it can be misleading

Mention scenarios like small sample sizes, non-normal errors, heteroscedasticity, multiple comparisons, or when the estimate is practically insignificant despite a large t-statistic.

Key Points to Mention

  • t-statistic as a signal-to-noise ratio (effect size relative to uncertainty)
  • Direct relationship to p-values: larger |t| implies smaller p-value
  • Role in constructing confidence intervals: width depends on standard error and critical value
  • Assumptions: independence, normality (or large sample), correct standard errors
  • Limitations: sensitive to outliers, multiple testing inflates false positives, statistical vs practical significance
  • Alternative approaches: bootstrap, Bayesian methods, or robust standard errors when assumptions fail

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.