Calculate variance for user retention
Last updated: May 11, 2026
Quick Overview
Given the following scenario about revenue per session, calculate the the sample size needed.
Two Sigma
May 11, 20261
5
3,291 solved
Given the following scenario about revenue per session, calculate the the sample size needed.
Two Sigma values data-driven decision making. This Take-home Project question assesses whether you can design experiments, interpret results correctly, and avoid common statistical pitfalls like p-hacking or Simpson's paradox.
What the Interviewer Expects
- Derive results from first principles when needed
- Handle complex scenarios with multiple interacting variables
- Design experiments that account for real-world complications
- Discuss advanced topics: Bayesian methods, causal inference, resampling
- Connect statistical concepts to business decision-making
- Identify subtle errors in reasoning (Simpson's paradox, survivorship bias)
Key Topics to Cover
How to Approach This
- Define your hypotheses (H0 and H1) clearly before performing any test.
- Calculate required sample size BEFORE running an experiment, using power analysis.
- Remember the Central Limit Theorem: sample means become approximately normal with large n.
- Watch for Simpson's paradox. Always segment data by key dimensions.
- Distinguish between statistical significance and practical significance.
Possible Follow-up Questions
- How would you handle multiple comparisons?
- What if the sample size is very small?
- How would you explain this result to a non-technical audience?
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