Calculate variance for user retention
Last updated: November 23, 2025
Quick Overview
Given the following scenario about user conversion, calculate the the sample size needed.
Adobe
Statistics & Math
Data Scientist
Adobe
November 23, 2025Data Scientist
Take-home Project
Statistics & Math
Medium
37
14
2,074 solved
Given the following scenario about user conversion, calculate the the sample size needed.
Adobe 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
- Set up the problem formally with proper notation
- Apply the correct statistical test with clear justification
- Interpret results with appropriate caveats and confidence levels
- Discuss practical significance vs statistical significance
- Identify potential confounders and how to address them
Key Topics to Cover
Bayesian vs frequentist inference
Confidence intervals and significance levels
Regression analysis
Hypothesis testing (H0, H1, p-values)
Power analysis and sample size calculation
Multiple testing correction (Bonferroni, FDR)
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
- What if the sample size is very small?
- How would you explain this result to a non-technical audience?
- How would you design a follow-up experiment based on these results?
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Browse Statistics QuestionsSample Answer
Problem Formulation
To calculate the sample size needed for user retention analysis at Adobe, we need to define the parameters of our study clearly. We will use the following notation:
- p: the estimated proportion ...
Solution Approach
- Estimate the proportion (p): We need a baseline estimate of user retention. For instance, if previous data suggests that 70% of users retain, then p = 0.7.
- **Determine the margin of error (d...
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