Calculate variance for A/B test results
Last updated: July 26, 2025
Quick Overview
Given the following scenario about user conversion, calculate the the sample size needed.
Dropbox
July 26, 2025263
5
3,422 solved
Given the following scenario about user conversion, calculate the the sample size needed.
This statistics question from Dropbox's Onsite tests your ability to apply mathematical reasoning to practical problems. The interviewer expects precise definitions, correct methodology, and awareness of assumptions and limitations.
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
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 design a follow-up experiment based on these results?
- How would you explain this result to a non-technical audience?
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Problem Formulation
To determine the sample size needed for an A/B test on user conversion rates, we need to establish the following parameters:
- Null Hypothesis (H0): There is no difference in conversion rates be...
Solution Approach
To calculate the required sample size (n) for each group, we use the formula for sample size in comparing two proportions:
n = (Zα/2 + Zβ)² * (p1(1-p1) + p2(1-p2)) / (p1 - p2)²
Where:
- Zα/2 is the ...
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