Calculate variance for coin flips
Last updated: November 23, 2025
Quick Overview
Given the following scenario about revenue per session, calculate the the sample size needed.
Twilio
November 23, 2025527
5
4,775 solved
Given the following scenario about revenue per session, calculate the the sample size needed.
Analytics questions at Twilio evaluate your ability to define metrics, design experiments, and derive actionable insights from data. This Phone Screen question tests your end-to-end analytical thinking.
What the Interviewer Expects
- Design a rigorous experiment with proper randomization and sample size calculation
- Define primary and guardrail metrics with clear rationale
- Address novelty effects, network effects, and interference
- Segment results appropriately and identify heterogeneous treatment effects
- Propose follow-up analyses when results are ambiguous
Key Topics to Cover
How to Approach This
- Define success metrics carefully. A good metric is measurable, actionable, and aligned with business goals.
- Run experiments long enough to account for novelty effects and weekly seasonality.
- Use funnel analysis to identify where users drop off for maximum optimization impact.
- Segment results by key dimensions (platform, country, user cohort) to catch hidden patterns.
- Consider network effects and interference between treatment and control groups.
Possible Follow-up Questions
- How would you handle an experiment where the control and treatment groups are different sizes?
- How would you handle seasonality in your experiment?
- How would you handle interference between treatment and control?
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Browse Analytics QuestionsSample Answer
Problem Setup
The analytical question here is to determine the sample size needed to accurately assess the variance in revenue per session for Twilio's services based on different coin flip scenarios (e.g., A/B tes...
Methodology
To calculate the sample size needed for our A/B test, we will use the formula for the sample size in comparing two means:
[ n = \left( \frac{(Z_{\alpha/2} + Z_{\beta}) \cdot (\sigma_1^2 + \sigma_2^2...
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