Calculate variance for click-through rates
Last updated: February 24, 2026
Quick Overview
Given the following scenario about revenue per session, calculate the the sample size needed.
Expedia
February 24, 2026112
6
127 solved
Given the following scenario about revenue per session, calculate the the sample size needed.
Expedia asks this during the Take-home Project to assess your experimentation skills. They want to see how you define success metrics, design controlled experiments, and interpret results with appropriate statistical rigor.
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 interference between treatment and control?
- How would you handle seasonality in your experiment?
- What would you do if a stakeholder wants to end the experiment early because initial results look good?
- What if you discover a bug in the logging during the experiment?
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Browse Analytics QuestionsSample Answer
Problem Setup
To calculate the variance for click-through rates (CTR) in the context of Expedia, we need to frame the analytical question: 'What sample size is necessary to detect a meaningful difference in click-t...
Methodology
For this problem, we will use the sample size formula for comparing two proportions, as CTR is a proportion of users who clicked:
[ n = \frac{(Z_{\alpha/2} + Z_{\beta})^2 \cdot (p_1(1-p_1) + p_2(1-p...
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