Calculate variance for click-through rates
Last updated: July 22, 2025
Quick Overview
Given the following scenario about user conversion, calculate the the p-value.
Citadel
July 22, 202515
5
3,087 solved
Given the following scenario about user conversion, calculate the the p-value.
Citadel asks this during the Technical Screen 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
- Define clear success metrics aligned with business goals
- Propose a basic experimental design with control and treatment groups
- Interpret results correctly and draw reasonable conclusions
- Identify obvious confounding variables
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 an experiment where the control and treatment groups are different sizes?
- How would you handle seasonality in your experiment?
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Browse Analytics QuestionsSample Answer
Problem Setup
To evaluate the effectiveness of a new marketing strategy implemented by Citadel, we need to calculate the variance for click-through rates (CTR) and ultimately determine the p-value to assess statist...
Methodology
For this analysis, we will conduct a two-proportion z-test to compare the CTRs of the two groups (control and treatment). The formula for the z-score is:
[ z = \frac{(p_1 - p_2)}{\sqrt{p(1 - p) \l...
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