Calculate variance for click-through rates
Last updated: February 20, 2026
Quick Overview
Given the following scenario about user conversion, calculate the the sample size needed.
PayPal
February 20, 2026567
5
1,746 solved
Given the following scenario about user conversion, calculate the the sample size needed.
Analytics questions at PayPal evaluate your ability to define metrics, design experiments, and derive actionable insights from data. This Technical Screen question tests your end-to-end analytical thinking.
What the Interviewer Expects
- Design complex experimentation strategies for tricky scenarios
- Handle multi-armed bandits, switchback experiments, and quasi-experiments
- Address long-term effects vs short-term metrics
- Propose causal inference methods when randomization is not possible
- Build a measurement framework that connects metrics to business value
- Discuss organizational experimentation culture and maturity
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?
- What if you discover a bug in the logging during the experiment?
- What would you do if a stakeholder wants to end the experiment early because initial results look good?
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Browse Analytics QuestionsSample Answer
Problem Setup
To analyze the click-through rates (CTR) for PayPal's user conversion, we need to define the analytical question: "What is the sample size required to detect a statistically significant difference in ...
Methodology
To calculate the required sample size, we will use the formula for comparing two proportions. The formula is:
[ n = \frac{(Z_{\alpha/2} + Z_{\beta})^2 \cdot (p_1(1 - p_1) + p_2(1 - p_2))}{(p_1 - p_...
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