Calculate conditional probability for click-through rates
Last updated: August 31, 2025
Quick Overview
Given the following scenario about user conversion, calculate the the sample size needed.
Brex
August 31, 20251
5
2,379 solved
Given the following scenario about user conversion, calculate the the sample size needed.
This analytics question from Brex's Technical Screen tests your ability to think critically about data. The interviewer expects you to consider confounding variables, selection bias, and the difference between correlation and causation.
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 interference between treatment and control?
- What if you discover a bug in the logging during the experiment?
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Problem Setup
The analytical question here is to calculate the conditional probability of click-through rates (CTR) for a specific marketing campaign at Brex, while also determining the sample size needed for a val...
Methodology
For this analysis, I would apply the formula for conditional probability and the sample size calculation for proportions. The conditional probability of conversion given a click can be expressed as:
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