Calculate expected value for A/B test results

Last updated: May 26, 2026

Quick Overview

Given the following scenario about user conversion, calculate the the sample size needed.

JPMorgan
Statistics & Math
Data Scientist
JPMorgan
May 26, 2026
Data Scientist
Take-home Project
Statistics & Math
Hard

90

6

2,690 solved


Given the following scenario about user conversion, calculate the the sample size needed.

JPMorgan values data-driven decision making. This Take-home Project question assesses whether you can design experiments, interpret results correctly, and avoid common statistical pitfalls like p-hacking or Simpson's paradox.

What the Interviewer Expects
  • Derive results from first principles when needed
  • Handle complex scenarios with multiple interacting variables
  • Design experiments that account for real-world complications
  • Discuss advanced topics: Bayesian methods, causal inference, resampling
  • Connect statistical concepts to business decision-making
  • Identify subtle errors in reasoning (Simpson's paradox, survivorship bias)
Key Topics to Cover
Bayesian vs frequentist inference
Regression analysis
Power analysis and sample size calculation
Central Limit Theorem
Causal inference basics
Multiple testing correction (Bonferroni, FDR)
How to Approach This
  1. Define your hypotheses (H0 and H1) clearly before performing any test.
  2. Calculate required sample size BEFORE running an experiment, using power analysis.
  3. Remember the Central Limit Theorem: sample means become approximately normal with large n.
  4. Watch for Simpson's paradox. Always segment data by key dimensions.
  5. Distinguish between statistical significance and practical significance.
Possible Follow-up Questions
  • How would you design a follow-up experiment based on these results?
  • How would you explain this result to a non-technical audience?
  • How would you handle multiple comparisons?
  • What alternative statistical method could you use here?
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Sample Answer
Problem Formulation

In this scenario, we want to conduct an A/B test to measure user conversion rates between two groups: the control group (A) and the treatment group (B). We need to determine the sample size required t...

Solution Approach

To compute the sample size, we need the following steps:

  1. Define parameters: Establish pAp_A, pBp_B, Δp\Delta p, α\alpha, and eta.
  2. Calculate pooled conversion rate...

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