Calculate variance for A/B test results

Last updated: March 3, 2026

Quick Overview

Given the following scenario about revenue per session, calculate the the p-value.

Jane Street

Statistics & Math

Data Scientist

Jane Street

March 3, 2026

Data Scientist

Onsite

Statistics & Math

Medium

4,534 solved

Given the following scenario about revenue per session, calculate the the p-value.

Statistics questions at Jane Street test your ability to reason quantitatively and design rigorous experiments. This Onsite question evaluates your understanding of statistical inference and its application to business decisions.

What the Interviewer Expects

Set up the problem formally with proper notation
Apply the correct statistical test with clear justification
Interpret results with appropriate caveats and confidence levels
Discuss practical significance vs statistical significance
Identify potential confounders and how to address them

Key Topics to Cover

Causal inference basics

Central Limit Theorem

Hypothesis testing (H0, H1, p-values)

Regression analysis

Confidence intervals and significance levels

Power analysis and sample size calculation

How to Approach This

Define your hypotheses (H0 and H1) clearly before performing any test.
Calculate required sample size BEFORE running an experiment, using power analysis.
Remember the Central Limit Theorem: sample means become approximately normal with large n.
Watch for Simpson's paradox. Always segment data by key dimensions.
Distinguish between statistical significance and practical significance.

Possible Follow-up Questions

What alternative statistical method could you use here?
What assumptions does this test make, and how would you validate them?
How would you explain this result to a non-technical audience?
How would you handle multiple comparisons?

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Sample Answer

Problem Formulation

To analyze the results of the A/B test on revenue per session, we formulate the problem using the following notation:

Let $A$ be the control group, and $B$ be the treatment group.
Let ( ...

Solution Approach

Calculate Sample Means and Variances:
- Compute the mean revenue per session for both groups: $\bar{x}_A$ and $\bar{x}_B$ .
- Calculate the sample variances: $s_A^2$ and ( s_B...

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