Calculate variance for user retention

Last updated: March 26, 2026

Quick Overview

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

Robinhood

Analytics & Experimentation

Data Scientist

Robinhood

March 26, 2026

Data Scientist

Phone Screen

Analytics & Experimentation

Easy

4,590 solved

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

Robinhood asks this during the Phone 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

Network effects and interference

Novelty and primacy effects

A/B testing methodology

Guardrail metrics

Simpson's paradox and ecological fallacy

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

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?
How would you handle interference between treatment and control?
How would you handle an experiment where the control and treatment groups are different sizes?

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Sample Answer

Problem Setup

To calculate the sample size needed for user retention analysis at Robinhood, we first need to define the analytical question: **What is the minimum sample size required to detect a statistically sign...

Methodology

To calculate the required sample size, we can use the following formula for proportions:

$n = \frac{(Z_{\alpha/2} + Z_{\beta})^2 \times (p_1(1 - p_1) + p_2(1 - p_2))}{(p_2 - p_1)^2}$

Where: ...

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