Calculate variance for user retention

Question

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

Codemia · Accepted Answer

To calculate the variance for user retention at Atlassian, we first need to define the analytical question: **How does user retention vary across different cohorts over time?** This involves determining the retention rate for various user segments based on factors such as the time since account creation, product usage frequency, and user demographics.

### Data Requirements:
1. User ID
2. Account creation date
3. Retention metrics over defined periods (e.g., 1 week, 1 month, 3 months)
4. User demographics (age, location, etc.)
5. Product usage metrics (frequency of logins, features used)
6. Any promotional campaigns or changes in product features during the observation period.

We will employ a cohort analysis framework to assess user retention and calculate the variance among retention rates across these cohorts. The key statistical approach here will involve:
- **Calculating retention rates** for different cohorts over specified time frames.
- **Using ANOVA (Analysis of Variance)** to determine if there are significant differences in retention rates between different cohorts. This will help us understand if certain user segments retain differently based on their characteristics.
- **Simpson's Paradox** will be a crucial consideration, as we must ensure that our analysis accounts for confounding variables that could skew results when aggregating data across cohorts.

Assume we have the following retention data for two cohorts over three months:
- **Cohort A (New Users)**: 
  - Month 1: 80 retained / 100 total users (80%)
  - Month 2: 60 retained / 100 total users (60%)
  - Month 3: 50 retained / 100 total users (50%)
- **Cohort B (Returning Users)**: 
  - Month 1: 90 retained / 100 total users (90%)
  - Month 2: 70 retained / 100 total users (70%)
  - Month 3: 60 retained / 100 total users (60%)

**Step 1:** Calculate mean retention for each cohort:
- Cohort A: (80% + 60% + 50%) / 3 = 63.33%
- Cohort B: (90% + 70% + 60%) / 3 = 73.33%

**Step 2:** Perform ANOVA to test if the differences are significant. Calculate variance for each cohort:
- Variance for Cohort A = [(80-63.33)^2 + (60-63.33)^2 + (50-63.33)^2] / 2 = 150.56
- Variance for Cohort B = [(90-73.33)^2 + (70-73.33)^2 + (60-73.33)^2] / 2 = 126.56

**Step 3:** Compare variances to understand the stability of retention across cohorts.

The ANOVA results will indicate whether the differences in retention rates between Cohort A and Cohort B are statistically significant. If Cohort B shows significantly higher retention with lower variance, it suggests that returning users are more stable in their engagement than new users. This could imply that investment in onboarding and retention strategies for new users is necessary to improve their retention rates. Moreover, the presence of Simpson's Paradox should be interpreted cautiously; if aggregated data shows an opposite trend, it may indicate that specific segments (e.g., demographic factors) skew the overall results.

Common pitfalls in this analysis include:
1. **Ignoring Confounding Variables**: Failing to account for external factors affecting retention can distort results. For instance, a newly implemented feature may influence retention but not be reflected in the cohorts analyzed.
2. **Misinterpretation of Simpson's Paradox**: Assuming that aggregated data accurately represents all cohorts can lead to erroneous conclusions about user behavior.
3. **Sample Size Issues**: Not ensuring adequate sample sizes can lead to unreliable variance calculations, making it difficult to draw meaningful conclusions about user retention.
4. **Short-term vs Long-term Focus**: Overemphasizing short-term retention rates without considering the long-term lifecycle of users can skew insights and lead to misguided strategies.

Calculate variance for user retention

Atlassian

What the Interviewer Expects

Key Topics to Cover

How to Approach This

Possible Follow-up Questions

Sharpen Your Skills on Codemia

Sample Answer

Problem Setup

Methodology

Submit Your Answer

Atlassian Data Scientist Interview Guide

Related Questions

Explain Bayesian vs frequentist with an example

Explain p-value with an example

Interpret no significant difference from an experiment

Design an A/B test for a recommendation algorithm

Calculate conditional probability for user retention