Test whether two user populations differ

Problem

Suppose you have two sets of users:

• Group A consists of users in North America
• Group B consists of users in Europe Every user is described by a vector of continuous features, such as session length, click-through rate, purchase conversion rate, and so on.

Task

Explain how you would assess whether the two groups show a significant difference in their overall multivariate distribution. Your response should address:

• Hypotheses: what exactly does “same distribution” mean?
• Preprocessing and normalization issues
• At least one statistical test or modeling method
• How to report significance and effect size
• Pitfalls such as multiple testing, confounding, non-IID data, heavy tails, and missing values Overview: The question tests skill in statistical inference and multivariate analysis, including stating hypotheses about equal distributions, handling preprocessing and normalization, selecting statistical tests or modeling approaches, and interpreting significance and effect size.