Choose tests and solve distribution parameters
Overview
This question evaluates proficiency in statistical inference for skewed count data, covering test selection for central tendency, negative binomial parameter estimation and zero-probability calculation, construction of confidence intervals for mean differences, and interpretation of p-values versus effect sizes within the Statistics & Math domain for a Data Scientist role. It is commonly asked to assess both conceptual understanding (assumptions, diagnostics, statistical versus practical significance, and multiple-testing considerations) and practical application (parameter solving, delta-method/GLM rationale, and robust effect-size estimation) when analyzing real-world count data.
Engagement Comparison: New vs Existing Users (2025-08-05 → 2025-09-01)
Context: You have per-user daily session counts (integer, skewed, many zeros) for two independent cohorts: new users and existing users. Your goal is to compare central tendency across cohorts and quantify the difference.
- Test selection for central tendency
- Which method would you use to compare central tendency between cohorts and why: two-sample t-test, Welch's t-test, Mann–Whitney U, or a GLM-based approach?
- State the key assumptions and the diagnostics you would run.
- Negative Binomial parameterization
- For existing users, assume daily sessions per user X ~ NB(r, p) with E[X] = r(1−p)/p and Var[X] = r(1−p)/p².
- Given μ = 2.40 and σ² = 6.96, solve for r and p, then compute P(X = 0).
- CI for difference in means
- For new users, μ = 1.85 and σ² = 4.20. With independent samples of size n_new = 5,000 and n_exist = 5,000, provide a 95% CI for the mean difference in sessions per user (new − existing) using a delta-method or GLM-based rationale. State approximations used.
- Interpreting t-test results and robust effect sizes
- A Welch's t-test yields p = 0.04 with Cohen's d = 0.08. Interpret practical vs statistical significance.
- If you also segmented by 5 countries, discuss multiple-testing control.
- Specify one robust effect-size metric for count data (e.g., ratio of means) and how to estimate its 95% CI.
Solution
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