Compute sample size and Bayes posterior
Company: Roblox
Role: Data Scientist
Category: Statistics & Math
Difficulty: hard
Interview Round: Online Assessment
You are implementing two small statistical utilities.
Part A — Power / sample size (two-sample z-test)
- Input:
- `x`: a 1D numeric array of historical observations of a metric (assume i.i.d.).
- `alpha`: significance level (e.g., 0.05).
- `power`: desired power (e.g., 0.8).
- `effect_size`: the minimum detectable absolute difference in means, Δ (same units as `x`).
- Task: Compute the required **per-group** sample size `n` for an **equal-sized** A/B test using a **two-sided two-sample z-test**.
- Assumptions:
- The metric variance is the same in both groups.
- Population standard deviation is unknown; estimate it from `x` using the sample standard deviation `s`.
- Independent samples, normal approximation.
- Output: return the smallest integer `n` that achieves the requested power (round up).
Part B — Bayes’ rule
- Input: probabilities `p_A = P(A)`, `p_B_given_A = P(B|A)`, `p_B_given_notA = P(B|¬A)`.
- Task: compute and return `P(A|B)`.
- Assumptions: `0 < p_A < 1` and all conditional probabilities are valid.
Overview: This question evaluates understanding of statistical inference and probabilistic reasoning by combining a frequentist power/sample-size computation for a two-sided two-sample z-test with a basic Bayesian conditional probability calculation.
Read the full Roblox Data Scientist interview experience this question came from