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Inference: Hypothesis Testing and Beyond
Hypothesis testing framework, t/z/chi-square tests, multiple testing (Bonferroni, FDR), and bootstrap inference for non-parametric problems.
Module Content
Hypothesis Testing — The Framework
The mental model behind every test. Null, alternative, test statistic, p-value, decision. FIND_VIDEO: search 'hypothesis testing framework null hypothesis' — recommended channel: StatQuest. Aim for 11 min or under.
QUIZ: Setting Up H0, H1, and the Test
Practice quiz: The five steps of any hypothesis test. Once you see them, every named test (t, z, chi-square) is the same shape.
T-Tests, Z-Tests, and When to Use Each
The most-used tests in practice. The choice of which is more about sample size and known variance than anything else. FIND_VIDEO: search 't-test z-test paired tutorial' — recommended channel: StatQuest. Aim for 10 min or under.
QUIZ: The Test Selection Decision Tree
Practice quiz: One- vs two-sample, paired vs unpaired, t vs z. Quick reference for picking the right test.
Chi-Square and Categorical Data
The right test when both variables are categorical. Two forms — independence and goodness-of-fit. FIND_VIDEO: search 'chi-square test independence goodness of fit' — recommended channel: StatQuest. Aim for 10 min or under.
QUIZ: Chi-Square in Practice
Practice quiz: When both inputs are categorical, chi-square is the tool. The two common forms cover most DS use cases.
Multiple Testing and the Family-Wise Error Rate
The single most-overlooked problem in DS practice. If you run 20 tests at α=0.05, you'll average one false positive — by design. FIND_VIDEO: search 'multiple testing Bonferroni FDR correction' — recommended channel: StatQuest. Aim for 11 min or under.
QUIZ: Bonferroni, FDR, and What Actually Works
Practice quiz: The three main correction strategies and when to use each. Plus the cultural problem (researchers ignoring it) and how to fix the workflow.
Bootstrap — Inference Without Distributional Assumptions
The single most powerful tool for non-parametric inference. Works on anything where formulas don't exist. FIND_VIDEO: search 'bootstrap statistics tutorial' — recommended channel: StatQuest. Aim for 11 min or under.
QUIZ: Building a Bootstrap CI From Scratch
Practice quiz: The bootstrap is the answer when textbook formulas don't apply. Master the basic algorithm — it's 5 lines of code.
SUBMISSION: Project 2 — End-to-End A/B Experiment Analysis with Sample Sizing & Welch's T-Test
Size, run, and correctly analyze a homepage-redesign A/B test: pre-registered power calculation, Welch's t-test on revenue-per-visitor, multiple-comparison guardrails, and a ship/no-ship decision memo.
SUBMISSION: Project 3 — Bootstrap Confidence Intervals & Permutation Tests on Non-Normal Retention Metrics
Replace fragile t-based CIs on skewed retention data with percentile bootstrap intervals, validate a feature-launch lift with an exact permutation test, and document when each non-parametric tool breaks.