Part XII — Hypothesis Testing

The formal machinery for asking whether an effect is real: hypotheses, test statistics, p-values, error types and power, and the main test families — likelihood ratio, parametric, nonparametric, permutation, and bootstrap.

Topics

Topic	Focus
The Hypothesis Testing Framework	Null and alternative hypotheses, errors, and power
Test Statistics	Levels, test statistics, and rejection regions
p-values	What p-values measure and how to read them
Type I and Type II Errors	False positives, false negatives, and the asymmetry between them
Statistical Power	The probability of detecting a real effect
Likelihood Ratio Tests	Comparing nested models by likelihood
Parametric Tests	t-tests and other tests that assume a distributional form
Nonparametric Tests	Rank-based and distribution-free tests
Permutation Tests	Exact tests from label shuffling
Bootstrap Tests	Hypothesis tests built on resampled null distributions