Summary and Practical Guide to Hypothesis Testing › Summary: Key Takeaways

Michael BrenndoerferJanuary 10, 20261 min read
Machine Learning from ScratchAll chapters
Part 2 of 9Hypothesis Testing
Chapter 22Summary and Practical Guide to Hypothesis Testing › Summary: Key Takeaways
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The Foundations

  1. P-values measure evidence against H₀, not the probability H₀ is true
  2. Confidence intervals show the range of plausible parameter values
  3. Effect sizes quantify magnitude independent of sample size
  4. Power determines your ability to detect effects that exist

The Tests

  1. Z-test: When σ is known (rare in practice)
  2. t-test: The workhorse for comparing means
  3. Welch's t-test: Default for two-group comparisons
  4. ANOVA: For comparing ≥3 groups
  5. Post-hoc tests: After significant ANOVA

The Errors

  1. Type I (α): False positive: rejecting true H₀
  2. Type II (β): False negative: failing to reject false H₀
  3. Multiple comparisons: Inflate error rates without correction

The Practice

  1. Plan before collecting data: Hypotheses, α, sample size
  2. Check assumptions: Normality, equal variances, independence
  3. Report completely: Effect size, CI, exact p-value, test used
  4. Interpret cautiously: Statistical ≠ practical significance