8. Hypothesis Testing

Summary

Hypothesis testing refers to the process of choosing between competing hypotheses about a probability distribution, based on observed data from the distribution. It is a core topic in mathematical statistics, and indeed is a fundamental part of the language of statistics. In this chapter, we study the basics of hypothesis testing, and explore hypothesis tests in some of the most important parametric models: the normal model and the Bernoulli model.

Topics

1. Introduction
2. Tests in the Normal Model
3. Tests in the Bernoulli Model
4. Tests in the Two-Sample Normal Model
5. Likelihood Ratio Tests
6. Chi-Square Tests

Apps

• Mean Test Experiment
• Proportion Test Experiment
• Variance Test Experiment
• Dice Goodness of Fit Experiment
• Sign Test Experiment
• Probability Plot Experiment
• quantile app

Sources and Resources

• Introduction to Probability and Mathematical Statistics. Lee J Bain and Max Engelhardt
• Statistical Inference. George Casella and Rober L Berger
• Statistics. David Freedman, Robert Pisani and Robert Purves
• An Introduction to Mathematical Statistics and Its Applications. Richard J Larsen and Morris L Marx
• Elementary Statistics. Mario Triola
• Introductory Statistics. Neil A Weiss
• Wikipedia statistics portal
• Wolfram MathWorld articles on probability and statistics

Quote

• We must be careful not to confuse data with the abstractions we use to analyze them.—William James