Chapter 6 M6: Hypothesis testing

For the grand finale, we get to…go back to another tool you’ve been using since intro :) But this time, we dig in to understand how the math underlying hypothesis testing actually works, as well as talking about some variations you may not have seen in earlier courses, including power, customized rejection regions, and the very-general likelihood ratio test.

Learning goals for this module include:

• Explain, conduct, and interpret the process of hypothesis testing
  • …in, like, a 300-level way! Think about this in terms of things like parameter spaces, simple and composite hypotheses, test statistics, rejection regions, etc. And yes, you still have to be able to interpret test results in the context of the application :)
• Describe and compare test rejection results and errors
  • Define error types, power, etc. – both the mathy definitions and what they mean in context
  • Explain the relationships between relevant concepts or choices: a test’s hypotheses, rejection region(s), p-value, error types, and power
• Work with likelihood ratio tests
  • In particular, explain what they are (what is the LR test stat?), how they relate/compare to other tests (what’s the relationship between the LR test stat and other test stats?), and why they’re useful (Neyman-Pearson Lemma).
  • As always, you wouldn’t have to work out super complex algebra on Assessments, but you might need to set up or explain a particular example.