Chapter 4 Hypothesis Testing
(I wasn’t entirely happy with the treatment of Wasserman and Casella & Berger. So I’m following the treatment of (Hogg, McKean, and Craig 2019))
A hypothesis test is a process to reject or not reject a well-defined statements. Intuitively, there are three components to a hypothesis test:
- Null hypothesis H0versus Alternative hypothesis H1
- Data
- Decision rule to reject H0 and accept H1 or to not reject H0 and reject H1.
The mathematical formulation of this is a bit more restrictive because of the need for well-defined and verifiable statements. We will restrict our attention to hypotheses about either:
- a parameter of a model, or
- a functional of the underlying density distribution f, i.e., a mapping T(f)∈R. For example, μ(f)=∫xf(x)dx.
References
Hogg, Robert V., Joseph W. McKean, and Allen T. Craig. 2019. Introduction to Mathematical Statistics. 8th ed. Boston: Pearson.