ABSTRACT
In Chapter 5 we studied general properties of hypothesis tests and illustrated the main
concepts using particular examples of hypothesis tests. However, we did not discuss
how such tests might be motivated in the first place. Just as we were able to provide
a general likelihood-based method for motivating estimators in Chapter 4, so too
are we able to provide general likelihood-based methods for motivating hypothesis
tests. The objective of this chapter is to present three such methods that can be used
in most situations where inference is based on a likelihood function. We begin by
presenting the motivation for these methods and describing them in detail when the
model involves a single parameter. After comparing the different approaches, we then
consider how they extend to situations where the model involves multiple parameters.
We will discuss a number of types of hypotheses in multiple parameter situations,
particularly the context of testing whether a model can be reduced to a simpler model
having a smaller number of parameters. Finally we return to the connection between
confidence intervals and hypothesis tests, and its relation to the methods introduced
in this chapter. The methods are illustrated using mortality comparisons within a
randomised clinical trial.
