ABSTRACT
In Chapter 2 we discussed using confidence intervals to conclude whether or not
particular values of the parameter are plausible. This introduced us to the notion of
hypothesis testing, the principles of which will be developed in the next two chapters.
In this chapter we will discuss some of the basic concepts in hypothesis testing,
including significance level, power and P-values, and further discuss the connection
between hypothesis testing and confidence intervals. Chapter 6 will then make use
of these concepts to develop general methods for carrying out hypothesis tests based
on the likelihood function. Our discussion in this chapter and the next will present
hypothesis tests as rules for deciding whether an hypothesis should be rejected or not,
based on the observed sample. This is useful for assessing the statistical significance
of observed departures from the hypothesis, but reliance on a simple dichotomy can
often lead to misinterpretation, so we will also discuss the importance of viewing
hypothesis testing as complementary to the process of confidence interval estimation.
These notions will be illustrated using an extended example involving randomised
treatment comparisons.
