Some of the most important applications of probability theory involve reasoning in the presence of uncertainty. In these applications, we analyze the observations of an experiment in order to make a decision. When the decision is based on the properties of random variables, the reasoning is referred to as statistical inference. In Chapter 10, we introduced two types of statistical inference for model parameters: point estimation and confidence-interval estimation. In this chapter, we introduce two more categories of inference: significance testing and hypothesis testing.
Statistical inference is a broad, deep subject with a very large body of theoretical knowledge and practical techniques. It has its own extensive literature and a vast collection of practical techniques, many of them valuable secrets of companies and governments. This chapter, Chapter 10, and Chapter 12 provide an introductory view of the subject of statistical inference. Our aim is to indicate to readers how the fundamentals of probability theory presented in the earlier chapters can be used to make accurate decisions in the presence of uncertainty.
Like probability theory, the theory of statistical inference refers to an experiment consisting of a procedure and observations. In all statistical inference methods, there is also a set of possible decisions and a means of measuring the accuracy of a decision. A statistical inference method assigns a decision to each possible outcome of the ...