08.01.01 introduction

Introduction

In the previous chapter we covered one of the major fields within statistical inference: estimation. As we hinted at the beginning of that chapter, the basic nature of an estimate is this:

Estimation

We don't know anything about a particular population parameter, so we collect a sample and measure the value of a sample statistic. Then, based on what that value is, we provide a range of values for the population parameter.

We now move on to the second major field in statistical inference: testing. In statistics, we often refer to a test as a hypothesis test, because we are always testing some hypothesis. This highlights the primary difference between estimation and testing. The basic nature of a test is this:

Testing

We don't know anything about a population parameter, but we hypothesize that it takes some specific proposed value. We collect a sample and calculate a value known as the test statistic. Then, based on what that value is, we decide to either:

reject the hypothesis that the proposed value for the population parameter is correct (because the evidence suggests that you should); or
not reject this hypothesis (because there is not enough evidence to do so)

Throughout this section we will explore the sorts of population parameters that can be included in a hypothesis test, the sorts of claims about these parameters that we can test, and what we can and cannot conclude after conducting such a test. In this chapter, we will focus our attention on testing claims about a single population parameter.