This chapter is a turning point. This is where we move from simply describing data to using data to make inferences about things we do not know. It is the beginning of inferential statistics. After all, “it's not the figures themselves, it's what you do with them that matters” (K.A.C. Manderville).1 Every semester, I try to convince my students that statistics is as interesting as the problems it is used to solve. I have taught statistics long enough to know that very few people enjoy the act of crunching numbers in a dataset. Admittedly, you would have to be pretty unique to like that. However, everyone is interested in something, and to answer interesting questions about any topic, we almost always turn to data.
The goal of inferential statistics is to use sample data to estimate unknown characteristics of a larger population. When polling agencies release early estimates for an upcoming election, they are relying on inferential statistics. Biochemists use inferential statistics to develop vaccines to prevent diseases. When businesses decide which marketing platforms to invest in, they use inferential statistics. In fact, most important data-driven decisions rely on statistical inference. In order to use sample data to gain insights into the larger population, we first must understand sampling distributions.
6.1 Defining a Sampling Distribution
Recall from Chapter 3 on descriptive statistics that a distribution of data is simply an organized ...