Chapter 9 Testing Associations I: Difference of Means, F-test, and χ2 Test

All the theory you had to suffer through in Chapter 8 (and all other theoretical chapters) was for the purposes of what we will do in this chapter and the next. All your efforts in introductory statistics will culminate in your ability to test bivarate associations for statistical significance — i.e., to make statistical inference about populations based on random samples.

Recall that we ended Chapter 7 with the knowledge that we describe/examine potential bivariate associations 1) between a discrete and a continuous variable through boxplots and difference of means, 2) between two discrete variables through contingency tables and difference of proportions, and 3) between two continuous variables through scatterplots and the correlation coefficient r, in a given dataset.

In this chapter and the next you will learn how to test these three types of bivariate associations for statistical significance, i.e. to check whether they can be generalizable to the population of interest. The current chapter is devoted to the first two types of bivariate associations. Chapter 10, the last chapter in this book, offers a preliminary first glimpse into a powerful technique for multivariate inference (that can be used for variables at any level of measurement), called statistical regression — albeit we only cover the continuous two-variable case to serve as introduction.

Now that you know how hypothesis testing works, most of the associations testing will seem straightforward and somewhat formulaic: pose hypotheses, test hypothesis, make a decision regarding hypotheses, interpret findings in a substantive manner. The only thing that differs is the tests, as different type of associations generally require different tests. Regression is the one procedure that adds more, as it were, to this predictable pattern, but we will deal with it when we get there.

And then you will be done. So what are you waiting for? Gird up your loins for this last final push and let’s get it over with!