Many of the most effective statistical studies are comparative. When the response is quantitative and only two groups are compared, we use the tools presented in Chapter 7 to answer the questions “What is the size of the treatment effect?” and “Is the difference between groups statistically significant?” Two-sample t procedures compare the means of two populations, and we saw that these procedures are sufficiently robust to be widely useful.

Many studies, however, involve more than two groups. Consider the following examples:

• People often choose to listen to background music when performing various tasks. Does this choice result in increased productivity? A study looked at the performance of various tasks under different conditions of background music.
• The student newspaper plans an article comparing the customer demographics at the five coffeehouses around campus.
• Guayule is a shrub grown in the Southwest that contains a type of rubber that can be used in tires. Cooper Tire & Rubber investigates the tread life of six concept tires made entirely of rubber from guayule.¹

Is analysis in these settings just a set of two-sample t tests, each one comparing a different pair of groups? This can involve a large number of tests (for example, the tire study would involve 15 t tests), and each test uses only a subset of the data. Surely a more unified approach would be better.

In this chapter, we discuss such an approach that allows us to compare any number of groups. These techniques generalize the two-sample t test and share its robustness and usefulness. They are also related to the regression methods of Chapter 11, so we continue to use the F distributions and analysis of variance.