# Lesson 42: Two-Factor Analysis of Variance

In the previous lesson, we learned how to conduct an analysis of variance in an attempt to learn whether a (that's one!) factor played a role in the observed responses. For example, we investigated whether learning method (the factor) influenced a student's exam score (the response). We also investigated whether tire brand (the factor) influenced a car's stopping distance (the response).

What happens if we're not interested in whether one factor is associated with the observed responses, but whether two or three or more factors are associated with the observed responses. For example, we might be interested in learning whether smoking history (one factor) and type of stress test (a second factor) are associated with the time until maximum oxygen uptake (the response). That's the kind of data that we'll learn to analyze in this lesson. Specifically, we'll learn how to conduct a two-factor analysis of variance, so that we can test whether either of two factors, or their interaction, are associated with some continuous response.

The reality is this on-line lesson only contains an example of a two-factor analysis of variance. For the theoretical development, you are asked to refer to the textbook chapter on Two-Factor Analysis of Variance. Pedagogically, it is material that lends itself well to getting practice at learning a new statistical method solely from the formal presentation of a statistical textbook.