Introduction to Multi-factor ANOVA

Researchers often identify more than one experimental factor of interest. In this situation one option is to set up separate, independent experiments in which a single treatment (or factor) is used in each experiment. Then the data from each experiment can be analyzed using the one-way ANOVA methods we learned about in previous lessons.

This approach might appear to have the advantage of a concentrated focus on a single treatment as well as simplicity of computations. However, there are several disadvantages.

• First, environmental factors or experimental material conditions may change during the process. This could distort the assessment of the relative importance of different treatments on the response variable.
• Second, it is inefficient. Setting up and running multiple separate experiments usually will involve more work and resources.
• Last, and probably the most important, this one-at-a-time approach does not allow the examination of how several treatments jointly impact the response.

ANOVA methodology can be extended to accommodate this multi-factor setting. Here is Dr. Rosenberger and Dr. Shumway talking about some of the things to look out for as you work your way through this lesson.

To put it into perspective, let’s take a look at the phrase ‘Experimental Design’, a term that you often hear. We are going to take this colloquial phrase and divide it into two formal components:

1. The Treatment Design
2. The Randomization Design

We will use the treatment design component to address the nature of the experimental factors under study and the randomization design component to address how treatments are assigned to experimental units. An experimental unit is defined to be that which receives a specific treatment level, or in a multi-factor setting, a specific treatment or factor combination. Note that the ANOVA model pertaining to a given study depends on both the treatment design and the randomization process.

The following figure illustrates the conceptual division between the treatment design and the randomization design. The terms that are in boldface type will be addressed in detail in this or future lessons.

Experimental Design