Factorial Designs

Advantages of Factorial Designs

Factorial designs have many advantages over nonfactorial designs. The key advantage of factorial designs is their ability to study interactions between independent variables. Many research questions can only be answered when multiple, interacting influences on a dependent variable are tested. For example, a researcher might learn that one level of factor A is effective only when combined with a certain level of factor B, but is not effective when alone or combined with the other levels of factor B. Without a factorial design, a researcher might incorrectly assume that factor A either always or never affects the dependent variable, and would not be able to identify circumstances that affect the effectiveness of factor A.

In addition to their ability to examine interaction effects, factorial designs are cost-efficient. A factorial design can increase the amount of information that a study can provide with little increase in cost (e.g., time, number of subjects) over a nonfactorial design. For example, a nonfactorial study might examine the effect of independent variable A on dependent variable Y. This study design can answer the question, What is the effect of A on Y? By adding the independent variable B, creating a factorial design, a researcher can now answer two additional questions: What is the effect of B on Y? and Do A and B interact to affect Y?

A third advantage of factorial designs is that they enhance external validity by determining the effects of a key variable under several different conditions. When effects are consistent across multiple conditions (as created by the juxtaposition of the factors), researchers can be more confident in their ability to generalize the findings to additional situations.

Notation

A factorial design is noted by listing each factor as a cross product with the other factors. For example, if a researcher has three independent variables, type of emotional appeal (hope, fear, or guilt appeal), message topic (climate change, influenza prevention, tanning), and gender (male, female), it is a 3 × 3 × 2 factorial design. This notation identifies the number of factors there are in the design. In the example, there are three factors because there are three numbers listed in the cross product (3, 3, and 2). Each number also identifies how many levels each factor has. The first 3 represents the three message conditions, the second 3 represents the three message topics, and the 2 represents the two genders included in the study. This notation also identifies how many conditions there are in the study, which is the cross product of the number of levels in each factor. In the example, there are 18 conditions (3 × 3 × 2 = 18).

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