Factorial Design

Factorial Research Design: What this Application Involves

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Factorial Research Design

A research design with 2 or more independent variables (IV) or "factors"

Example:

A researcher who wants to examine the effect of style of dress (e.g., formal versus causual) and manner of interaction (e.g., 10 questions versus 10 comments about the job) on hiring rate. In this example there are two IVs (style of dress and manner of interaction) and 1 dependent variable (hiring rate). Each of the IVs has 2 levels. Factorial research designs are described by use of an equation. In this example, the study is described as a 2 (dress) X 2 (interaction) factorial research design.

Other examples of factorial designs:

3 x 2

2 x 3 x 2

 The number of digits refers to the number of independent variables (IVs).

• 3 x 2 refers to 2 IVs
• 2 x 3 x 2 refers to 3 IVs

 The digit refers to the number of levels of that IV.

• 3 x 2 refers to 3 levels of the first IV and 2 levels of the second IV.
• 2 x 3 x 2 refers to 2 levels of the first IV, 3 levels of the second IV, and 2 levels of the third IV.

Example of a 2 (weather) X 2 (shampoo) factorial design

In this study, 25 participants were randomly assigned to one of the four conditions and asked to:

"Rate the degree of frizziness of Dr. Margolin's hair along the following scale:"

The frizziness rating is the dependent variable or variable being measured in the study.

Example of a (weather) X 2 (shampoo) factorial design with dependent variable measures

On average, Dr. Margolin's hair was rated as most frizzy when shampoo B was used and the weather was humid. Her hair was less frizzy when shampoo A and humid conditions and shampoo B and sunny conditions were present. Least of all was the frizziness mean rating when shampoo A and sunny conditions were present.

Main Effects: Factorial Design

Main effect = separate effects of each independent variable regardless of the other independent variable

• A 2 X 2 factorial designs yields 2 main effects, one for each factor

• The row mean differences depict the main effect for one factor

• The column mean differences depict the main effect for the second factor

• When there is a difference in means between levels of a factor, then a main effect may be present. A statistical analysis (e.g., 2-way ANOVA) must be applied to verify whether a significant difference between mean scores/ratings exist.

There may be a main effect of shampoo because shampoo A mean score (1.5) differs from shampoo B mean score (4.5).

There may be a main effect of weather because sunny mean score (2) differs from humid mean score (4).

Use of statistical analyses would allow determination of whether significant differences in mean ratings between conditions exist.

Another Example: Main Effect of Factor A (Gender)?

In the following example, participants' improvement scores are measured to

evaluate the effect of three different treatments as they relate to participants' gender.

Is there a main effect of gender?

Main Effect of Factor B (Type of Treatment)?

In the following example, participants' improvement scores are measured to

evaluate the effect of three different treatments as they relate to participants' gender.

Is there a main effect of type of treatment?

Factorial Design: Interaction Effect & What It Is

An interaction effect occurs when the effects of one factor modify the effects of a second factor.

An interaction is present when the effect of one independent variable changes over the levels of the second. An interaction represents the joint effect of the IVs on the DV. An interaction effect is depicted in a graph by the presence of nonparallel data lines, or lines that cross or appear to cross at some time in the future.

Note that the above graphs represent the SAME data and only differ in terms of which IV is represented on the X axis.

On average, Dr. Margolin's hair was rated as most frizzy when shampoo B was used and the weather was humid. Her hair was less frizzy when shampoo A and humid conditions and shampoo B and sunny conditions were present. Least of all was the frizziness mean rating when shampoo A and sunny conditions were present.

In this example, the levels of one variable depends on levels of the other variable. Further statistical analysis would be necessary to confirm whether an interaction effect was actually present.

Interaction Effect: Example 2

As another example, one type of therapy may work better for certain types of people and not others as illustrated below.

Note that an interaction effect can occur when there is:

a) no main effect(s) for any independent variable (as in the above example);

b) a main effect for independent variable A but not B;

c) a main effect for independent variable B but not A; or

d) a main effect for independent variables A and B.

Why Use a Factorial Research Design?

More information is provided in an efficient manner. You don't have to conduct multiple studies, just one study can do the job of several. Few participants are needed. Answers to many questions (i.e., main effects and interaction effects) are provided. Moreover, the complexity of the situation studied may be more comparable to the complexity inherent in the real world.

We hope you enjoyed learning about factorial research design!

If you have any suggestions to improve this application, please contact Marcie Desrochers, mdesroch@brockport.edu