## Explain the factorial design with the help of a suitable example

Experimental design is a plan to conduct research in an objective and controlled manner, so that conclusions can be made or a hypothesis can be tested. Part of the experimental design process involves determining what the independent and dependent variables are. The independent variable (also known as ”factor”), or cause, is what the researcher controls. It doesn’t depend on any other variable in the study. The dependent variable, or effect, is the variable that changes in response to the independent variable and is what the researcher measures.

The definition of factorial design is an experiment that has multiple factors or independent variables. It requires a minimum of two independent variables, whereas a basic experiment only requires one independent variable. A factorial design allows the researcher to examine the main effects of two or more independent variables simultaneously. It also allows the researcher to determine interactions among variables.

### Factorial Research Design: Main Effect

In a factorial research design, the main effect is an important feature to consider. The main effect refers to the effect of a factor on a dependent variable, averaged across the levels (factor subdivisions) of the other factors. Thus, each factor has one main effect.

This concept can be further illustrated with an example:

1. Experiment: A researcher evaluates the effect of two medications to treat pain. The pain medications are Drug X and Drug Y. Thus, there are two independent variables or factors, Drug X and Drug Y, because these are variables that the researcher is controlling. The dependent variable is effective pain relief because it changes in response to the factors and is what the researcher is measuring.
2. Levels: There are two levels (or subdivisions) of each factor. The two levels for each of the drugs (or factors) is ”Yes, the patient received the drug.” or ”No, the patient did not receive the drug.”
3. Main Effect: Thus, the main effect of Drug X would be its effect on pain relief. And the main effect of Drug Y would be its effect on pain relief. Results could be any of the following:
• Drug X could have a main effect, where Drug Y has no effect.
• Drug Y could have a main effect, where Drug X has no effect.
• Drug X and Drug Y both have independent main effects, but these drugs are not interacting.
• Drug X and Drug Y interact. This will be explained in the next subsection.

## Examples of Factorial Designs

A university wants to assess the starting salaries of their MBA graduates. The study looks at graduates working in four different employment areas: accounting, management, finance, and marketing. In addition to looking at the employment sector, the researchers also look at gender. In this example, the employment sector and gender of the graduates are the independent variables, and the starting salaries are the dependent variables. This would be considered a 4×2 factorial design.

Researchers want to determine how the amount of sleep a person gets the night before an exam impacts performance on a math test the next day. But the experimenters also know that many people like to have a cup of coffee (or two) in the morning to help them get going. So, the researchers decide to look at how the amount of sleep and the amount of caffeine influence test performance.  The researchers then decide to look at three levels of sleep (4 hours, 6 hours, and 8 hours) and only two levels of caffeine consumption (2 cups versus no coffee). In this case, the study is a 3×2 factorial design.