Factorial experiments are studies which consider two or more factors at one time and can consider these factors at multiple levels. Not only do these types of experiments consider the main effect of these factors at various levels, but also their interaction effect. Factorial experiments are efficient when a researcher is aiming to examine the interaction effect between different factors.
The main effect of a factor is known as the average change in the output response which takes place for a specific level1. For example, pretend that there were two factors, let’s call them X and Y and two levels, (+) and (-). The main effect of factor X would be the average of the response produced when X stays (+) and Y changes from (+) to (-) and vice versa (X stays (-) and Y goes from (-) to (+)). So if the two numbers were 35 and 37, the main effect would be 36.
On the other hand, interaction effects occur when two or more factors are interacting with each other and are causing a change in the output process response1. When the effect of one factor changes as the level of another factor(s) is altered, an interaction takes place. Factorial experiments allow multiple factors to be considered at one time, rather than analyzing each factor individually.
Furthermore, there are two different types of factorial experiments: symmetrical and asymmetrical factorial experiments. Symmetrical factorial experiments are when all factors occur at the same level, whereas asymmetrical experiments are when factors occur at more than one level.
Factorial experiments examine both main and interaction effects and in some cases, the main effect can be seen as less significant if the interaction effect is very large. The main objective of factorial experiments in statistics is to produce experimental designs which are very effective when looking at multiple factors at once.
1. Batra, P.K. and Jaggi, S. (2014). Factorial Experiments. Retrieved from: http://www.iasri.res.in/ebook/EB_SMAR/e-book_pdf%20files/Manual%20III/5-Factorial-Expts.pdf
Image Credit: Green-Planet-Solar-Energy. (July 2, 2012). Water Science Experiment: Brownian Motion. Retrieved from: http://www.green-planet-solar-energy.com/water-science-experiment.html