The way in which a scientific experiment is set up is called a design. A Factorial Design is an experimental setup that consists of multiple factors and their separate and conjoined influence on the subject of interest in the experiment. A factor is an independent variable in the experiment and a level is a subdivision of a factor. Factors and levels are different conditions that the experimental subjects are exposed to. A study or experiment is used to see if any of the conditions influence the subject and in what ways they are influential.
The benefit of a factorial design is that it allows the researchers to look at multiple levels at a time and how they influence the subjects in the study. An example would be a researcher who wants to look at how recess length and amount of time being instructed outdoors influenced the grades of third graders. One factor would be recess length with two levels (long recess and short recess). The other factor in this study is outdoor instruction time with two levels (outdoor instruction and indoor only instruction). This would be called a 2x2 factorial design because there are two factors that each have two levels which create four groups (long recess with outside instruction, short recess with outside instruction, long recess with inside only instruction, and short recess with inside only instruction). Four classes of third grader would be each placed in one of these four groups and receive different factors and levels. Statistical tests then can be used to determine the differing effects that these factors and levels have on the students grades.