What is factorial design?

Answer 1

A design for an experiment that allows the experimenter to find out the effect levels of each factor on levels of all the other factors.

A Simple ExampleProbably the easiest way to begin understanding factorial designs is by looking at an example. Let's imagine a design where we have an educational program where we would like to look at a variety of program variations to see which works best. For instance, we would like to vary the amount of time the children receive instruction with one group getting 1 hour of instruction per week and another getting 4 hours per week. And, we'd like to vary the setting with one group getting the instruction in-class (probably pulled off into a corner of the classroom) and the other group being pulled-out of the classroom for instruction in another room. We could think about having four separate groups to do this, but when we are varying the amount of time in instruction, what setting would we use: in-class or pull-out? And, when we were studying setting, what amount of instruction time would we use: 1 hour, 4 hours, or something else?

With factorial designs, we don't have to compromise when answering these questions. We can have it both ways if we cross each of our two time in instruction conditions with each of our two settings. Let's begin by doing some defining of terms. In factorial designs, a factor is a major independent variable. In this example we have two factors: time in instruction and setting. A level is a subdivision of a factor. In this example, time in instruction has two levels and setting has two levels. Sometimes we depict a factorial design with a numbering notation. In this example, we can say that we have a 2 x 2 (spoken "two-by-two) factorial design. In this notation, the number of numberstells you how many factors there are and the number valuestell you how many levels. If I said I had a 3 x 4 factorial design, you would know that I had 2 factors and that one factor had 3 levels while the other had 4. Order of the numbers makes no difference and we could just as easily term this a 4 x 3 factorial design. The number of different treatment groups that we have in any factorial design can easily be determined by multiplying through the number notation. For instance, in our example we have 2 x 2 = 4 groups. In our notational example, we would need 3 x 4 = 12