Factorial Design Variations

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  • 0:05 Factorial Design
  • 1:17 Factors
  • 2:42 Groups
  • 5:27 Lesson Summary
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Lesson Transcript
Instructor: Natalie Boyd

Natalie is a teacher and holds an MA in English Education and is in progress on her PhD in psychology.

When a study has more than one factor, it is called a factorial design. In this lesson, we'll go through different variations on factorial designs, including those involving factor levels and those involving between- or within-groups measurement.

Factorial Design

Lois is a psychologist. She's interested in whether age plays a role in how quickly a person can learn how to use a phone-based app. She believes that younger adults will learn how to use it much more quickly than older adults will.

In Lois' experiment, her independent variable is age, and her dependent variable is how quickly they learn the app.

That's a pretty straightforward study, but what if there's something else Lois wants to know? For example, what if Lois believes that, in addition to age, the amount of noise in the room when learning the app will affect how quickly they learn?

Now Lois has two independent variables: age and noise. Lois is doing a factorial design, or an experiment done with more than one independent variable. Factorial design gets its name from the fact that independent variables are sometimes called factors.

There are many different types of factorial designs, and they are named for two different aspects of the study: the levels of the factors and the way the groups are sorted. Let's look closer at each of those aspects and the different types of factorial designs.


OK, so Lois wants to do a study with two different factors, age and noise. One of the first things that a researcher will do when planning a study is to draw a design table. Essentially, this is a table where one factor is labeled on the top and the other factor is labeled on the side.

So for Lois' study, she would draw a table where each column is an age group, like young, middle, old. Then each row would be noise level: quiet or noisy.

Factorial Design Chart

If you look at Lois' table, you can see that there are two levels (or possible outcomes) for the factor of noise and three levels for the factor of age. This is called a 2x3 factorial design.

There are endless possibilities for factorial designs based on the levels of the factors. If Lois decides to just study old and young subjects and not middle-aged ones, then she'd have a 2x2 factorial design.

She can add a variable, too, like income: upper, middle, lower class. Then, she'd have a 2x3x3 factorial design. The list goes on and on, but the basic formula is the same: whenever you have a factorial design, one part of the name of that design comes from the levels of the factors. The first number is the number of levels of the first factor, the second number is the number of levels of the second factor, and so on.


But naming an experimental design doesn't stop with the levels of factors. The way the groups are measured also impacts the name of a study.

Let's say that Lois decides on her original 2x3 factorial design. She's going to look at each subject's age, and she's going to put the subjects in either a room that's noisy or quiet to learn an app. But how will she measure those variables?

Age group is relatively easy. She can ask the person their age and then sort them into young, middle, and old. But what about noisy and quiet rooms? Should she have half of the subjects in a noisy room and half in a quiet room? Or should all subjects be given the opportunity to work in both rooms?

Let's say that Lois decides that she's going to divide her subjects into two groups. One group will learn the app in the noisy room, and the other will learn it in the quiet room. She'll then compare how well they learned the app.

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