# Interactions in Factorial Design

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• 0:06 Factorial Design
• 1:30 Interactions
• 3:50 Crossover Interactions
• 4:54 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 a factorial design, the two independent variables can interact with each other to affect the dependent variable. In this lesson, we'll look at what interactions are, what they look like, and what a crossover interaction is.

## Factorial Design

Nicole is a psychologist. She's interested in studying the differences in concentration levels for introverts and extroverts when they are around other people versus when they are alone. She thinks that introverts, in particular, will work best when they are in a room alone rather than when they are in a room with other people.

So, Nicole sets up her study. She separates her subjects into introverts and extroverts. Then she gives each of them an article to read and a set of questions about the article to answer. She puts them into a room alone to work and then gives them a different article and puts them in a room with other people.

Nicole is looking at the effect of two independent variables (introversion and aloneness) on the dependent variable of concentration. Factorial design is a type of experimental design that involves two or more independent variables and one dependent variable. It is called 'factorial design' because independent variables are usually called 'factors.'

So, Nicole has a factorial design for her study. But when she gets her results back, what do they mean? What can she say about the effects of her factors on her dependent variable?

There are two types of results that a factorial study produces: main effects and interactions. Let's look closer at interactions, including what they mean, what they look like, and a special type of interaction called a crossover interaction.

## Interactions

Let's say that Nicole gets her results back. She puts the data into her computer and comes up with a graph to see what it looks like. When she does, she sees something interesting: the introverts and extroverts both do better when they are alone than when they are in a room with other people. But the introverts have a steeper slope on their line than the extroverts do.

In other words, introverts are more sensitive to other people being in the room. They do much worse when other people are in the room with them and much better when they are alone. Extroverts, on the other hand, do a little better on their own, but not that much better.

What's going on with Nicole's results? What she's seeing is an interaction of her factors. In other words, introversion and number of people in the room are working together to affect concentration level. If there was no interaction, then introversion would affect concentration and having other people in the room or not would affect concentration. But they wouldn't be working together.

If Nicole didn't have an interaction, the lines on her graph would be parallel to each other. But since her lines are not parallel, she has an interaction. Maybe introverts and extroverts concentrate at different levels, and maybe they both concentrate better when alone. But if the effect of working alone is the same for both introverts and extroverts, they are not interacting.

Think about multiplication and addition. If introversion is a 3 and being alone is a 4, you can add them up to get 7. But if you multiply them, you get 12. That's essentially what happens with interactions: the effects of both factors multiply to get a much larger number than just what each one brings to the table alone.

Interactions can happen with more than two factors, as well. For example, imagine that Nicole wanted to see if introversion, aloneness, and how familiar the subject matter is affect concentration. She might look at introverts and extroverts, in a room alone or with others, reading a passage dealing with their major versus an unfamiliar subject.

In that case, there might be a three-way interaction involving introversion, aloneness, and subject matter familiarity. If that sounds complicated, that's because it can get very complicated very quickly!

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