47.269 Research I:  Basics

Factorial Designs

 

Lecture 2.  When the Action is in the  Interaction.

 

Okay, so imagine you are a preschool teacher who runs a little study in her preschool classroom to find out which toys are more effective as potential reinforcers—(a) Little cars with track or (b) Small dolls with dollhouse. 

 

You decide to leave these in the “choice area” to see how often children play with each of these throughout free play time.  Here is what you found as an average time children spent playing with each.  So, on average, children spent 30 minutes playing with the cars and 30 minutes playing with the dolls.

 

Sound right? Note that these boxes are not the conceptual design of the study (as in Lecture 1) but are arranged like they are.  These are the results or average (mean) minutes played for all the observations in a category (below, for cars and for dolls).

 

 

Minutes Played

Toy

Cars

Dolls

30

30

 

 

 

So, do we conclude that they are equally reinforcing?  Well, you might decide to examine who is choosing what before you come to that conclusion, so let’s look at what the boys played with and what the girls played with.

 

 

Minutes played

 

 

Toy

 

 

Cars

Dolls

Gender

Boy

45

15

Girl

15

45

 

Mean =

30

30

 

 

In the table above, we see that there really does seem to be a difference in the cars and dolls, but it depends on the gender of the child.

 

In other words, the independent variable (toy) and the antecedent variable (gender) are not independent of each other—they have a complex and interactive influence on the dependent variable (number of minutes of play).

 

Notice also that the toy minutes on average—averaging across genders within toy as in the bold black lines above—are equal. There is not an effect of the toy by itself.

 

 

Minutes Played

 

 

Toy

 

 

 

Cars

Dolls

Mean =

Gender

Boy

45

15

30

Girl

15

45

30

 

Mean =

30

30

 

 

 

 

To put these results in ANOVA terms:

 

A little stereotypical you say?  Definitely, but it makes a good example and there are data to support the general trend, if not the specific finding.

 

How would we graph this interaction? 

 

We could use a bar graph:

 

 

 

More commonly, we would use a line graph.  Non-parallel lines, crossing as they do below, provide a classic interaction example. 

 

 

 

 

 

So, remember:

 

An interaction exists when the dependent variable depends

on the value of more than one factor at a time.

 

In the example above, there is only an interaction effect and no main effects.  However, it is possible to have both interactions AND main effects. 

 

Here, for example, is a main effect of gender (boys playing more than girls) AND an interaction of gender and toy type.

 

 

 

 

Final Thoughts

 

 

This material should explicate the boxes or cells that your text uses to illustrate main and interaction effects. 

 

·        Notice that the data reported in many of the figures are the Means of all the scores that “live” in that cell. 

 

·        Remember that each cell represents a condition with multiple participants.

 

·        Remember:

·         Participants in one cell may be the same as participants in the next row or column for a within factor.

·         Participants will be different than those in adjacent cells for a between factor.

 

·        When you are trying to make sense of Figure 11.12, plot the mean data as they do on Figures 11.13 and 11.14.  You should see that the lines are the same.

 

·        You may also find it helpful to look at some of the resources at the University of Washington Psych Dept website on research methods and statistics.  The section on Interactions is at

 

o       http://courses.washington.edu/smartpsy/interactions.htm

 

 

 

Questions?  Bring them to discussion and Chat!