Adding Another Dimension to the Simple Experiment:
The 2 X 2 Factorial Design

I. How this particular four-group experiment compares to the simple experiment

A. We can look at two independent variables rather than just one.

B. We can look at interaction between the two variables. That is, we can ask the question:

"Does the effect of one variable depend on level of the other independent variable?"

II. Understanding the importance of interactions to psychology

A. General rules are often already known, what we need to discover are the moderating variables.
Ex: Most people know that attractive people are better liked than unattractive people--but when isn't this the case? We know people often loaf in groups--but when don't they?

B. Simple answers and questions don't work

1. "Is it Personality or the Situation?" replaced by

"How do personality and situations interact?"

2. Is it Heredity or Environment?" replaced by

"How do heredity and environment interact?"

3. "What type of therapy is best?" replaced by

"What type of patient responds best to what type of therapy?"

4. "It depends" is often the correct answer to a question about the effect of a given action.

C. External validity questions boil down to interactions between treatment and participants or settings.

III. Potential results of a 2 X 2 experiment

Main effect for IV 1 Main effect for IV 2 Interaction between
IV1 and IV2
No No No
Yes No No
No Yes No
Yes Yes No
No No Yes
Yes No Yes
No Yes Yes
Yes Yes Yes

Visualizing some of these patterns

IV. Examining the ANOVA table for the 2 X 2

A. Understanding the design from the ANOVA summary table

1. Df rules for total number of subjects (N-1)

2. Df rules for main effects (Levels-1)

3. Df rules for interactions

(df Main effect for IV1 X df Main effect for IV2)

B. Making sense of results not involving interactions--Just follow the main effects

V. Interpreting a significant interaction

A. The treatment doesn't have the same effect on all your participants. Some groups of participants are affected differently than others. Thus, you should not talk about your main effects without qualifying them by saying there was an interaction. In other words, it is misleading to talk about the average effect of your treatment.

B. To better understand the interaction, graph it! Graphing will help you determine:

1. The pattern of the interaction

2. Whether interaction may be due to having ordinal data. Ordinal data might be the result of

1. using a measure that always produces ordinal scale data

2. ceiling or floor effects causing data to be ordinal

VI. Interpreting more complex factorial designs

A. More than two levels: Possibility for trend analysis

B. More than two factors: Interpreting higher-order interactions

Lecture 12.2

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