Psych 212 - Chapter 12: Experiments With More Than One Independent Variable

Interaction

When the effect of one independent variable on the dependent variable depends on the level of another independent variable.

Interaction (b): The interaction is often considered more important than the main effects because it shows whether the effect of one independent variable depends on the level of the other independent variable. In other words, it tells you if the relationship between one IV and the DV changes depending on the level of the other IV, which provides more nuanced and insightful information about how the variables work together.

Factorial Design

An experiment with two or more independent variables (factors), each with levels.

Independent Variable (Factor)

A variable that is manipulated in an experiment; in factorial designs, multiple IVs are used to examine interactions.

Participant Variable

A variable that is selected rather than manipulated (e.g., age, gender) but treated as an IV in factorial designs.

Cell

A unique treatment condition; calculated by multiplying the number of levels of each IV.

Association in Factorial Designs

Factorial designs test whether the relationship (association) between one independent variable and the dependent variable holds across different levels of another variable—revealing if the association is consistent or moderated by a second factor.

Moderator in Factorial Designs

A moderator is a variable that changes the strength or direction of the relationship between an independent variable and a dependent variable. In factorial designs, an interaction effect indicates the presence of a moderator.

Think of it like this:

Conceptual Term	Statistical Test	What It Tells You
Moderator	Interaction effect	The effect of the IV depends on the level of the moderator.
Your hypothesis	Your test result	Confirmation (or not) of your prediction.

Main Effect

The overall effect of one IV on the DV, averaging across levels of the other IV.

Marginal Means

The mean for each level of an IV, the average for one level of an independent variable, regardless of what level the other independent variable is at. It is the average outcome for each IV level, and it is used to later determine and interpret effects of the data.

Visualized:

Reaction Time	Positive Word	Negative Word
Neutral Photo	400 ms	420 ms
Aggressive Photo	450 ms	470 ms

• Marginal mean for Neutral Photos = (400 + 420) / 2 = 410 ms

• Marginal mean for Aggressive Photos = (450 + 470) / 2 = 460 ms

Interaction Effect

the interaction effect is basically the recognition that the strength of each iv is dependent on the other, labelled as a difference in differences. By recognizing the interaction effect in the outcome, we can recognize an interaction formally through later calculations.

Main Effect of Photo Type

The average effect of photo type on reaction time, across all levels of word type.

• You average the reaction times for aggressive photos and neutral photos, but you're considering both the aggressiveand neutral word types together.

• This gives you an overall understanding of how photo type (aggressive vs. neutral) impacts the dependent variable (e.g., reaction time), ignoring whether the word presented was aggressive or neutral.

Main Effect of Word Type

The average effect of word type on reaction time, across all levels of photo type.

2x2 Factorial Design

A design with two IVs, each with two levels, resulting in four unique conditions or cells.

Independent-Groups Factorial Design

Both IVs are manipulated between-subjects; participants are in only one cell.

Within-Groups Factorial Design

Both IVs are manipulated within-subjects; participants experience all conditions.

Mixed Factorial Design

In a mixed factorial design, one independent variable is manipulated as a between-subjects variable (where different groups of participants experience different levels of that variable), and the other is manipulated as a within-subjectsvariable (where the same participants experience all levels of that variable). This design allows researchers to investigate the effects of multiple treatment conditions while using fewer participants than a fully between-subjects design.

Factorial Notation

A shorthand that tells you how many IVs and how many levels each has (e.g., 2x2, 3x2).

Increasing Levels of an IV

Expanding a factor to more than two levels to examine more complex effects.

Increasing Number of IVs

Adding more IVs to the design to test for more complex interactions and main effects.

Two-Way Interaction

A situation in which the interaction between two IVs affects the DV.

Three-Way Interaction

A situation in which a third IV changes the interaction between the other two IVs.

Simple Main Effect

The effect of one IV at a specific level of another IV.

Difference in Differences

The hallmark of an interaction effect; one difference depends on the level of another variable.

"Difference in differences": The interaction is the difference between these two differences.

Example:

• IV1 (photo type): Emotional vs. neutral

• IV2 (word type): Aggressive vs. calm

• DV (reaction time): How fast participants respond

External Validity in Factorial Designs

Examining whether effects generalize across different people, situations, or contexts.

Theory Testing with Factorials

Factorial designs allow researchers to test if theoretical variables interact in hypothesized ways.

Example of Interaction

Enjoyment of food depends on both type (ice cream vs. pancakes) and temperature (hot vs. cold).

Why Study Interactions

Most psychological effects are not just main effects; understanding interactions reveals complex relationships.

Interpreting Factorial Results

Look for main effects and interactions; interactions often provide deeper insight.

Cell Count in Factorials

Number of conditions is the product of the levels of each IV (e.g., 2x3 design = 6 cells).

Role of Moderators in Interactions

If the strength of the IV–DV relationship changes based on another variable, that variable is a moderator. When we label something as a moderator, we acknowledge its role in the interaction.

Same Participants in All Conditions

Occurs in within-subjects factorial designs, where each participant experiences every combination of levels.