After studying Chapter 9, you should know and understand the following key points:

Researchers use complex designs to study the effects of two or more independent variables in one experiment.

In complex designs, each independent variable can be studied with an independent groups design or with a repeated measures design.

The simplest complex design is a 2 X 2 design-two independent variables, each with two levels.

The number of different conditions in a complex design can be determined by multiplying the number of levels for each independent variable (e.g., 2 X 2 = 4).

The overall effect of each independent variable in a complex design is called a main effect and represents the differences among the average performance for each level of an independent variable collapsed across the levels of the other independent variable.

An interaction between independent variables occurs when the effect of one independent variable differs depending on the levels of the second independent variable.

Evidence for interactions can be identified using descriptive statistics presented in graphs (nonparallel lines) or tables (subtraction method); the presence of an interaction is confirmed using inferential statistics.

More powerful and efficient complex designs can be created by including more levels of an independent variable or by including more independent variables in the design.

In a complex design with two independent variables, inferential statistics are used to test three effects: the main effects for each independent variable and the interaction between the two independent variables.

Descriptive statistics are needed to interpret the results of inferential statistics.

How researchers interpret the results of a complex design differs depending on whether a statistically significant interaction is present or absent in the data.

Analysis Plan with an Interaction

If the analysis of a complex design reveals a statistically significant interaction, the source of the interaction is identified using simple main effects analyses and tests of simple comparisons.

A simple main effect is the effect of one independent variable at one level of a second independent variable.

Analysis Plan with No Interaction

If the analysis of a complex design indicates the interaction between independent variables is not statistically significant, the next step is to determine whether the main effects of the variables are statistically significant.

The source of a statistically significant main effect can be specified more precisely by performing analytical comparisons that compare means two at a time.

Interactions and Theory Testing

Theories frequently predict that two or more independent variables interact to influence behavior; therefore, complex designs are needed to test theories.

Tests of theories can sometimes produce contradictory findings. Interaction effects can be useful in resolving these contradictions.

Interactions and External Validity

When no interaction occurs in a complex design, the effects of each independent variable can be generalized across the levels of the other independent variable; thus, external validity of the independent variables increases.

The presence of an interaction identifies boundaries for the external validity of a finding by specifying the conditions in which an effect of an independent variable occurs.

Interactions and Ceiling and Floor Effects

When participants' performance reaches a maximum (ceiling) or a minimum (floor) in one or more conditions of an experiment, results for an interaction are uninterpretable.

Interactions and the Natural Groups Design

Researchers use complex designs to make causal inferences about natural groups variables when they test a theory for why natural groups differ.

Three steps for making a causal inference involving a natural groups variable are to state a theory for why group differences exist, manipulate an independent variable that should demonstrate the theorized process, and test whether the hypothesized interaction occurs between the manipulated independent variable and natural groups variable.