PsychoMetrics Introduction to Complex Designs
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Researchers often investigate the effects of two or more independent variables simultaneously; this type of experiment is referred to as a complex design.

The simplest complex design has two independent variables (IVs) and one dependent variable (DV).

The simplest independent variable has two levels (conditions).

Factorial Combination refers to how we combine independent variables in an experiment to describe their effects on the dependent variable(s).

We factorially combine independent variables by pairing each level of one independent variable with each level of the other independent variable.

The factorial design with 2 independent variables both with 2 levels is called a 2 x 2 design (read “2 by 2"). It has four conditions.

The overall effect of an independent variable in a complex design is called a main effect.

The main effect is the effect of the independent variable on the dependent variable as if only that variable was manipulated in the experiment.

The combined effect of independent variables in a complex design is called an interaction effect.

An interaction effect occurs when the effect of an independent variable differs depending on the level of the second independent variable.

Complex designs have at least two independent variables.

The independent variables can be manipulated using an independent groups design or a repeated measures design, or both.

When different types of independent variables are used, the complex design is called a mixed design.

When we look for interaction effects between independent variables, we often use the subtraction method or non-parallel graph.

Subtraction method in 2 x 2 design: find differences of the means in both columns by subtracting the cells in one row from the cells in the other. If one of the differences of the means is larger than the other, there is probably an interaction.

Non-parallel graph: draw the lines for two sets of data. If the two lines are not parallel, the diverging lines indicate an interaction effect is likely present in the data;

However, when subtraction method or non-parallel graph indicate an interaction effect is likely, a statistical test is used to determine whether the interaction effect is statistically significant.

Interaction Effects and Ceiling/Floor Effects

Floor and Ceiling Effects

Sometimes an interaction effect can be statistically significant “by mistake.”

This occurs when the means for one or more condition reach the highest possible score (ceiling effect) or the lowest possible score (floor effect).

When floor or ceiling effects occur, an interaction effect is uninterpretable.

Interaction Effects and Natural Groups Designs

Using complex designs, researchers can test causal inferences for natural groups variables.

We can’t make causal inferences with natural groups variables; natural groups variables are correlational.

We can make causal inferences about natural groups when we test a theory for why the natural groups differ.

Steps for making causal inferences about natural groups variables in a complex design:

1.         State your theory. Why are the groups different? What is the theoretical process?

2.         Identify a relevant independent variable. This IV should influence the likelihood that the theorized process will occur (e.g., relationship maintenance).

3.         Look for an interaction effect. In order to make a causal inference, the natural groups variable and manipulated variable should produce a statistically significant interaction effect in the predicted direction.

This interaction effect allows us to make causal inferences about why individuals differ — that is, we begin to understand why people differ.

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