Factorial Designs in Research

Factorial Designs

Definition

  • Factorial Designs: Research designs that involve two or more independent variables (IVs) treated as factors. Each factor is present across all levels of the other factors.

Structure

  • Levels and Factors: Each factor consists of two or more levels; factors are manipulated in a crossed manner.
    • Example: A 2x2 factorial design involves two factors, each with two levels.

Types of Factorial Designs

  • 2x2 Between-Subjects Factorial Design: Simplest case with two factors and two levels. Participants are randomly assigned to different conditions based on factors.

Advantages of Factorial Designs

  • Enables examination of effects of multiple IVs individually and collectively on the dependent variable (DV).
  • Combination of simpler experimental designs allows for more comprehensive analysis of interactions.

Hypotheses Tested in 2x2 Factorial Design

  1. Main Effect of Factor A

    • Evaluates overall impact of Factor A across all levels of Factor B.
    • Example: Does providing a context improve idea recall more than no context?

  2. Main Effect of Factor B

    • Assesses overall impact of Factor B across all levels of Factor A.
    • Example: Do participants remember more ideas when rewarded with $1 versus $0.01?

  3. Interaction Between Factors A and B

    • Investigates if the effect of Factor A differs at different levels of Factor B.
    • Example: Does the effect of increased monetary reward depend on whether participants receive contextual cues?

Main Effects

  • Definition: Indicates the individual effect of an IV on the DV, analyzed separately from other variables.
  • Determining Main Effects:
    • Calculate means collapsed across levels of the other IVs for comparison.

Interaction Effects

  • Definition: Occurs when the relationship between one IV and the DV changes at different levels of another IV.
  • Determining Interactions: Conduct statistical analyses; non-parallel lines or differences indicate an interaction. Parallel lines suggest no interaction.
  • Example:
    • Increased payment leads to improved performance with context, but reduced performance without context.

Higher Order Factorial Designs

  • Can include any number of levels for factors; complexity increases with additional factors.
  • Example: A 2x2x2 design yields multiple main effects and interactions (A, B, C main effects; AxB, AxC, BxC interactions; AxBxC three-way interaction).

Analysis of Factorial Designs

  • Data analyzed using ANOVA (Analysis of Variance) to check for:
    • Main effect of Factor A
    • Main effect of Factor B
    • A x B interaction