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10.5: Summary of Factorial Designs

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    Key Takeaways

    • Researchers often include multiple independent variables in their experiments. The most common approach is the factorial design, in which each level of one independent variable is combined with each level of the others to create all possible conditions.
    • Each independent variable can be manipulated between-subjects or within-subjects.
    • Non-manipulated independent variables (gender) can be included in factorial designs, however, they limit the causal conclusions that can be made about the effects of the non-manipulated variable on the dependent variable.
    • In a factorial design, the main effect of an independent variable is its overall effect averaged across all other independent variables. There is one main effect for each independent variable.
    • There is an interaction between two independent variables when the effect of one depends on the level of the other. Some of the most interesting research questions and results in psychology are specifically about interactions.
    • A simple effects analysis provides a means for researchers to break down interactions by examining the effect of each independent variable at each level of the other independent variable.

    What's Next?

    Factorial designs are the biggest type of designs that we will cover. Up next are small-N designs, or experiments with just a few participants.

    Exercises
    • Practice: Create a factorial design table for an experiment on the effects of room temperature and noise level on performance on the MCAT. Be sure to indicate whether each independent variable will be manipulated between-subjects or within-subjects and explain why.
    • Practice: Complete the Examples and Exercises in Oja (2021)'s 13.1.1: Factorial Notations and and Square Tables to practice identifying IVs, the DV, and the type of factorial designs.
    • Practice: Review the chapter on factorial designs in any (behavioral) statistics textbook on LibreTexts. Behavioral Statistics, Ed. 1 (Oja, 2021) provided some of the information in this chapter.
    • Discussion: Compare and contrast (find similarities and differences) between Introduction to Main Effects and Interactions (section 13.2) and the information presented in this chapter, then discuss which section is better and why.
    • Discussion: Compare and contrast (find similarities and differences) between Graphing Main Effects and Interactions (section 13.2.2) and the information presented in this chapter, then discuss which section is better and why.

    This page titled 10.5: Summary of Factorial Designs is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Rajiv S. Jhangiani, I-Chant A. Chiang, Carrie Cuttler, & Dana C. Leighton via source content that was edited to the style and standards of the LibreTexts platform.