Factorial Analysis of Variance

Factorial ANOVA Concepts

A factor is a categorical variable used for analysis with two or more categories. Each category represents a value on the factor and can be used to group participants in the study. Factorial ANOVAs are defined based on the number of factors and the number of categories on each factor used in the [Page 534]study. For example, a study using biological sex (male and female) and three treatments would be a 2 × 3 factorial ANOVA. The factors are crossed in the study and create six groups that represent the factor categories: male, treatment 1; male, treatment 2; male, treatment 3; female, treatment 1; female, treatment 2; female, treatment 3. Factorial ANOVAs can be more complex and include more than two factors. A study with three factors all with two categories would be a 2 × 2 × 2, whereas a factorial ANOVA with two factors with four categories each would be a 4 × 4.

A one-way ANOVA uses one factor to measure change in a dependent (continuous) variable. This produces a single F value when differences are present, and post hoc tests are used to find where the differences lie. Factorial ANOVAs have two or more independent variables, meaning multiple F tests and post hoc analyses are used to find differences between categories. Main effects refer to the mean comparisons for each factor. These effects point to differences between categories on each individual factor included in the design. Along with the main effects for each factor, factorial ANOVAs measure interaction effects. Interaction effects test how the effect of one factor is impacted by the categories on one or more other factors. Interaction effects explore how the combined categories created by the two main effects differ from each other, and can show how combinations of categories can influence the dependent variable. Using the earlier example, a study using sex and three treatments as factors would have an interaction effect result that compares the six groups created (Male, Treatment 1 × Male, Treatment 2 × Male, Treatment 1 × Female, Treatment 2 × Female, Treatment 2 × Female, Treatment 3). By creating means based on the factor groupings, researchers can see how multiple combinations of factors influence change in the dependent variable. The interaction effects also allow researchers to find potential differences that may not exist within a single factor and can highlight how specific characteristics (e.g., sex, year in school) may influence treatments in an experiment.

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