Week 4: Factorial ANOVA

• What is the focus of factorial designs in ANOVA?

  They analyze the effects of multiple independent variables on a dependent variable.
• What are the independent variables (IVs) in the Dixson and Brooks (2013) study?

  Gender and facial hair type.
• What is the dependent variable (DV) in the Dixson and Brooks (2013) study?


  Rated attractiveness.
• How many levels of facial hair were investigated in the study?

  Four levels: clean shaven, light stubble, heavy stubble, and full-beard.
• What statistical test would be used to analyze the data from the Dixson and Brooks (2013) study?

  Factorial ANOVA.
• What are the main effects tested in factorial designs?

  • Main effect of each independent variable (IV) on the dependent variable (DV).
  • Example: Effect of age and income on optimism.
• What is an interaction effect in the context of factorial designs?

  An interaction effect occurs when the effect of one IV on the DV depends on the level of a second IV.
• How can you visually identify an interaction effect in a graph?

  By observing non-parallel lines in the graph.
• What does the "Partial Eta-Squared" value indicate in factorial ANOVAs?

  It indicates the effect size of the independent variables.
• What are the effect size guidelines according to Cohen (1988)?

  .01 = Small effect size, .06 = Medium effect size, .14 = Large effect size.
• How should factorial ANOVAs be reported?

  • Report F-value, degrees of freedom, p-value, and effect size for each main effect and interaction.
• What preliminary analyses were performed before conducting the two-way ANOVA?

  Analyses to ensure no violation of the assumptions of normality and homogeneity of variance.
• What are the key components to report in factorial ANOVA results?

  • Main effects for each IV
  • Interaction effects
  • F-values, p-values, and effect sizes
• What is the significance of effect sizes in research findings?

  They indicate the importance of findings and are less susceptible to sample size than p-values.
• What does a small effect size indicate according to Cohen's guidelines?

  A small effect size indicates a minimal impact of the independent variable on the dependent variable.
• What is the purpose of conducting a two-way between-groups ANOVA?

  To explore the impact of two independent variables on a dependent variable.
• What does it mean if the interaction effect is not statistically significant?

  It means that the effect of one independent variable does not depend on the level of the other independent variable.
• What should researchers do if they find significant main effects in their ANOVA results?

  They should conduct post-hoc comparisons to explore differences between group means.
• What was the main effect for sex in the study?

  The main effect for sex did not reach statistical significance
• What are the key components to report in a factorial ANOVA?

  • F statistic (F)
  • Degrees of freedom (df)
  • Error degrees of freedom
  • Significance (p)
  • Partial η² (for significant results)
• What are the possible interactions in a 3-factor ANOVA?

  • Factor 1 (IV1) x Factor 2 (IV2) - two-way interaction
  • Factor 1 (IV1) x Factor 3 (IV3) - two-way interaction
  • Factor 2 (IV2) x Factor 3 (IV3) - two-way interaction
  • Factor 1 x Factor 2 x Factor 3 - three-way interaction
• Why are studies with more than three IVs unusual in ANOVA?

  • Large number of experimental conditions/groups
  • Requires a larger number of participants
  • Difficult to visualize interactions
• What is counterbalancing in experimental design?

  • A method to control for order effects
  • Ensures each condition appears equally across participants
  • Can involve complex designs like Latin Squares
• What is the benefit of using a Latin Square for counterbalancing?

  • Reduces order effects
  • Requires fewer participant blocks (e.g., 6 instead of 720)
  • Each condition appears once in each row and column
• What was the main finding of Bernard et al. (2012) regarding sexualized images?


  They investigated whether sexualized images of women are processed as objects
• What were the independent variables in the Bernard et al. (2012) study?

  Sex, target sex, and target orientation
• What was the dependent variable in the Bernard et al. (2012) study?

  Proportion of correctly identified pictures
• What are the assumptions for homogeneity of variance in ANOVA?

  • Homogeneity of variance can be assumed for 50% of the groups
  • Equal numbers in each between-groups condition help robustness
• What is the significance of Box’s M Statistic in ANOVA?

  • Checks homogeneity of intercorrelations
  • Sensitive statistic requiring an alpha of .001
  • Non-significant result is desired
• Why were post-hoc tests not needed in the Bernard et al. (2012) study?

  No post-hoc tests were needed because there were only two levels and the main effect was not significant
• What should be included in interaction plots for ANOVA results?

  • Visual representation of interaction effects
  • Helps to interpret the relationship between independent variables