Factorial ANOVAs

 Factorial Analysis of Variance (ANOVA)  Allows you to enter multiple predictors and parcel out the variance in the outcome due to each predictor and the combination of the predictors  Main effect for each predictor + interactions among the predictors

 Use it when:  You are examining differences between groups  The participants in the study were only tested once  You are comparing more than two groups  You are dealing with more than one factor

 Main Effect of Each Predictor Variable ◦ Is there a mean difference among the levels of Variable A? ◦ Is there a mean difference among the levels of Variable B? ◦ And so on…  Interaction Effect of Predictor Variables ◦ Is the effect of Variable B different for the groups of Variable A? ◦ And so on… ◦ (can have 3, 4, 5-way interactions)

 State the hypotheses ◦ Null:  There is no main effect of gender:  μ male = μ female  There is no main effect of video game:  μ violent = μ modviolent = μ nonviolent  There is no interaction between gender and video game:  μ male*violent = μ male*modviolent = μ male*nonviolent = μ female*violent = μ female*modviolent = μ female*nonviolent ◦ Research:  There is a main effect of gender:  X male ≠ X female  There is a main effect of video game:  X violent ≠ X modviolent ≠ X nonviolent  There is an interaction between gender and video game:  X male*violent ≠ X male*modviolent ≠ X male*nonviolent ≠ X female*violent ≠ X female*modviolent ≠ X female*nonviolent

Source Type III Sum of Squaresdf Mean SquareFSig. Corrected Model (a) Intercept gender video gender * video Error Total Corrected Total

gender videogame violenceMean Std. DeviationN femalevery violent moderately violent non violent Total malevery violent moderately violent non violent Total Totalvery violent moderately violent non violent Total

 An ANOVA was conducted with gender (male, female) and video game (violent, moderately violent, nonviolent) as between-subjects factors. There was a significant main effect of gender, such that men had higher aggression scores (M = 6.13, SD = 2.11) than women (M = 2.47, SD =.51), F(1, 54) = , p <.001. There was a significant main effect of video game, F(2, 54) = , p <.001. There was also a significant interaction between gender and video game, F(2, 54) = , p <.001.

Source Type III Sum of Squaresdf Mean SquareFSig. Corrected Model (a) Intercept gender video gender * video Error Total Corrected Total

Source Type III Sum of Squaresdf Mean SquareFSig. Corrected Model (a) Intercept gender video gender * video Error Total Corrected Total