11. Experimental Research: Factorial Design What are factorial experimental designs, and what advantages do they have over one-way experiments? What is meant by crossing the factors in a factorial design? What are main effects, interactions, and simple effects? What are some of the possible patterns that interaction can take? How are the data from a factorial design presented in the research reports? What is a mixed factorial design? What is the purpose of comparing means, and what statistical techniques are used to do this?

Factorial Experimental Designs Experimental designs with more than one independent variable. The term factor refer to each of manipulated independent variables. Example. IV. Sex (male, female), Ethnicity (Black, White, Asian, Latino) DV. Self-esteem MFMF Black White Asian Ratino 4 levels 2 levels Cells 2  4 designs 2 Factors

The Two-Way Design Example. Violent cartoons and children’s frustrated state increase their aggressive behavior. IV: Violent Cartoons vs. Nonviolent Cartoons Frustrated State vs. Non Frustrated State DV: Children’s aggressive behaviors. Frustrated Not frustrated Violent Nonviolent M = 2.68 N= 10M = 3.25 N= 10 M = 5.62 N= 10M = 2.17 N= 10 Av. M = 4.15 Av. M = 2.71 Av. M = 2.97 Av. M = 3.90

Main Effects, Interactions, and Simple Effects Frustrated Not frustrated Violent Nonviolent M = 2.68 N= 10M = 3.25 N= 10 M = 5.62 N= 10M = 2.17 N= 10 Av. M = 4.15 Av. M = 2.71 Av. M = 2.97 Av. M = 3.90 Main Effects Interactions Simple Effects The effect of each factors The effects in which the influence of one factor on the DV is different at different levels of another factors. The effect of one factor within a level of another factor

ANOVA Summary Table Source Sum of df Mean F p-value Squares Square DV: Aggressive Play Cartoon * Prior State Cartoon by Prior State * Residual Total

Chart Residual Cartoon Prior State C & PS

Understanding Interactions DV Frustrated Nonfrustrated Violent Nonviolent Patterns with Main Effects Only DV Violent Nonviolent

Understanding Interactions DV Frustrated Nonfrustrated Violent Nonviolent Patterns with Main Effects & Interaction Only DV Violent Nonviolent Crossover Interaction

Interpretation and Presentation of Main Effects and Interpretations 2 (cartoon)  2 (prior state) ANOVA was conducted. The results indicated that there were significant main effect of cartoon, F (1, 38) = 4.45, p <.05. Children who viewed the violent cartoon (M = 2.89) were rated as playing more aggressively than children who had viewed the nonviolent cartoon (M = 1.52). This main effect, however, should be qualified by the interaction with prior state, F (1, 36) = 4.42, p <.05. Children who were frustrated and viewed the violent cartoon (M = 5.55) were rated as playing more aggressively than children in other conditions (M = 1.11, 1.48, 1.54, respectively).