11. experimental research: factorial design

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 DesignsFactorial 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

M

F

Black White Asian Ratino

4 levels

2 levels

20 24 19 20

24 18 20 21

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 StateDV: Children’s aggressive behaviors.

Frustrated

Not frustrated

Violent Nonviolent

M = 2.68 N= 10 M = 3.25 N= 10

M = 5.62 N= 10 M = 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= 10 M = 3.25 N= 10

M = 5.62 N= 10 M = 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:AggressivePlay

Cartoon 23.56 1 23.56 4.56 .04* Prior State 11.33 1 11.33 2.00 .17 Cartoon byPrior State 29.45 1 29.45 5.87 .03*

Residual 41.33 36 5.17 Total 94.67 39 59.51

Chart

Residual

Cartoon

PriorState

C & PS

Understanding InteractionsDV DV Frustrated

Nonfrustrated

Violent Nonviolent Violent Nonviolent

Patterns with Main Effects Only

DV

Violent Nonviolent

Understanding InteractionsDV DV Frustrated

Nonfrustrated

Violent Nonviolent Violent Nonviolent

Patterns with Main Effects & Interaction Only

DV

Violent Nonviolent

Crossover Interaction

Interpretation and Presentation ofMain 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 violentcartoon (M = 2.89) were rated as playing more aggressively than children who had viewed the nonviolent cartoon (M = 1.52). Thismain 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).