Chapter 14 - Factorial ANOVA

Factorial ANOVA

• when you have more than 1 factor (IV)

  • factors can be…

    • all between-subjects

    • all within-subjects

    • a mix of between- and within-subjects

Naming Factorial ANOVAs

2(gender) x 2(condition) factorial ANOVA

• indicates two levels of gender and two levels of condition.

3 Questions in Two-Factor ANOVA

• how does gender (male vs. female) affect aggression

  • main effect of Gender

• how does condition (violent vs. non-violent game) affect aggression

  • main effect of Condition

• does the effect of condition on aggression depend on one’s gender? Or does the effect of gender depend on one’s condition? Or is aggression affected by specific combinations of condition and gender?

  • interaction between gender and condition

ANOVA Matrix

• a table that organizes the results of an ANOVA test and displays the effects of each factor and their interactions

• use “appear” or “seem” when reporting results because it looks like there is a main effect but we have to test to be sure

ANOVA Matrix — Main effect of gender

• average aggression from males across both conditions

• average aggression from females across both conditions

ANOVA Matrix — Main effect of Condition

• average aggression in violent condition across both genders

• average aggression in non-violent condition across both genders

ANOVA Matrix — Interaction

• are the males and females both affected by the condition in the same way?

  • look at difference between conditions across both rows

    • Male Non-violent = 7, Male violent = 9 — +2 difference

    • Female Non-violent = 3, Female violent = 5 — +2 difference

      • so seems like there’s no interaction

Interactions

• the effect of one variable depends on another variable

• the effect of one variable differs based on another variable

• there is additional variability beyond the 2 main effects — your conclusion from your main effects changes across levels of another variable

  • ex; drug interactions (this medication will help you, unless, you are also taking drug X)

The power of Factorial ANOVA

• allows us to answer a more complex research questions

• can take into consideration the interaction of factors

• helps to guide human behaviour and interventions from research

  • perhaps a therapy is only effective for younger and not older children

  • perhaps social media use is more harmful for girls than boys

    • harmful for everybody but more for girls

Statistical Hypotheses — Main effect of factor A

• H₀ = μ_A1 = μ_A2

• H₁ = μ_A1 ≠ μ_A2

Statistical Hypotheses — Main effect of factor B

• H₀ = μ_B1 = μ_B2

• H₁ = μ_B1 ≠ μ_B2

Statistical Hypotheses — Interaction

• H₀: there is no interaction between factors A and B

• H₁: there is an interaction between factors A and B

Results Statement

• results indicated that there were no significant main effects of food type, F(1,16) = 3.75, p > .05, or room temperature, F(1, 16) = 3.75, p > .05. However, there was a significant interaction between food type and room temperature, F(1,16) = 10.42, p < .05.

Simple Main Effects

• when you find a significant interaction, you need to run follow-up teests to test which levels of your interaction are significant

  • significant interaction does not tell you which specific levels of the variables are significantly different…you need to run simple main effects to find out