Two Way ANOVA A way to look at the effects of two independent variables and their interactions.

Research Designs The study has two independent variables, factor 1 (e.g. personality) and factor 2 (e.g. situation) Each factor has a certain number of levels (e.g. 2 personality traits and 2 situations). They are completely crossed to create the appropriate number of conditions (e.g. 2 traits X 2 situations = 4 cells)

Research Designs Factor 1: Half the participants have personality trait A and half the participants have trait B Factor 2: Half the participants were observed in private and half were observed in public Dependent variable: amount of food consumed

Research Designs 100 140 70 85 Trait A Trait B µpublic µprivate In public In private This allows us to ask three important research questions: 1. On average, is there a difference between the two situations? H0: µpublic = µprivate HA: µpublic ≠ µprivate Testing the “Main Effect” of Situation

Research Designs 100 140 70 85 Trait A Trait B µpublic µprivate In public In private µtraitA µtraitB This allows us to ask three important research questions: 2. On average, is there a difference between the two personality types? H0: µtraitB = µtraitB HA: µtraitB ≠ µtraitB Testing the “Main Effect” of Trait

Research Designs 100 140 70 85 Trait A Trait B µpublic µprivate In public In private µtraitA µtraitB This allows us to ask three important research questions: 3. Does the effect of situation depend on personality? (or vice versa) H0: no interaction HA: interaction Testing the Interaction Effect

Bar Graphs A main effect of situation. No main effect of trait.

Bar Graphs A main effect of situation. No main effect of trait. A main effect of trait. No main effect of situation

Bar Graphs Two main effects

Bar Graphs Two main effects

Bar Graphs Two main effects No interaction

Bar Graphs Two Main Effects and an Interaction “The effect of trait is more pronounced in public”

Bar Graphs Two Main Effects and an Interaction Same data! “The effect of situation is more pronounced in people who have trait A2”

Bar Graphs No Main Effects and an Interaction

Line Graphs A main effect of situation. No main effect of trait.

Line Graphs A main effect of situation. No main effect of trait. A main effect of trait. No main effect of situation

Line Graphs Two main effects

Line Graphs Two Main Effects and an Interaction “The effect of trait is more pronounced in public”

Line Graphs Two Main Effects and an Interaction Same data! “The effect of situation is more pronounced in people who have trait B”

Line Graphs No Main Effects and an Interaction

Graphing Same Data Different Ways How you graph it influences what you see

Graphing Same Data Different Ways

Graphing Same Data Different Ways

Graphing Same Data Different Ways