Ch 10: Basic Logic of Factorial Designs & Interaction Effects Part 1: Nov. 5, 2013

Using a factorial research design Note: only cover p. 377-402 in Ch 10 (skip the calculation sections of this chapter “Advanced Topic: Figuring 2-Way ANOVA) Using a factorial research design Effect of two or more independent (group) variables examined at once Efficient research design Interaction of the 2 independent variables are possible Interaction effect: Combination of variables has a special effect such that the effect of one variable depends on the level of another variable

Interaction Effects Example: Lambert et al study Manipulated job description for flight attendant to give stereotype-appropriate or inappropriate info (1 factor); and manipulated mood (sad v. neutral – 2nd factor) A Factorial design – 2-way ANOVA (indicates 2 IV’s)

Basic Logic of Interaction Effects 2 way ANOVA includes a focus on: 2 possible main effects: Stereotype-appropriateness; Mood That is, regardless of mood, does stereotype appropriateness affect hiring decisions? And, regardless of stereotype-appropriateness, does mood affect hiring decisions? 1 possible interaction effect – does the impact of mood on hiring depend on stereotype appropriateness?

Cont. In 2-way ANOVA, with 2x2 table, each group is called a “Cell” Notice 4 cell means and 4 marginal means Cell mean is each group’s mean Marginal mean is overall mean for 1 var, regardless of group

2X2 Table (2-way ANOVA) Cell Mean 1 7.73 Cell Mean 2 5.80 Cell Mean 3 Mood Sad Neutral Cell Mean 1 7.73 Cell Mean 2 5.80 Cell Mean 3 5.83 Cell Mean 4 6.75 Marginal Mean 1= 6.77 Appropriate Stereotype Marginal Mean 4 = 6.29 Inappropriate Marginal Mean 3 = 6.78 Marginal Mean 4 = 6.28 Note: group sizes were equal

Basic Logic of the Two-Way ANOVA We calculate 3 F ratios: Column main effect (for variable 1) Row main effect (for variable 2) Interaction effect (of variable 1 x variable 2) F ratios for the row and column main effects Based on deviations from marginal means F ratio for the interaction effect Based on deviations from cell means

Cont. To examine main effects, focus on the marginal means Main effect of Mood: what is compared ? Main effect of Stereotype: what is compared? To examine the interaction, focus on pattern of cell means Mood Sad Neutral 7.73 5.80 5.83 6.75 6.77 Appropriate Stereotype 6.29 Inappropriate 6.78 6.28

Interpreting Interactions: Examining 2x2 Tables Is the difference in cell means across the 1st row the same (direction and magnitude) as the difference in cell means in 2nd row? If yes (same direction AND magnitude)  no interaction, If no (different direction OR magnitude)  interaction Here, for stereotype-appropriate row, difference is 7.73-5.80= 1.93 For stereotype-inappropriate row, difference is 5.83-6.75 = -.92 So, in this example…does it ‘look’ like an interaction? Examples on board of combinations of main effects and interactions