Ch 10: Basic Logic of Factorial Designs & Interaction Effects Part 1: Apr 1, 2008

Note: skip the calculation sections of this chapter – stop at “Advanced Topic: Figuring 2-Way ANOVA on p. 406  start again at 424. 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 – 2 nd 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 Cell Mean Cell Mean Cell Mean Mood SadNeutral Stereotype Appropriate Inappropriate Marginal Mean 3 = 6.78 Marginal Mean 4 = 6.28 Marginal Mean 1= 6.77 Marginal Mean 4 = 6.29 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 SadNeutral Appropriate Inappropriate Stereotype Mood

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