# Ch 10: Basic Logic of Factorial Designs & Interaction Effects Part 1: Oct. 28, 2014.

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Ch 10: Basic Logic of Factorial Designs & Interaction Effects Part 1: Oct. 28, 2014

Note: we’ll only cover p. 377-402 in Ch 10 (skip the calculation sections of this chapter “Advanced Topic: Figuring 2-Way ANOVA”) A 2-way ANOVA uses 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 1 7.73 Cell Mean 2 5.80 Cell Mean 3 5.83 Cell Mean 4 6.75 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

Two-Way ANOVA Design a) Column between-gp variance based on diff between mean of column 1 (shaded) & column 2 (unshaded) b) Row between-gp variance based on diff between mean of row 1 (shaded) & row 2 (unshaded) c) Within-gps variance estimate is based on variation among scores in each cell

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 7.735.80 5.836.75 SadNeutral Appropriate Inappropriate 6.786.28 6.77 6.29 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 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

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