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Understanding Interaction Effects in Factorial Designs

This chapter covers the basic logic of factorial designs, focusing on interaction effects between independent variables. It explains the efficient research design of 2-way ANOVA and provides examples to help interpret interactions. Learn how to analyze main effects and interactions using 2x2 tables.

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Understanding Interaction Effects in Factorial Designs

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

  2. 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

  3. 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)

  4. 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?

  5. 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

  6. 2X2 Table (2-way ANOVA) Mood Sad Neutral 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

  7. 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

  8. 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 6.77 Appropriate Stereotype 6.29 Inappropriate 6.78 6.28

  9. 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

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