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

2. Using a factorial research design
Note: only cover p 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) 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

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
7.73
5.80
5.83
6.75
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 = 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