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 – 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

5.83

Cell Mean 4

6.75

MoodSad Neutral

Stereotype

Appropriate

Inappropriate

MarginalMean 3 =6.78

MarginalMean 4 =6.28

MarginalMean 1=6.77

MarginalMean 4 =6.29

Note: groupsizes 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

7.73 5.80

5.83 6.75

Sad Neutral

Appropriate

Inappropriate

6.78 6.28

6.77

6.29Stereotype

Mood

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