Ch 10: Basic Logic of Factorial Designs

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Ch 10 Basic Logic of Factorial Designs
Interaction Effects

• Part 1 Apr 1, 2008

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• 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

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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
  IVs)

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Basic Logic of Interaction Effects

• 2 way ANOVA includes a focus on
• 2 possible main effects Stereotype-appropriatenes
  s 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?

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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 groups mean
• Marginal mean is overall mean for 1 var,
  regardless of group

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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
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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

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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
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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 exampledoes it look like an
  interaction?
• Examples on board of combinations of main effects
  and interactions