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Chapter 10

Chapter 10. Factorial Analysis of Variance Part 2 – Nov. 7, 2013. F tests in factorial ANOVA. REVIEW: Conduct 3 F tests 2 possible main effects (variable 1, variable 2) 1 possible interaction (variable 1 X variable 2) Look at cell means and from them, find marginal means

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Chapter 10

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  1. Chapter 10 Factorial Analysis of Variance Part 2 – Nov. 7, 2013

  2. F tests in factorial ANOVA • REVIEW: Conduct 3 F tests • 2 possible main effects (variable 1, variable 2) • 1 possible interaction (variable 1 X variable 2) • Look at cell means and from them, find marginal means • Marginal means can show main effects • Cell means can show an interaction • When subtracting cell means in row 1 versus row 2 (etc. if more rows) and notice a difference in direction or magnitude of the difference  evidence of an interaction • Note that any combination can be signif • With signif interaction and main effects, always interpret the interaction 1st meaning of main effects may change if there is an interaction!

  3. Main Effects and/or Interaction • If no interaction, you can interpret the main effect (or effects, if both…) as you would the one-way ANOVAs • See table 10-4, Result D (p. 384) • There is a main effect of age on income, such that older workers make significantly more than younger workers. • There is no main effect of education and no interaction • The impact of age on income did not depend on level of education

  4. If significant interaction and main effects – report F statistics for interaction & main effects, but… • focus on the interaction • See Result F (Table 10-4 p. 384) • 2 main effects (37.5 v. 47.5 and 32.5 v. 52.5) and an interaction (row 1 diff = -15, row 2 diff = -25) • Workers with college education make more than those with high school BUT the difference is more extreme for older than younger workers.

  5. Recognizing and Interpreting Interaction Effects • Graphically, will see an interaction if pattern of bars for 1st section of graph differs from 2nd section… For inappropriate group, hiring chances decreased from neutral  sad… For appropriate group, hiring chances increased from neutral  sad

  6. Basic Logic of 2-way ANOVA • Calculate 3 F ratio’s comparing between group variance to within-group variance • 1st F ratio for column main effect • 2nd F ratio for row main effect • 3rd F ratio for interaction effect • Only the numerator will change (betw-gp variance); denominator (within-gp variance) is same for all 3, just an average of pop variance based on all scores in sample

  7. Two-Way ANOVA table • Reports SS, df, MS, and F ratios for all 3 sources (column main effect, row main effect, interaction)…SPSS output looks like this, too!

  8. Factorial ANOVA in research articles (see book for example!) A two-factor ANOVA yielded a significant main effect of voice, F(2, 245) = 26.30, p < .001. As expected, participants responded less favorably in the low voice condition (M = 2.93) than in the high voice condition (M = 3.58). The mean rating in the control condition (M = 3.34) fell between these two extremes. Of greater importance, the interaction between culture and voice was also significant, F(2, 245) = 4.11, p < .02. See Figure 1 for a graph of the interaction effect. (note: Fig 1 isn’t actually included in these notes, just written as an example of how you would cite this).

  9. SPSS example • Analyze General Linear Model  Univariate • Pop-up box, indicate ‘Dependent Variable” (here, ‘harass’), and “Fixed factor” (here, ‘year’ & ‘working’) • Don’t need to specify anything in the other boxes… • Choose ‘options’  ‘display means for’ choose year, working, & year*working • Choose ‘plots’  ‘horizontal axis’ choose year; ‘separate lines’ choose working, hit ‘Add’, then ‘Continue’, then ‘OK’ • See Output handout for interpretation

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