lecture 18 - dealing with multiple factors - 2-way ANOVA

Question 1

Beyond one factor

Answer 1

• In many situations it is important to consider more than one variable. Especially where the effect of one “thing” might differ as a function of another. For example:
  
  • Does a drug work the same for women and men?
  • Do different forms of persuasion work the same in “East” and “West”?
• ANOVA can “extend” to this sort of situation – to simultaneously ask:
  
  • Is there an effect of factor 1 (while holding factor 2 constant)?
  • Is there an effect of factor 2 (while holding factor 1 constant)?
  • Does the effect of factor 1 differ depending on factor 2?
    Does the effect of factor 2 differ depending on factor 1? (Note –these last two things are mathematically identical).

Question 2

Main effects and interactions

Answer 2

• Imagine an experiment comparing the effects of (A) audio vs visual distractors, and (B) relevant vs irrelevant distractors, on a comprehension task.
  
  • So, 4 groups: Audio & Relevant; Audio & Irrelevant; Visual & Relevant; Visual & Irrelevant.
• Asking about audio vs visual (holding relevance constant) is examining the “main effect” of modality.
• Asking about relevant vs irrelevant (holding modality constant) is examining the “main effect” of relevance.
• Asking whether modality and relevance are independent of each other is examining the interaction.
  Remember the chi-square contingency analysis? That was also about interactions.

Question 3

look at graphs in notes

Question 4

2-way between subject ANOVA

Answer 4

• Return to mood and season example – but now have data from UK and UAE.
  
  • Appears effect of season v different across countries – but needs formal analysis
    Do different forms of persuasion work the same in “East” and “West”?

graphs in notes

Question 5

2-way between subject ANOVA - maths

Answer 5

• As with 1-way, MS = SS/df – just doing this for both main effects and the interaction.
• As before F = MSeffect / MSresidual
  
  • Again, now doing separately for each main effect and interaction.
    Same MSresidual for each factor/interaction.

table in notes

Question 6

2-way between subject ANOVA
reporting

Answer 6

• Report as: Between subject ANOVA revealed no significant effect of Season, F(3,152) = 0.60, p = 0.613, a significant effect of Country, F(1,152) = 4.88, p = 0.029, and a significant interaction between them, F(3,152) = 6.06, p < 0.001
  Data is made up, but “makes sense” – winter is icky in the UK (but summer is nice), while summer is stupidly hot in the UAE: so different effect of season on mood countries is expected.

table in notes

Question 7

Within-subject 2-way ANOVA

Answer 7

• As with 1-way ANOVA, can do on within-subject data if have data from every subject in every condition.
  Imagine 40 people tested in the four different conditions described before - Audio & Relevant; Audio & Irrelevant; Visual & Relevant; Visual & Irrelevant.

examples, tables and graphs in notes

• Note – different “residuals” for each factor. Due to way variance due to subject is “taken out” as a function of what factor/interaction is being examined.
  Still compute F-ratio the same way MSeffect / MSresidual (and report the same way)

Question 8

Going beyond today’s material

Answer 8

• Presented between-subject and within-subject 2-way ANOVA today. Can also combine between and within-subject factors (Called mixed ANOVA).
  
  • For example, within-subject factor of Season, between-subject factor of Country.
• ANOVA (between, within, or mixed) can actually go beyond 2 factors (again, not covered here).
  
  • But ANOVA gets increasingly hard to interpret as the number of factors increases.
    But in all types of ANOVA, logic remains the same, examine F = MSeffect / MSresidual (where “effect” includes main effects and interactions, and “residual” can depend on what effect is examined).