Two-way ANOVAs (W5-7) ✅

Question 1

What does a factorial ANOVA tell us?

Answer 1

1. The main effects: for each of the independent variable
2. The interaction between IVs
   -> The combined effects of multiple IVs/factors on the DV
   -> A significant interaction indicates that the effect of manipulating one IV depends on the level of the other IV
3. Factorial ANOVA controls the familywise error rate
4. There is no parametric equivalent for factorial ANOVA -> if seriously violate assumptions, can attempt a ‘fix’ or simplify the design

Question 2

What are the variances of a 2-way Independent ANOVA?

Answer 2

1. Variance between IV levels:
   - IV 1
   - IV 2
   - IVs interaction
2. Variance within IV levels
   - Errors
   -> including individual differences & experimental errors

Question 3

What are cell means and marginal means? What test we can do for Factorial ANOVA to determine each type of mean?

Answer 3

• Cell means: mean scores for each condition (e.g. IV 1A + IV 2B)
  -> When there is a significant interaction
  => simple effects (t-test with Bonferroni corrections)
  => effect size (Cohen’s d)
• Marginal means: mean scores across all IV levels (of 1 IV) AND ignoring the other IV
  => main effects (ANOVA)
  => Measure effect size (partial h2)

Question 4

What is the partial h2 for factorial ANOVA?

Answer 4

• Partial h2: proportion of the total variance attributable to the
  factor
• The calculation of partial h2 only takes into account the variance from one IV at a time

Question 5

When should we use Mauchly’s W test for sphrecity?

Answer 5

Only when the IVs of a 2-way Repeated Measure ANOVA have more than 2 levels