5: FACTORIAL ANOVA (INDEPENDENT DESIGN)

Question 1

factorial ANOVA

Answer 1

used to test for differences when we have more than 1 IV
- including more than 1 IV we can explore the effects of each IV and interactions between IVs

each IV will have 2 or more levels

3 broad factorial ANOVA designs:
- all IV’s are between subjects (independent)
- all IV’s are within-subjects (RM)
- a mixture of between-subjects and within subjects IVs (mixed)

Question 2

factorial ANOVA terminology

Answer 2

the terms ‘IV’ and ‘factor’ are interchangeable
- ANOVAs with more than 1 IV called factorial ANOVAs

Factorial ANOVAs can include:
2-way …, 3 way…, 4 way…

IVs/ factors always have at least 2 levels
- 22 ANOVA: 2 IVS, each 2 levels
- 24 ANOVA: 2 IVs, one 2 lvls, one 4

Question 3

benefits of factorial ANOVA

Answer 3

• controls familywise error rate
• tells us about interaction effects

Question 4

2-way independent ANOVA: partitioning the Variance

Answer 4

Variance between IV levels:
- IV1
- IV2
- interaction

variance within IV levels:
- error (incl. individual diffs & experimental error)

Question 5

2 way independent ANOVA: F ratio

Answer 5

F = variance between IV levels / variance within
= MSm/MSr

F(IV1) = variance due to manipulation of IV1 (+ error) / variance due to error alone

Question 6

interaction effects: factorial ANOVA

Answer 6

• 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

Question 7

interpretation of main effects when the interaction is significant: factorial ANOVA

Answer 7

• for a main effect to be genuine and meaningful, it would influence the measurement of the DV across all conditions
• sometimes when an interaction is present it’s not meaningful to draw conclusions from the main effects (the interpretation of the interaction is far more informative)

Question 8

assumptions: 2-way independent ANOVA

Answer 8

• normality: the DV should be normally distributed, within each condition
• homogeneity of variance: the variance in the DV, within each condition, should be (reasonably) equivalent (SPSS checks with levenes, no correction)
• equivalent sample size: sample size within each condition should be roughly equal
• independence of observations: scores within each condition shoudl be independent

no parametric equivalent, can only attempt to ‘fix’ or simplify the design

Question 9

effect size: n^2 vs. partial n^2

Answer 9

classical eta^2: pproportional of total variance attributable to the factor
- n^2 = SSm/SSt

partial n^2 = SSm/ SSm + SSr
- only takes into account variance from one IV at a time
- proportion of the total variance attributable to the factor, partialling out (excluding) variance due to other factors

Question 10

interaction F value

Answer 10

F(IV1xIV2) = MS(IV1xIV2) / MSr

Question 11

2-way independent ANOVA: simple effects

Answer 11

the ANOVA looks for differences between marginal means to determine main effects (deals with 1 IV at a time, ignoring the other IV)

the presence of an interaction suggests we need to consider differences at the level of cell means (simple effects)
- the effect of the main IV at different levels of the secondary IV

simple effects: the effect of an IV at a single level of another IV (comparison of cell means (conditions))

to determine whether simple effects are significant, we conduct t-tests between individual cell means (only when interaction significant)

run cohen’s d for each test of simple effects considered