Three-Way ANOVAs Flashcards
What is a strength of a three-way ANOVA?
Higher external validity as the world is complicated and has many variables and interactions
What is a main effect in a three-way ANOVA?
A difference between marginal means of one factor averaging over levels of the other two factors
What is a two-way interaction in a three-way ANOVA?
When the effect of one factor changes depending on the level of another factor, averaging over the levels of the third factor
What is a simple interaction?
A two-way interaction within the level of a moderator
How do you identify a three-way interaction from simple interactions?
If the pattern of one simple interaction within one level of a moderator is different from the pattern of the other simple interaction within the other level of the moderator
What is a simple simple effect?
The effect of a focal IV in one level of each moderator
What is a three-way interaction?
When the two-way interaction between two factors changes depending on the level of the third factor
How many omnibus tests does a three-way ANOVA have?
7: 3 main effects, 3 two-way interactions and 1 three-way interaction
What are the parts of the structural model of a three-way ANOVA?
Grand mean
Main effect of A
Main effect of B
Main effect of C
AB interaction
AC interaction
BC interaction
ABC interaction
Error
What is dftotal?
N - 1
What are the degrees of freedom for the main effects in a three-way ANOVA?
j-1
k-1
l-1
What are the degrees of freedom for the two-way interactions in a three-way ANOVA?
(j - 1)(k - 1)
(j - 1)(l- 1)
(k - 1)(l - 1)
What is the degrees of freedom for the three-way interaction in a three-way ANOVA?
(j - 1)(k - 1)(l -1)
What follow-up test is required for a significant main effect in a three-way ANOVA?
Main effect comparisons (pairwise comparisons)
What follow-up tests are required for a significant 2- way interaction?
- Simple effect tests
- Simple comparisons (if 2+ levels)
What follow up test is required for a significant simple effect test in a three-way ANOVA?-
Simple comparisons (if 2+ levels)
What follow-up tests are required for a significant 3-way interaction in a three-way ANOVA?
- Simple interaction effects
- Simple simple effects
- Simple simple comparisons (if 2+ levels)
What follow-up tests are required for a significant simple interaction effect in a three-way ANOVA?
- Simple simple effects
- Simple simple comparisons (if 2+ levels)
What follow-up tests are required for a significant simple simple effect in a three-way ANOVA?
Simple simple comparisons (if 2+ levels)
What do simple interactions effects do?
Break down the 3-way interaction into a series of 2-way interactions at each level of the least interesting factor
What variable are simple simple effects and simple simple comparisons only conducted for?
The focal IV
What is the advantage of doing a three-way ANOVA as opposed to 2 two-way ANOVAs?
The error term is more powerful and smaller as variance is accounted for by 3 main effects, 3 two-way interactions and 1 three-way interaction
What is the difference between doing simple interaction effects and doing a two-way ANOVA?
Simple interaction effects uses a pooled error term from the 3-way omnibus ANOVA as opposed to two seperate MSerrors from the 2-way omnibus ANOVA for each level of the moderator
What do simple simple effects do?
Examine the effect of the focal IV at each level of each moderator
How many simple simple effects are done?
One for every level of the two moderators
