A Factorial ANOVA

Question 1

What is the difference between a factorial and regular ANOVA?

Answer 1

A factorial ANOVA analyses the variance of multiple independent variables with two or more categories, whereas a one-way independent ANOVA analyses the variance of one independent variable with two or more categories.

Question 2

What are the three types of factorial ANOVAs?

Answer 2

1. Independent factorial design
   There are multiple independent variables with two or more categories and the groups use different entities.
2. Repeated measures factorial design
   There are multiple independent variables with two or more categories and the groups use the same entities.
3. Mixed design
   There are multiple independent variables with two or more categories and the groups use the same entities in some conditions and different entities in another.

Question 3

What are the assumptions of the factorial ANOVA?

Answer 3

same as the assumptions of the one-way independent ANOVA

Question 4

How does the model variance differ for the independent factorial ANOVA?

Answer 4

The explained variance now consists of more than one independent variable. Therefore, the model variance (explained variance), consists of the variance explained by independent variable A, independent variable B up until independent variable n.

Question 5

What else explains part of the variance?

Answer 5

The interaction between independent variable A and independent variable B

Question 6

What formula is used for the interaction?

Answer 6

𝑆𝑆𝐴∗𝐵 = 𝑆𝑆𝑚𝑜𝑑𝑒𝑙 − 𝑆𝑆𝐴 − 𝑆𝑆𝐵

𝑑𝑓𝐴∗𝐵 = 𝑑𝑓𝐴 ∗ 𝑑𝑓𝐵

Question 7

When should a main effect not be interpreted?

Answer 7

A main effect should not be interpreted if there is a significant interaction effect involving one of the variables in the main effect.

Question 8

What do simple effects analysis examine?

Answer 8

Simple effects analysis looks at the effect of one independent variable at individual levels of the other independent variable.

Question 9

What are the two rules for judging interaction graphs?

Answer 9

1. Non-parallel lines on an interaction graph indicate some sort of interaction. The more non- parallel the lines are, the stronger the interaction.
2. Lines that cross hint at a significant interaction, but do not necessarily imply this.