Week 10 + 11: Two-Way Between Subjects ANOVA

Question 1

• What is a two-way between-subjects ANOVA? What is the goal of this method?

Answer 1

Two-way = 2 IVs = sometimes referred to as factors/ factorials
*Remember each IV consists of levels (groups)

Goal = to compare group means (DV) based on 2 IVs

Question 2

• What does an IV consists of? Provide an example.

Answer 2

If your IV is sex, you have two levels

• Levels 1 (males) and 2 (females)
• often, “two-way” is represented in a different way:
• # by # :ex: 2 x 3
• having 2 # tells us that we have 2 IVs
• each # tells us how many levels are in each IV

Example: 1 IV has 2 levels, the other (1 other IV) has 3 levels
ex: 2x3x5x7 = 4 independent variables, 2,3,5,7, indicates levels.

Question 3

• What is another way to represent a “two-way” analysis? (Hint: “2 X 3” – what does this mean?) What does a “2 X 2” mean?

Answer 3

Although we can often compare 3 or more levels (groups) of an IV in an ANOVA you can still use ANOVAs when comparing 2 levels

A 2x2 is commonly used in a two way between-subjects ANOVA because they are easier to interpret

What does a “2 X 2” mean?:

• 1 IV has 2 levels
• The other IV has 2 levels

*between-subjects - each person can only be in one group for each IV

Question 4

• 2 IVs and DV: categorical or continuous?

Answer 4

2 Independent Variables = both IVs are categorical

Dependent Variable = continuous

Question 5

• What are the assumptions of a two-way between-subjects ANOVA?

Answer 5

Independent observations - people can only be one group for both IV

DV should b normally distribution
DV has no outliers - can result in bias

Homogeneity in variance

Question 6

• When you have 2 IVs, how many F statistics should you report?

Answer 6

How you interpret 2 IVs:
- You start with omnibus test using f-test
-There are 3 f-statistics you have to report:
+ 2 main effects
+ 1 interaction

Question 7

• What does a main effect mean? Provide an example. What does an interaction mean? Provide an example.

Answer 7

Main Effect = focus on each IV independently; tells you whether there are group differences for a DV based on each IV

Example: IVs - sex and study group; DV - test scores

1. Main effect for sex - focuses on if there is a significant difference in test scores between males and females
2. Main effect for study group - focuses on if there is a significant difference in test scores between study and no study groups only.

*Look at omnibus test for the interaction
Interaction = looks at group difference based on 2 IVs together